Emulsion

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Malipeddy Reddy A, Sarkar K, 2019 “Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops,” Journal of Fluid Mechanics, 868, 5-25.

The shear-induced collective diffusivity down a concentration gradient in a viscous
emulsion is computed using direct numerical simulation. A layer of randomly packed
drops subjected to a shear flow, shows the layer width to increase with the 1=3
power of time, consistent with a semi-dilute theory that assumes a diffusivity linear
with concentration. This characteristic scaling and the underlying theory are used
to compute the collective diffusivity coefficient. This is the first ever computation
of this quantity for a system of deformable particles using fully resolved numerical
simulation. The results match very well with previous experimental observations.
The coefficient of collective diffusivity varies non-monotonically with the capillary
number, due to the competing effects of increasing deformation and drop orientation.
A phenomenological correlation for the collective diffusivity coefficient as a function
of capillary number is presented. We also apply an alternative approach to compute
collective diffusivity, developed originally for a statistically homogeneous rigid sphere
suspension – computing the dynamic structure factor from the simulated droplet
positions and examining its time variation at small wavenumber. We show that
the results from this alternative approach qualitatively agree with our computation
of collective diffusivity including the prediction of the non-monotonic variation of
diffusivity with the capillary number.

Malipeddy Reddy A, Sarkar K, 2019 “Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops,” Journal of Fluid Mechanics, 868, 5-25.

The shear-induced collective diffusivity down a concentration gradient in a viscous
emulsion is computed using direct numerical simulation. A layer of randomly packed
drops subjected to a shear flow, shows the layer width to increase with the 1=3
power of time, consistent with a semi-dilute theory that assumes a diffusivity linear
with concentration. This characteristic scaling and the underlying theory are used
to compute the collective diffusivity coefficient. This is the first ever computation
of this quantity for a system of deformable particles using fully resolved numerical
simulation. The results match very well with previous experimental observations.
The coefficient of collective diffusivity varies non-monotonically with the capillary
number, due to the competing effects of increasing deformation and drop orientation.
A phenomenological correlation for the collective diffusivity coefficient as a function
of capillary number is presented. We also apply an alternative approach to compute
collective diffusivity, developed originally for a statistically homogeneous rigid sphere
suspension – computing the dynamic structure factor from the simulated droplet
positions and examining its time variation at small wavenumber. We show that
the results from this alternative approach qualitatively agree with our computation
of collective diffusivity including the prediction of the non-monotonic variation of
diffusivity with the capillary number.

Malipeddy Reddy A, Sarkar K, 2019 “Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops,” Journal of Fluid Mechanics, 868, 5-25.

The shear-induced collective diffusivity down a concentration gradient in a viscous
emulsion is computed using direct numerical simulation. A layer of randomly packed
drops subjected to a shear flow, shows the layer width to increase with the 1=3
power of time, consistent with a semi-dilute theory that assumes a diffusivity linear
with concentration. This characteristic scaling and the underlying theory are used
to compute the collective diffusivity coefficient. This is the first ever computation
of this quantity for a system of deformable particles using fully resolved numerical
simulation. The results match very well with previous experimental observations.
The coefficient of collective diffusivity varies non-monotonically with the capillary
number, due to the competing effects of increasing deformation and drop orientation.
A phenomenological correlation for the collective diffusivity coefficient as a function
of capillary number is presented. We also apply an alternative approach to compute
collective diffusivity, developed originally for a statistically homogeneous rigid sphere
suspension – computing the dynamic structure factor from the simulated droplet
positions and examining its time variation at small wavenumber. We show that
the results from this alternative approach qualitatively agree with our computation
of collective diffusivity including the prediction of the non-monotonic variation of
diffusivity with the capillary number.

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Malipeddy AR, Sarkar K 2019 “Collective diffusivity in a sheared viscous emulsion: effects of viscosity ratio,” Physical Review Fluids, 4, 093603.

