RESEARCH ACTIVITIES IN OUR GROUP

Our current research is on the dynamical behavior of emulsions and foams including the particlescale and collective behavior of these systems. In addition to their rich dynamical behavior and relevance to engineering applications, emulsions and foams are an interesting system because they
provide a well-characterized model system for understanding important aspects of more
complicated systems of deformable particles such as polymer blends, gels, and biological fluids.

We have worked in four problem areas which are described below:

(1) Film drainage and drop coalescence
(2) Drop breakup
(3) Emulsion rheology
(4) Hydrodynamics of surfactant-covered interfaces

Film drainage and drop coalescence
Recently, we developed new analytical theories and accurate numerical simulations for coalescence of drops with clean and surfactant-covered interfaces. The focus of these studies is on the ratelimiting step of drainage of the thin liquid film between drop interfaces just prior to coalescence.

The fundamental understanding of drop coalescence furthered by these studies is important in engineering applications where the evolution of a drop size distribution must be reliably predicted or controlled.

We obtained an analytical solution for the long-time asymptotic evolution of the thin liquid film between deformable drops with mobile interfaces. This had been an unsolved puzzle since the 1978 study of Jones & Wilson [J. Fluid Mech. vol. 87, p. 263, 1978] who concluded that there was “no
prospect” for solving the nonlinear integro-differential equation which governs the evolution of the thin film.

In another recent study, we demonstrated that the previously-ignored influence of internal circulation within drops qualitatively affects coalescence rates. This new hydrodynamic mechanism for controlling drop coalescence has promising practical applications in fields such as microfluidics. A surprising result is the prediction of flow-stabilized non-coalescing drops, which may explain recent experiments, where non-coalescence was observed but attributed to a nonhydrodynamic repulsive
force.


Drop breakup
We developed an adaptive restructuring algorithm for computational meshes on evolving surfaces. Resolution of the relevant local length scale on the evolving surface is everywhere maintained with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations. The resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history. Our algorithm made feasible well-resolved three-dimensional boundary integral simulations of drop breakup event by our group and is being widely used for a variety of problems by research groups elsewhere.

Ultimately, our numerical simulations provide a guide for developing and testing theoretical descriptions of drop breakup. We used our simulations to explore criteria for breakup and the dynamics of breakup events in simple flows, and the statistics of breakup events in stochastic flows. Useful results include the discovery that the volume of daughter drops produced by breakup events scales with the volume of the critical-size drop, not the the mother drop as was previously assumed in population balance models. We developed a theory for the near-critical dynamics of breaking drops, according to which a single slow-mode undergoes a saddle-node bifurcation at the critical point, analogous to the Landau theory for phase transitions. Our theory provides a reliable method for
determining critical parameters from experimental data or numerical simulations.

In another study, we derived analytical expressions for the critical parameters for drop breakup in strain-dominated flows. Our analysis and numerical simulations demonstrate, for the first time, distinct coexisting stationary states for drops in Stokes flows. The coexisting states are shown to correspond to a balance between distorting viscous stresses, and either the rotation of the drop by the imposed flow or surface-tension-driven relaxation of the drop shape. Coexisting coiled and stretched configurations of polymer molecules in viscous flows may be similarly explained by the balance of viscous stresses, and the rotation or the entropically-driven relaxation of the molecule.


Rheology of suspensions with deformable particles
We have conducted several studies which provide a rigorous drop-scale interpretation of emulsion rheology. This work involved the development of the first many-drop three-dimensional boundary integral simulations for flows of concentrated suspensions of hydrodynamically-interacting deformable particles, and small deformation analyses for the dynamics of surfactant-covered drops in dilute emulsions, and for emulsions that are concentrated up to and beyond the jamming threshold.

