• Cao Q, Sarkar K, Prasad AK 2004 “Direct numerical simulation of two-layer viscosity-stratified flow,”International Journal of Multiphase Flow, 30, 1484-1508.

    Two-dimensional simulations of flow instability at the interface of a two-layer, density-matched, viscos-ity-stratified Poiseuille flow are performed using a front-tracking/finite difference method. We presentresults for the small-amplitude (linear) growth rate of the instability at small to medium Reynolds numberfor varying thickness ration, viscosity ratiom, and wavenumber. We also present results for large-ampli-tude non-linear evolution of the interface for varying viscosity ratio and interfacial tension. For the linearcase, the interfacial mode is neutrally stable forn¼ffiffiffiffimpas predicted by analysis. The growth rate is pro-portional to Reynolds number for smallRe, and increases with viscosity ratio. The growth rate alsoincreases when the thickness of the more viscous layer is reduced. Strong non-linear behavior is observedfor relatively large initial perturbation amplitude. The higher viscosity fluid is drawn out as a finger thatpenetrates into the lower viscosity layer. The simulated interface shape compares well with previouslyreported experiments. Increasing interfacial tension retards the growth rate of the interface as expected,whereas increasing the viscosity ratio enhances it. Drop formation at the small Reynolds number consid-ered in this study is precluded by the two-dimensional nature of the calculations.

  • Chatterjee D, Sarkar K 2003 “A Newtonian rheological model for the interface of microbubble contrast agents,” Ultrasound in Medicine and Biology, 29, 1749-1757.

    A quantitative model of the dynamics of an encapsulated microbubble contrast agent will be avaluable tool in contrast ultrasound (US). Such a model must have predictive ability for widely varyingfrequencies and pressure amplitudes. We have developed a new model for contrast agents, and successfullyinvestigated its applicability for a wide range of operating parameters. The encapsulation is modeled as acomplex interface of an infinitesimal thickness. A Newtonian rheology with surface viscosities and interfacialtension is assumed for the interface, and a modified Rayleigh–Plesset equation is derived. The rheologicalparameters (surface tension and surface dilatational viscosity) for a number of contrast agents (Albunex,Optisonand Quantison) are determined by matching the linearized model dynamics with experimentallyobtained attenuation data. The model behavior for Optison(surface tension 0.9 N/m and surface dilatationalviscosity 0.08 msP) was investigated in detail. Specifically, we have carried out a detailed interrogation of themodel, fitted in the linear regime, for its nonlinear prediction. In contrast to existing models, the new model isfound to capture the characteristic subharmonic emission of Optisonobserved by Shi et al. (1999). A detailedparametric study of the bubble behavior was executed using the ratio of scattering to attenuation (STAR). Itshows that the encapsulation drastically reduces the influence of resonance frequency on scattering cross-section,suggesting possible means of improvement in imaging at off-resonant frequencies. The predictive capability of thepresent model indicates that it can be used for characterizing different agents and designing new ones.

  • Sarkar K, Schowalter WR 2002 “Computation of a viscous jet with embedded drops,” Journal of Non-Newtonian Fluid Mechanics, 102, 263-280.

    An inertialess jet containing Newtonian drops in a gravitation-free field has been modeled by incorporating thedetailed micro-structural dynamics. Interactions of the drops with the continuous phase, with the wall, and with thejet surface are accounted for, thereby eliminating the need for additional constitutive assumptions. The deformationof the jet and drops, and the dispersion of drops are predicted. The present paper serves two purposes. First, acomplete description of the modeling process and its limitation is presented. Second, preliminary results for singleand for small clusters of drops indicate the potential inherent in this computational approach. The model flow issolved in two dimensions using the boundary element method (BEM). Effects of different drop parameters, such astheir number, relative position, and interfacial tension are investigated.

  • Sarkar K, Schowalter WR 2001 “Deformation of a two-dimensional drop in time-periodic extensional flows: analytic treatment,” Journal of Fluid Mechanics, 436, 207-230.

    In Sarkar & Schowalter (2001), we reported results from numerical simulations of dropdeformation in various classes of time-periodic straining flows at non-zero Reynoldsnumber. As often occurs, analytical solutions provide more e ective understanding ofthe structure and signi cance of a phenomenon. Here we describe drop deformationpredicted from analytical solutions to linear time-periodic straining flows. Threedi erent limiting cases are considered: an unsteady Stokes flow that retains all butthe nonlinear advection terms, a Stokes flow that neglects inertia altogether, and aninviscid potential flow. The rst limit is in clear contrast to the common approachin emulsion literature that resorts almost always to the Stokes flow assumption.The analysis clearly shows the forced{damped mass{spring system underlying thephysical phenomena, which distinguishes it from the inertialess Stokes flow. Thepotential flow also depicts resonance, albeit of an undamped system, and provides animportant limit of the problem. The drop deformation is assumed to be small, and aperturbative approach has been employed. The rst-order problem has been solvedto arrive at either an evolution equation (in Stokes and potential flow limits) or thelong-time periodic drop response (for unsteady Stokes analysis). The analytical resultscompare satisfactorily with those obtained from the numerical simulation in Sarkar &Schowalter (2001), and the resonance characteristics are quantitatively explained. Thethree di erent solutions are compared with each other, and the results are presentedfor di erent parameters such as frequency, interfacial tension, viscosity ratio, densityratio and Reynolds number. Furthermore, the simple ODE model presented in theAppendix of Sarkar & Schowalter (2001) is shown to explain the asymptotic limitsof the present solution.