The shear-induced collective or gradient diffusivity in an emulsion of viscous drops,
specifically as a function of viscosity ratio, was computed using a fully resolved numerical method. An initially randomly packed layer of viscous drops spreading due to drop-drop interactions in an imposed shear has been simulated. The collective diffusivity coefficient was computed using a self-similar solution of the drop concentration profile. We also obtained the collective diffusivity (the collective diffusivity coefficient multiplied by the average drop volume fraction), computing the dynamic structure factor from the simulated drop positions—an analysis typically applied only to homogeneous systems. The two quantities computed using entirely different methods are in broad agreement, including their predictions of nonmonotonic variations with increasing capillary number and viscosity ratio. The computed values were also found to match with past experimental
measurements. The collective diffusivity coefficient computed here, as expected, is 1 order of magnitude larger than the self-diffusivity coefficient for a dilute emulsion previously computed using pairwise simulation of viscous drops in shear. The collective diffusivity coefficient computed here shows a nonmonotonic variation with viscosity ratio, in contrast to self-diffusivity computed using pairwise computation. The difference might point to an intrinsic difference in physics underlying the two diffusivities. Alternatively, it also might
arise from drops not reaching equilibrium deformation in the period after one interaction and before the next—an effect absent in the pairwise simulation used for the computation of self-diffusivity. We offer a qualitative explanation of the nonmonotonic variation by relating it to average nonmonotonic drop deformation with increasing viscosity ratio. We
also provide empirical correlations of the collective diffusivity as a function of viscosity ratio and capillary number.

Malipeddy AR, Sarkar K 2019 “Collective diffusivity in a sheared viscous emulsion: effects of viscosity ratio,” Physical Review Fluids, 4, 093603.

The shear-induced collective or gradient diffusivity in an emulsion of viscous drops,
specifically as a function of viscosity ratio, was computed using a fully resolved numerical method. An initially randomly packed layer of viscous drops spreading due to drop-drop interactions in an imposed shear has been simulated. The collective diffusivity coefficient was computed using a self-similar solution of the drop concentration profile. We also obtained the collective diffusivity (the collective diffusivity coefficient multiplied by the average drop volume fraction), computing the dynamic structure factor from the simulated drop positions—an analysis typically applied only to homogeneous systems. The two quantities computed using entirely different methods are in broad agreement, including their predictions of nonmonotonic variations with increasing capillary number and viscosity ratio. The computed values were also found to match with past experimental
measurements. The collective diffusivity coefficient computed here, as expected, is 1 order of magnitude larger than the self-diffusivity coefficient for a dilute emulsion previously computed using pairwise simulation of viscous drops in shear. The collective diffusivity coefficient computed here shows a nonmonotonic variation with viscosity ratio, in contrast to self-diffusivity computed using pairwise computation. The difference might point to an intrinsic difference in physics underlying the two diffusivities. Alternatively, it also might
arise from drops not reaching equilibrium deformation in the period after one interaction and before the next—an effect absent in the pairwise simulation used for the computation of self-diffusivity. We offer a qualitative explanation of the nonmonotonic variation by relating it to average nonmonotonic drop deformation with increasing viscosity ratio. We
also provide empirical correlations of the collective diffusivity as a function of viscosity ratio and capillary number.

Malipeddy Reddy A, Sarkar K, 2019 “Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops,” Journal of Fluid Mechanics, 868, 5-25.

The shear-induced collective diffusivity down a concentration gradient in a viscous
emulsion is computed using direct numerical simulation. A layer of randomly packed
drops subjected to a shear flow, shows the layer width to increase with the 1=3
power of time, consistent with a semi-dilute theory that assumes a diffusivity linear
with concentration. This characteristic scaling and the underlying theory are used
to compute the collective diffusivity coefficient. This is the first ever computation
of this quantity for a system of deformable particles using fully resolved numerical
simulation. The results match very well with previous experimental observations.
The coefficient of collective diffusivity varies non-monotonically with the capillary
number, due to the competing effects of increasing deformation and drop orientation.
A phenomenological correlation for the collective diffusivity coefficient as a function
of capillary number is presented. We also apply an alternative approach to compute
collective diffusivity, developed originally for a statistically homogeneous rigid sphere
suspension – computing the dynamic structure factor from the simulated droplet
positions and examining its time variation at small wavenumber. We show that
the results from this alternative approach qualitatively agree with our computation
of collective diffusivity including the prediction of the non-monotonic variation of
diffusivity with the capillary number.