These studies explain the rich rheological behavior of emulsions (e.g., shear thinning viscosities, nonzero normal stresses, and nonlinear frequency response) in terms of the interplay between the distinct time scales of the system, including the relaxation times associated with the drop shape and surfactant distribution, and the time scales associated with convective distortion and rotation of the drop shape and surfactant distribution. The shape modes corresponding to the spectrum of
relaxation times reveal interesting features, such as fine-scale oscillatory structures at the contact lines in jammed emulsions which contribute significantly to the stress in the system. Qualitative features of the predicted rheology are observed in a variety of other systems, such as shear-thinning resulting from drop rotation in polymer blends and gels and transient shear stress oscillations in micelle solutions which suggests that our work has broad application to complex fluids with deformable particles. Indeed, our results have been used by theorists elsewhere who are attempting to formulate coarse-grained models and generic theories of complex fluids.


Hydrodynamics of surfactant-covered interfaces

We developed a theory for the hydrodynamics of incompressible surfactant films, which applies to a broad class of problems where capillary stresses dominate viscous stresses. According to the theory, constant surfactant density is maintained by Marangoni stresses (surface tension gradients) on the interface. The situation is closely analogous to the theory of (three-dimensional) incompressible fluid flow, where constant mass density is maintained by pressure in the fluid.

We also developed a theory for film drainage between drops with surfactant-covered interfaces which describes a hydrodynamic back-flow mechanism by which compressible surfactant films hinder coalescence more than immobile interfaces (e.g., rigid particles). An expression was derived for the critical concentration of adsorbed surfactant below which coalescence occurs rapidly.

Liquid flow and transport in foams is another research area where our group is working. Here, one of the principal questions is the permeability of liquid in foams and the effects of surfactants. We developed an analytical solution for the permeability and surfactant transport in foams. Our analysis is the first to properly incorporate Marangoni stresses and the predicted permeabilities are twenty times larger than expected in the absence of Marangoni stresses. Recent microscopic measurements of the bubble scale flow by research groups elsewhere support the distinct countergravity flow pattern predicted by our theory.

PUBLICATIONS

  1. Loewenberg, M., Bellan, J. & Gavalas, G.R. 1987 A simplified description of char combustion. Chem. Eng. Commun. 58, 89-103.

  2. Loewenberg, M. & Gavalas, G.R. 1988 Steady-state reactant flux into a medium containing spherical sinks. Chem. Eng. Sci. 43, 2431-2444.

  3. Levendis, Y.A., Nam, S., Loewenberg, M., Flagan, R.C. & Gavalas, G.R. 1989 The effects of the catalytic activity of calcium in the combustion of carbonaceous particles. Energy Fuels 3, 28-37.

  4. Loewenberg, M. & Gavalas, G.R. 1989 Time-dependent, diffusion-controlled reactions: the influence of boundaries. J. Chem. Phys. 90, 177-182.

  5. Loewenberg, M. 1989 Reactant flux into a medium containing spherical sinks: the time dependent problem. Chem. Eng. Sci. 44, 2394-2398.

  6. Loewenberg, M. & Levendis, Y.A. 1991 Combustion behavior and kinetics of synthetic and coal-derived chars: comparison of theory and experiment. Combust. Flame. 84, 47-65.

  7. Loewenberg, M. & O’Brien, R. W. 1992 The dynamic mobility of nonspherical particles. J. Colloid Interface Sci. 150, 158-168.

  8. Loewenberg, M.&Davis, R.H. 1993 Near-contact thermocapillary migration of a nonconducting viscous drop normal to a planar interface. J. Colloid Interface Sci. 160, 265-274.

  9. Loewenberg, M. 1993 The unsteady Stokes resistance of arbitrarily oriented, finite-length cylinders. Phys. Fluids A 5, 3004-3006.

  10. Loewenberg, M. & Davis, R.H. 1993 Near-contact, thermocapillary motion of two nonconducting drops. J. Fluid Mech. 256, 107-131.

  11. Loewenberg, M. 1993 Stokes resistance, added mass, & Basset force for arbitrarily oriented,finite-length cylinders. Phys. Fluids A. 5, 765-767.

  12. Loewenberg, M. 1994 Unsteady, electrophoretic motion of a nonspherical, colloidal particle in an oscillating electric field. J. Fluid Mech., 278, 149-174.

