Session E9: Focus Session: The Impact of Andy Acrivos on Today's Fluid Mechanics Science II

Interfacial effects on droplet electrohydrodynamics: particle vortices, patchy membranes, and vesicle drums

The analytical work by Acrivos group on drop dynamics in linear flows and rheology of dilute emulsions (papers with Frankel and Barthes-Biesel) have provided solid basis for more than 40 years of research on drops and capsules. These classical papers have inspired my research on drops with ``complex'' interfaces - surfactant-laden and particle-covered drops, and vesicles (drops encapsulated with lipid bilayer membranes). I will present some of our recent experimental observations on these systems in uniform DC and AC electric fields, where the coupling of the electric-field-induced flow and complex mechanics of the interface drives peculiar (and yet to be explained) behaviors: drum-like and asymmetric dumbbell shapes of vesicles; domains formation and motion in multicomponent membranes; particle assembly in dynamic vortices; drop kayaking. Possible implications of our findings to the design of patchy particles and electrorheology of emulsions will be discussed.   

Binding and Unbinding of Vesicles and Capsules in Axisymmetric Flow

Prof. Andreas Acrivos pioneered the use of scaling and asymptotic analysis, as well as the use of boundary integral methods, by chemical engineers in fluid flow and transport problems. These are skills that have been used by many of his former students in their own research. Here we consider the title problem using a combination of boundary-integral based numerical methods and scaling analysis to study the dynamics and mechanisms of adhesion and de-adhesion of vesicles at a solid boundary in the presence of flow. The adhesion process is dominated by drainage of the thin film down to a point where non-hydrodynamic attractive forces cause adherence. The unbinding process is dominated by peeling, though the final force to pull a vesicle from a solid surface is larger than expected due to lubrication effects.   

Discontinuous shear thickening and steady-state multiplicity in a granular suspension

A concentrated suspension of neutrally buoyant non-Brownian spheres sheared between concentric cylinders with an inner radius-to-gap ratio of 0.037 undergoes discontinuous shear thickening under shear rate control but passes through an S-shaped viscosity curve with multiple states under stress control. This behavior is well described by simulation results that incorporate particle-particle frictional forces into the hydrodynamic description and lead to an analytical interpolation relation between low friction and high friction states that predicts an S-shaped viscosity curve.   

Force v. force-free motion in colloids

Consider a neutrally buoyant particle suspended in a fluid. Since the particle and fluid densities are the same there is no force on the particle and no motion. Now add a very large number of other particles to the fluid. These other particles are more dense than the fluid and so will settle due to gravity. Will the first particle move? In which direction and how fast? And viewed in a frame moving with the first particle what is the velocity disturbance caused by this force-free particle? These questions arise in the context of phoretic motion in colloidal dispersions.   

Global symmetry relations in linear and viscoplastic mobility problems

The mobility tensor of a textured surface is a homogenized effective boundary condition that describes the effective slip of a fluid adjacent to the surface in terms of an applied shear traction far above the surface. In the Newtonian fluid case, perturbation analysis yields a mobility tensor formula, which suggests that regardless of the surface texture (i.e. nonuniform hydrophobicity distribution and/or height fluctuations) the mobility tensor is always symmetric. This conjecture is verified using a Lorentz reciprocity argument. It motivates the question of whether such symmetries would arise for nonlinear constitutive relations and boundary conditions, where the mobility tensor is not a constant but a function of the applied stress. We show that in the case of a strongly dissipative nonlinear constitutive relation --- one whose strain-rate relates to the stress solely through a scalar Edelen potential --- and strongly dissipative surface boundary conditions --- one whose hydrophobic character is described by a potential relating slip to traction --- the mobility function of the surface also maintains tensorial symmetry. By extension, the same variational arguments can be applied in problems such as the permeability tensor for viscoplastic flow through porous media, and we find that similar symmetries arise. These findings could be used to simplify the characterization of viscoplastic drag in various anisotropic media.   

Effective reaction rate for porous surfaces under strong shear: Beyond Damkohler

Traditonally, surface reactive porous media are modeled via an effective reaction/mass transfer rate based on the original ansatz of Damkohler, i.e, reaction limited transport at the microscale in the absence of flow. We are interested in modeling the microscale mass transfer to porous surfaces occuring in leaky tumor vasculature, where the Damkohler number can be O(1) and the Peclet number may be large. We model it as a uniform bath of a species in unbound shear flow over a wall with first order reactive circular patches (pores). We analyze the flux through a single pore using both analytic and boundary element simulations and observe the formation of a 3-D depletion region (wake) downstream of the pore. Wake sharing between adjacent pores in a multibody setting such as 2 pores aligned in the shear direction leads to a smaller flux per pore. Obtaining this interaction length scale and using the renormalized periodic Green's function, we study the flux through a periodic and disordered distribution of pores. This flux appears as the reaction rate in an effective boundary condition, valid up to non-dilute pore area fractions, and applicable at a wall-normal effective slip distance. It replaces the details of the surface and can be used directly in large scale physics simulations.