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Malipeddy Reddy A, Sarkar K, 2019 “Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops,” Journal of Fluid Mechanics, 868, 5-25.

The shear-induced collective diffusivity down a concentration gradient in a viscous
emulsion is computed using direct numerical simulation. A layer of randomly packed
drops subjected to a shear flow, shows the layer width to increase with the 1=3
power of time, consistent with a semi-dilute theory that assumes a diffusivity linear
with concentration. This characteristic scaling and the underlying theory are used
to compute the collective diffusivity coefficient. This is the first ever computation
of this quantity for a system of deformable particles using fully resolved numerical
simulation. The results match very well with previous experimental observations.
The coefficient of collective diffusivity varies non-monotonically with the capillary
number, due to the competing effects of increasing deformation and drop orientation.
A phenomenological correlation for the collective diffusivity coefficient as a function
of capillary number is presented. We also apply an alternative approach to compute
collective diffusivity, developed originally for a statistically homogeneous rigid sphere
suspension – computing the dynamic structure factor from the simulated droplet
positions and examining its time variation at small wavenumber. We show that
the results from this alternative approach qualitatively agree with our computation
of collective diffusivity including the prediction of the non-monotonic variation of
diffusivity with the capillary number.

Malipeddy Reddy A, Sarkar K, 2019 “Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops,” Journal of Fluid Mechanics, 868, 5-25.

The shear-induced collective diffusivity down a concentration gradient in a viscous
emulsion is computed using direct numerical simulation. A layer of randomly packed
drops subjected to a shear flow, shows the layer width to increase with the 1=3
power of time, consistent with a semi-dilute theory that assumes a diffusivity linear
with concentration. This characteristic scaling and the underlying theory are used
to compute the collective diffusivity coefficient. This is the first ever computation
of this quantity for a system of deformable particles using fully resolved numerical
simulation. The results match very well with previous experimental observations.
The coefficient of collective diffusivity varies non-monotonically with the capillary
number, due to the competing effects of increasing deformation and drop orientation.
A phenomenological correlation for the collective diffusivity coefficient as a function
of capillary number is presented. We also apply an alternative approach to compute
collective diffusivity, developed originally for a statistically homogeneous rigid sphere
suspension – computing the dynamic structure factor from the simulated droplet
positions and examining its time variation at small wavenumber. We show that
the results from this alternative approach qualitatively agree with our computation
of collective diffusivity including the prediction of the non-monotonic variation of
diffusivity with the capillary number.

Malipeddy Reddy A, Sarkar K, 2019 “Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops,” Journal of Fluid Mechanics, 868, 5-25.

The shear-induced collective diffusivity down a concentration gradient in a viscous
emulsion is computed using direct numerical simulation. A layer of randomly packed
drops subjected to a shear flow, shows the layer width to increase with the 1=3
power of time, consistent with a semi-dilute theory that assumes a diffusivity linear
with concentration. This characteristic scaling and the underlying theory are used
to compute the collective diffusivity coefficient. This is the first ever computation
of this quantity for a system of deformable particles using fully resolved numerical
simulation. The results match very well with previous experimental observations.
The coefficient of collective diffusivity varies non-monotonically with the capillary
number, due to the competing effects of increasing deformation and drop orientation.
A phenomenological correlation for the collective diffusivity coefficient as a function
of capillary number is presented. We also apply an alternative approach to compute
collective diffusivity, developed originally for a statistically homogeneous rigid sphere
suspension – computing the dynamic structure factor from the simulated droplet
positions and examining its time variation at small wavenumber. We show that
the results from this alternative approach qualitatively agree with our computation
of collective diffusivity including the prediction of the non-monotonic variation of
diffusivity with the capillary number.