  13. Loewenberg, M. & Davis, R.H. 1994 Flotation efficiencies of fine, spherical particles and drops. Chem. Eng. Sci., 49, 3923-3941.

  14. Loewenberg, M. 1994 Asymmetric, unsteady Stokes flow past an oscillating, finite-length cylinder; the macroscopic effect of particle edges. Phys. Fluids 6, 1095-1107.

  15. Loewenberg, M. 1994 Diffusion-controlled, heterogeneous reaction in a material with a bimodal pore-size distribution. J. Chem. Phys. 100, 7580-7589.

  16. Loewenberg, M. 1994 Axisymmetric, unsteady Stokes flow past an oscillating, finite-length cylinder. J. Fluid Mech. 265, 265-288.

  17. Loewenberg, M. & Davis, R.H. 1995 Near-contact, electrophoretic particle motion. J. Fluid Mech., 288, 103-122.

  18. Nichols, C.S., Loewenberg, M. & Davis, R.H. 1995 Electrophoretic particle aggregation. J. Colloid Interface Sci., 176, 342-351.

  19. Loewenberg, M. & Hinch, E.J. 1996 Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 321, 395-419.

  20. Wang, H., Zheng, S., Loewenberg, M. & Davis, R.H. 1997 Particle aggregation due to combined gravitational and electrophoretic motion. J. Colloid Interface Sci. 187, 213-220.

  21. Loewenberg, M. & Hinch, E.J. 1997 Collision of deformable drops in shear-flow. J. Fluid Mech. 338 299-315.

  22. Loewenberg, M. 1998 Numerical simulation of concentrated emulsion flows. J. Fluids Eng. 120, 824-832.

  23. Manga, M., Castro, J., Cashman, K.V. & Loewenberg, M. 1998 Rheology of bubble-bearing magmas: theoretical results. J. Volcanology & Geothermal Res. 87, 15-28.

  24. Cristini, V., Blawzdziewicz, J. & Loewenberg, M. 1998 Drop breakup in three-dimensional viscous flows. Phys. Fluids Letters 10, 1781-1783. [pdf]

  25. Cristini, V., Blawzdziewicz, J. & Loewenberg, M. 1998 Near-contact motion of spherical surfactant-covered droplets. J. Fluid Mech. 366, 259-287. [pdf]

  26. Ramirez, J., Zinchenko, A., Loewenberg, M. & Davis, R.H. 1999 The flotation rates of fine spherical particles under Brownian and convective motion. Chem. Eng. Sci 54, 149-157.

  27. Blawzdziewicz, J., Wajnryb, E. & Loewenberg, M. 1999 Hydrodynamic interactions and collision efficiencies of surfactant-covered spherical drops: incompressible surfactant films. J. Fluid Mech. 395, 29-59. [pdf]

  28. Blawzdziewicz, J., Cristini, V. & Loewenberg, M. 1999 Near-contact motion of spherical surfactant-covered droplets: ionic surfactants. J. Colloid Interface Sci. 211, 355-366. [pdf]

  29. Kraynik, A.M., Reinelt, D.A. & Loewenberg, M. 1999 Foam Microrheology. In Foams and Films D. Weaire and J. Banhart (eds.), Verlag MIT.

  30. Blawzdziewicz, J., Cristini, V. & Loewenberg, M. 1999 Stokes flow in the presence of a planar interface covered with incompressible surfactant. Phys. Fluids 11, 251-258. [pdf]

  31. Blawzdziewicz, J., Vlahovska, P., & Loewenberg, M. 2000 Rheology of a dilute dispersion of surfactant-covered spherical drops. Physica A 276, 50-85. [pdf]

  32. Nemer, M., Blawzdziewicz, J. & Loewenberg, M. 2001 Linear viscoelasticity of concentrated emulsions. In Mechanics for a new millennium, 75-84, H. Aref and J.W. Phillips (eds.), Kluwer. [pdf]

  33. Cristini, V., Blawzdziewicz, J. & Loewenberg, M. 2001 An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence. J. Comp. Phys. 168 445- 463. [pdf]

  34. Manga, M. & M. Loewenberg, 2002 Viscosity of magmas containing highly deformable bubbles. J. Volcanology & Geothermal Res. 105 19-24.

