A front tracking method for a deformable intravascular bubble in a tube with soluble surfactant transport

Almgren, 1998, A conservative adaptive projection method for the variable density incompressible Navier–Stokes equations, J. Comput. Phys., 142, 1, 10.1006/jcph.1998.5890 Branger, 2002, Accelerated arteriolar gas embolism reabsorption by an exogenous surfactant, Anesthesiology, 96, 971, 10.1097/00000542-200204000-00027 Bunner, 2002, Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles, J. Fluid Mech., 466, 17, 10.1017/S0022112002001179 Bunner, 2002, Dynamics of homogeneous bubbly flows. Part 2. Rise velocity fluctuations, J. Fluid Mech., 466, 53, 10.1017/S0022112002001180 Cavanagh, 1999, Interfacial dynamics of stationary gas bubbles in flows in inclined tubes, J. Fluid Mech., 398, 225, 10.1017/S0022112099006230 Ceniceros, 2003, The effects of surfactants on the deformation and evolution of capillary waves, Phys. Fluids, 15, 245, 10.1063/1.1528940 Chang, 1995, Adsorption dynamics of surfactants at air/water interface: a critical review of mathematical models, data and mechanism, Colloid Surface, A100, 1, 10.1016/0927-7757(94)03061-4 Chhabra, 1988, Encyclopedia Fluid Mech., 7, 253 Chhabra, 1993 Cuenot, 1997, The effects of slightly soluble surfactants on the flow around a spherical bubble, J. Fluid Mech., 339, 25, 10.1017/S0022112097005053 De Kee, 1992 De Kee, 2002, Bubble shape in non-Newtonian fluids, J. Appl. Mech., 69, 703, 10.1115/1.1480822 Drumright-Clarke, 2004, The effects of insoluble surfactant at dilute concentration on drop breakup under shear with inertia, Phys. Fluids, 16, 14, 10.1063/1.1628232 Eckmann, 2003, Microvascular gas embolization clearance following perfluorocarbon administration, J. Appl. Physiol., 94, 860, 10.1152/japplphysiol.00719.2002 Eggleton, 1999, Insoluble surfactant on a drop in an extension flow: a generalization of the stagnated surface limit to deforming interfaces, J. Fluid Mech., 385, 79, 10.1017/S0022112098004054 Eggleton, 2001, Tip streaming from a drop in the presence of surfactants, Phys. Rev. Lett., 87, 10.1103/PhysRevLett.87.048302 Ghadiali, 2003, The influence of non-equilibrium surfactant dynamics on the flow of a semi-infinite bubble in a rigid cylindrical capillary tube, J. Fluid Mech., 478, 165, 10.1017/S002211200200335X Ghadiali, 2001, A dual-reciprocity boundary element method for evaluating bulk convective transport of surfactant in free-surface flows, J. Comput. Phys., 171, 534, 10.1006/jcph.2001.6792 Gibou, 2002, A second order accurate symmetric discretization of the Poisson equation on irregular domains, J. Comput. Phys., 176, 205, 10.1006/jcph.2001.6977 James, 2004, A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant, J. Comput. Phys., 201, 685, 10.1016/j.jcp.2004.06.013 Jan, 1991, Computational studies of contaminated bubbles, vol. 119, 46 Juric, 1996, A front-tracking method for dendritic solidification, J. Comput. Phys., 123, 127, 10.1006/jcph.1996.0011 Juric, 1998, Computations of boiling flows, Int. J. Multiphase Flow, 24, 387, 10.1016/S0301-9322(97)00050-5 Leppinen, 1996, The effects of surfactants on droplet behavior at intermediate Reynolds numbers I. The numerical model and steady state results, Chem. Eng. Sci., 51, 479 Li, 1997, The effect of surfactant on drop deformation and on the rheology of dilute emulsion in Stokes flow, J. Fluid Mech., 341, 165, 10.1017/S0022112097005508 Li, 2001, The effect of surfactant on the motion of a buoyancy-driven drop at intermediate Reynolds number: a numerical approach, J. Colloid Interf. Sci., 240, 307, 10.1006/jcis.2001.7587 Liao, 2000, Bubble motion in aqueous surfactant solutions, J. Colloid Interf. Sci., 224, 297, 10.1006/jcis.2000.6741 Milliken, 1994, The influence of surfactant on the deformation and breakup of a viscous drop, J. Colloid Interf. Sci., 166, 275, 10.1006/jcis.1994.1296 Minion, 1996, On the stability of Godunov-projection methods for incompressible flow, J. Comput. Phys., 123, 435, 10.1006/jcph.1996.0035 Og̃uz, 1988, Effects of soluble and insoluble surfactants on the motion of drops, J. Fluid Mech., 194, 563, 10.1017/S0022112088003118 Park, 1992, Influence of soluble surfactant on the motion of a finite bubble in a capillary tube, Phys. Fluids A, 4, 2335, 10.1063/1.858475 Peskin, 1977, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25, 220, 10.1016/0021-9991(77)90100-0 Renardy, 2002, A new volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at a low viscosity ratio, Eur. J. Mech. B, 21, 49, 10.1016/S0997-7546(01)01159-1 Rodrigue, 2001, Generalized correlation for bubble motion, Am. Inst. Chem. Eng., 47, 39, 10.1002/aic.690470106 Rodrigue, 2002, A simple correlation for gas bubbles rising in power-law fluids, Can. J. Chem. Eng., 80, 289, 10.1002/cjce.5450800214 Rodrigue, 1999, The slow motion of a single gas bubble in a non-Newtonian fluid containing surfactants, J. Non-Newtonian Fluid Mech., 86, 211, 10.1016/S0377-0257(98)00209-2 Sadhal, 1997 Stone, 1990, A simple derivation of the time dependent convection diffusion equation for surfactant transport along a deforming interface, Phys. Fluids A, 2, 111, 10.1063/1.857686 Sussman, 2000, A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comput. Phys., 162, 301, 10.1006/jcph.2000.6537 Sussman, 2003, A second order coupled level set set and volume-of-fluid method for computing growth and collapse of vapor bubbles, J. Comput. Phys., 187, 110, 10.1016/S0021-9991(03)00087-1 Takemura, 2005, Adsorption of surfactants onto the surface of a spherical rising bubble and its effect on the terminal velocity of the bubble, Phys. Fluids, 17, 048104, 10.1063/1.1879712 Tsai, 1994, Dynamics of a drop in a constricted capillary tube, J. Fluid Mech., 274, 197, 10.1017/S0022112094002090 Tsai, 1997, The effects of surfactant on the dynamics of bubble snap-off, J. Fluid Mech., 337, 381, 10.1017/S0022112097004898 Tryggvason, 2001, A front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169, 708, 10.1006/jcph.2001.6726 Unverdi, 1992, Computations of multi-fluid flows, Physica D, 60, 70, 10.1016/0167-2789(92)90227-E Weatherburn, 1927, vol. I Xu, 2003, An Eulerian formulation for solving partial differential equations along a moving interface, J. Sci. Comp., 19, 573, 10.1023/A:1025336916176 Yon, 1998, A finite volume/boundary-element method for flow past interfaces in the presence of surfactants, with application to shear flow past a viscous drop, Comput. Fluids, 27, 879, 10.1016/S0045-7930(98)00013-9 H. Zhou, V. Cristini, J. Lowengrub, C.W. Macosko, 3D adaptive finite element simulations of deformable drops with soluble surfactant: pair interactions and coalescence, Phys. Fluids (submitted).