Malipeddy AR, Sarkar K 2019 “Collective diffusivity in a sheared viscous emulsion: effects of viscosity ratio,” Physical Review Fluids, 4, 093603.

The shear-induced collective or gradient diffusivity in an emulsion of viscous drops,
specifically as a function of viscosity ratio, was computed using a fully resolved numerical method. An initially randomly packed layer of viscous drops spreading due to drop-drop interactions in an imposed shear has been simulated. The collective diffusivity coefficient was computed using a self-similar solution of the drop concentration profile. We also obtained the collective diffusivity (the collective diffusivity coefficient multiplied by the average drop volume fraction), computing the dynamic structure factor from the simulated drop positions—an analysis typically applied only to homogeneous systems. The two quantities computed using entirely different methods are in broad agreement, including their predictions of nonmonotonic variations with increasing capillary number and viscosity ratio. The computed values were also found to match with past experimental
measurements. The collective diffusivity coefficient computed here, as expected, is 1 order of magnitude larger than the self-diffusivity coefficient for a dilute emulsion previously computed using pairwise simulation of viscous drops in shear. The collective diffusivity coefficient computed here shows a nonmonotonic variation with viscosity ratio, in contrast to self-diffusivity computed using pairwise computation. The difference might point to an intrinsic difference in physics underlying the two diffusivities. Alternatively, it also might
arise from drops not reaching equilibrium deformation in the period after one interaction and before the next—an effect absent in the pairwise simulation used for the computation of self-diffusivity. We offer a qualitative explanation of the nonmonotonic variation by relating it to average nonmonotonic drop deformation with increasing viscosity ratio. We
also provide empirical correlations of the collective diffusivity as a function of viscosity ratio and capillary number.

Aliabouzar M, Kumar KN, Sarkar K, 2018 “Acoustic vaporization threshold of lipid coated perfluoropentane droplets,” Journal of the Acoustical Society of America, 143, 2001-2012.

Phase shift droplets vaporizable by acoustic stimulation offer the advantages of producing micro-bubbles as contrast agentsin situas well as higher stability and the possibility of achieving smallersizes. Here, the acoustic droplet vaporization (ADV) threshold of a suspension of droplets with aperfluoropentane (PFP) core (diameter 400–3000 nm) is acoustically measured as a function of theexcitation frequency in a tubeless setup at room temperature. The changes in scattered responses—fundamental, sub-, and second harmonic—are investigated, a quantitative criterion is used to deter-mine the ADV phenomenon, and findings are discussed. The average threshold obtained using threedifferent scattered components increases with frequency—1.0560.28 MPa at 2.25 MHz,1.8960.57 MPa at 5 MHz, and 2.3460.014 MPa at 10 MHz. The scattered response from vapor-ized droplets was also found to qualitatively match with that from an independently prepared lipid-coated microbubble suspension in magnitude as well as trends above the determined ADV thresh-old value.

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Sarkar K, Singh R 2013 “Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear,” Physics of Fluids, 25, 051702.

Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated

Li X, Sarkar K 2005 “Effects of inertia on the rheology of a dilute emulsion of viscous drops in steady shear,” Journal of Rheology, 49, 1377-1394.

Li X, Sarkar K 2005 “Negative normal stress elasticity of emulsion of viscous drops at finite inertia,” Physical Review Letters, 95, 256001.

Li X, Sarkar K 2005 “Numerical investigation of the rheology of a dilute emulsion of drops in an oscillating extensional flow,” Journal of Non-Newtonian Fluid Mechanics, 102, 263-280.

Aggarwal, N, Sarkar K 2008 “Rheology of an emulsion of viscoelastic drops in steady shear,” Journal of Non-Newtonian Fluid Mechanics, 150, 19-31.