  35. Vlahovska, P., Blawzdziewicz, J. & Loewenberg, M., 2002, Nonlinear rheology of a dilute emulsion of surfactant-covered spherical drops in time-dependent flows. J. Fluid Mech. 463, 1–24. [pdf]

  36. Blawzdziewicz, J, Cristini, V. & Loewenberg, M. 2002, Critical behavior of drops in linear flows: I. phenomenological theory for drop dynamics near critical stationary states. Phys. Fluids 14 2709–2718. [pdf]

  37. Blawzdziewicz, J., Cristini, V. & Loewenberg, M., 2003, Multiple stationary drop shapes in strain-dominated linear Stokes flows. Phys. Fluids Letters 15, L37-40. [pdf]

  38. Patel, P.D., Shaqfeh, E.S.G., Butler, J.E., Cristini, V.,Blawzdziewicz J. & Loewenberg, M., 2003, Drop breakup in the flow through fixed fiber beds: An experimental and computational investigation. Phys. Fluids 15, 1146-1157.

  39. Cristini, V., Blawzdziewicz, J., Loewenberg, M. & Collins, L.R. 2003 Breakup in stochastic Stokes flows: sub-Kolmogorov drops in isotropic turbulence. J. Fluid Mech. 492, 231–250. [pdf]

  40. Cristini, V., Guido, S., Alfani, A., Blawzdziewicz, J. & Loewenberg, M. 2003 Drop breakup and fragement size distribution in shear flow. J. Rheol. 47, 1283–1298.

  41. Cunha, F.R. & Loewenberg M. 2003 A study of emulsion expansion by a boundary integral method. Mech. Res. Commun. 30, 639–649.

  42. Nemer, M., Chen, X., Papadopoulos, D. H., Blawzdziewicz, J.& Loewenberg, M., 2004, Hindered and accelerated coalescence of drops in Stokes flow. Phys. Rev. Letters 92, 114501. [pdf]

  43. Ismail A.E. & Loewenberg, M. 2004 Long-time evolution of a drop size distribution by coalescence in a linear flow. Phys. Rev. E. 69 46307.

  44. Vlahovska, P., Blawzdziewicz, J. & Loewenberg, M., 2005, Deformation of a surfactant-covered drop in a linear flow. Phys. Fluids, bf 17, 103103.

  45. Nemer, M.B., Chen, X., Papadopoulos, D.H., Blawzdziewicz, J, & Loewenberg, M., 2007, Comment on ”Two touching spherical drops in uniaxial extensional flow: Analytical solution to the creeping flow problem”. J. Colloid Interface Sci., 308, 1–3.

  46. Hashmi, S.M., Loewenberg, M. & Dufresne, E.R., 2007, Spatially extended FCS for visualizing and quantifying high-speed multiphase flows in microchannels. Optics Express, 15 6528-6533.

  47. Vlahovska, P.M., Blawzdziewicz, J. & Loewenberg, M., 2009, Small deformation theory for a surfactant-covered drop in linear flows. J. Fluid Mech., 624 293-337.

  48. Santoro, P. & Loewenberg, M., 2009, Coalescence of drops with tangentially mobile interfaces: effects of ambient flow. Ann. N.Y. Acad. Sci. 1161, 277–291.

  49. Janssen, P.J.A., Anderson, P.D. & Loewenberg, M., 2010, A slender-body theory for low-viscosity drops in shear-flow between parallel walls. Phys. Fluids, 22 042002.

  50. Ramachandran, A., Loewenberg, M. & Leighton, D.T., 2010, A constitutive equation for droplet distribution in unidirectional flows of dilute emulsions for low capillary numbers. Phys. Fluids, 22 083301.
 

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