Singh R, Li X, Sarkar K 2014 “Lateral migration of a capsule in plane shear near a wall,” Journal of Fluid Mechanics, 739, 421-443.

Mukherjee S, Sarkar K 2014 “Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall,” Physics of Fluids, 26, 103102.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonianfluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distancefrom the wall. The drop migration velocity and the deformation scale inversely withthe square and the cube of the distance from the wall, respectively. The migration ve-locity varies non-monotonically with increasing viscoelasticity (increasing Deborahnumber); initially increasing and then decreasing. An analytical explanation has beengiven of the effects by computing the migration velocity as arising from an imagestresslet field due to the drop. The semi-analytical expression matches well with thesimulated migration velocity away from the wall. It contains a viscoelastic stressletcomponent apart from those arising from interfacial tension and viscosity ratio. Themigration dynamics is a result of the competition between the viscous (interfacialtension and viscosity ratio) and the viscoelastic effects. The viscoelastic stressletcontribution towards the migration velocity steadily increases. But the interfacialstresslet—arising purely from the drop shape—first increases and then decreases withrising Deborah number causing the migration velocity to be non-monotonic. The ge-ometric effect of the interfacial stresslet is caused by a corresponding nonmonotonicvariation of the drop inclination. High viscosity ratio is briefly considered to showthat the drop viscoelasticity could stabilize a drop against breakup, and the increase inmigration velocity due to viscoelasticity is larger compared to the viscosity-matchedcase.

Singh R, Sarkar K 2015 “Hydrodynamic interactions between pairs of capsules and drops in a simple shear: effects of viscosity ratio and heterogeneous collision,” Physical Review E, 92, 063029.

Srivastava P, Malipeddi Reddy A, Sarkar K 2016 “Steady shear rheology of a viscous emulsion in the presence of finite inertia at moderate volume fractions: sign reversal of normal stress differences,” Journal of Fluid Mechanics, 85, 494-522.

The shear rheology of an emulsion of viscous drops in the presence of finite inertiais investigated using direct numerical simulation. In the absence of inertia, emulsionsdisplay a non-Newtonian rheology with positive first and negative second normalstress differences. However, recently it was discovered that a small amount ofdrop-level inertia alters their signs – the first normal stress difference becomesnegative and the second one becomes positive, each in a small range of capillarynumbers (Li & Sarkar,J. Rheol., vol. 49, 2005, pp. 1377–1394). Sign reversal wasshown numerically and analytically, but only in the limit of a dilute emulsion wheredrop–drop interactions were neglected. Here, we compute the rheology of a density-and viscosity-matched emulsion, accounting for the interactions in the volume fractionrange of 5 %–27 % and Reynolds number range of 0.1–10. The computed rheologicalproperties (effective shear viscosity and first and second normal stress differences) inthe Stokes limit match well with previous theoretical (Choi–Schowalter in the dilutelimit) and simulated results (for concentrated systems) using the boundary elementmethod. The two distinct components of the rheology arising from the interfacialstresses at the drop surface and the perturbative Reynolds stresses are investigated asfunctions of the drop Reynolds number, capillary number and volume fraction. Thesign change is caused by the increasing drop inclination in the presence of inertia,which in turn directly affects the interfacial stresses. Increase of the volume fractionor capillary number increases the critical Reynolds number for sign reversals due toenhanced alignment of the drops with the flow directions. The effect of increasingthe volume fraction on the rheology is explained by relating it to interactions andspecifically to the contact pair-distribution function computed from the simulation.The excess stresses are seen to show an approximately linear behaviour with theReynolds number in the range of 0.1–5, while with the capillary number and volumefraction, the variation is weakly quadratic.

Malipeddy AR, Sarkar K 2019 “Collective diffusivity in a sheared viscous emulsion: effects of viscosity ratio,” Physical Review Fluids, 4, 093603.

The shear-induced collective or gradient diffusivity in an emulsion of viscous drops,
specifically as a function of viscosity ratio, was computed using a fully resolved numerical method. An initially randomly packed layer of viscous drops spreading due to drop-drop interactions in an imposed shear has been simulated. The collective diffusivity coefficient was computed using a self-similar solution of the drop concentration profile. We also obtained the collective diffusivity (the collective diffusivity coefficient multiplied by the average drop volume fraction), computing the dynamic structure factor from the simulated drop positions—an analysis typically applied only to homogeneous systems. The two quantities computed using entirely different methods are in broad agreement, including their predictions of nonmonotonic variations with increasing capillary number and viscosity ratio. The computed values were also found to match with past experimental
measurements. The collective diffusivity coefficient computed here, as expected, is 1 order of magnitude larger than the self-diffusivity coefficient for a dilute emulsion previously computed using pairwise simulation of viscous drops in shear. The collective diffusivity coefficient computed here shows a nonmonotonic variation with viscosity ratio, in contrast to self-diffusivity computed using pairwise computation. The difference might point to an intrinsic difference in physics underlying the two diffusivities. Alternatively, it also might
arise from drops not reaching equilibrium deformation in the period after one interaction and before the next—an effect absent in the pairwise simulation used for the computation of self-diffusivity. We offer a qualitative explanation of the nonmonotonic variation by relating it to average nonmonotonic drop deformation with increasing viscosity ratio. We
also provide empirical correlations of the collective diffusivity as a function of viscosity ratio and capillary number.

Malipeddy Reddy A, Sarkar K, 2019 “Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops,” Journal of Fluid Mechanics, 868, 5-25.

The shear-induced collective diffusivity down a concentration gradient in a viscous
emulsion is computed using direct numerical simulation. A layer of randomly packed
drops subjected to a shear flow, shows the layer width to increase with the 1=3
power of time, consistent with a semi-dilute theory that assumes a diffusivity linear
with concentration. This characteristic scaling and the underlying theory are used
to compute the collective diffusivity coefficient. This is the first ever computation
of this quantity for a system of deformable particles using fully resolved numerical
simulation. The results match very well with previous experimental observations.
The coefficient of collective diffusivity varies non-monotonically with the capillary
number, due to the competing effects of increasing deformation and drop orientation.
A phenomenological correlation for the collective diffusivity coefficient as a function
of capillary number is presented. We also apply an alternative approach to compute
collective diffusivity, developed originally for a statistically homogeneous rigid sphere
suspension – computing the dynamic structure factor from the simulated droplet
positions and examining its time variation at small wavenumber. We show that
the results from this alternative approach qualitatively agree with our computation
of collective diffusivity including the prediction of the non-monotonic variation of
diffusivity with the capillary number.

Preziosi V, Tarafder A, Tomaiuolo G, Sarkar K, Guido S 2024, "Does dispersed phase inertia affect the shape of sheared emulsion droplets?" Physics of Fluids, 36, 073115

Inertial effects on sheared emulsion droplets are a topic of scientific and industrial interest for several applications from processing to microfluidics. Most of the literature have addressed so far the role of inertia of the continuous phase, which is known to affect shear-induced droplet deformation and migration at values of the Reynolds number of the external fluid Rec > 1. However, less attention has been paid to the case of inertial effects inside the droplets, corresponding to values of the Reynolds number of the droplet fluid Red > 1. Such a case is especially relevant when the viscosity ratio k between the droplet and the external fluid is
1, which is typical of water-in-oil emulsions where the low values of droplet viscosity can result in Red > 1, while Rec < 1 due to the larger oil viscosity. Here, we focus on the effect of droplet inertia under shear flow at k
1 by high-speed video microscopy experiments in a microcapillary and by numerical simulations based on a front-tracking finite-difference method. The results unveil the droplet’s three-dimensional shape under shear flow at low viscosity ratios and show that droplet inertia tends to increase droplet deformation and orientation along the flow direction and to form two vortices inside the droplets even at small Rec. The latter findings are at variance with the case of external fluid inertia, where droplets become more aligned with the velocity gradient direction