Flow dynamics of fluid-filled particles with complex interfaces [electronic resource] : a study of surfactant-contaminated droplets, red blood cells, and vesicles
Keywords: Chemical Engineering.

We study three projects regarding the fluid mechanics of droplets with complex interfaces -- i.e., interfaces that are no longer described by a constant surface tension. Project 1: Recently, researchers found that adding a small amount of surfactant to high Reynolds number bubbly suspensions can create concentration instabilities expressed as regions of crescent-like bubble clusters. We demonstrate another mechanism for bubble clustering at low Reynolds number, in the limit where the surfactant's motion on the interface is dominated by diffusion rather than convection (i.e., small surface Peclet numbers). This instability caused by lateral motions of surfactant-contaminated bubbles due to variations in surface tension at their interface (i.e., the Marangoni effect). When the bubble rises under gravity, the surfactant on its interface gets swept from the front of the bubble to the rear. In a dilute suspension, the particle also experiences the disturbance velocity caused by all other particles in the suspension. This velocity advects the surfactant cap at the back of the bubble, producing a force that creates lateral motion. If the bubble drifts up the disturbance velocity gradient, we expect to observe concentration amplification since bubbles migrate toward higher concentration regions. This coupling of gravity with a particle's intrinsic microstructural variable (i.e., location of the surfactant cap) is a common motif to create lateral motion and aggregation in low Reynolds number, dilute suspensions. Project 2: When blood flows in our microcirculation, it is concentrated at the core of the vessel, but leaves a clarified layer of fluid near the wall (cell-free layer). The size and shape of this layer plays an important role in controlling plasma skimming at bifurcations as well as controlling the transport of particles embedded in the suspension such as platelets or nanoparticles. We understand the origin of this layer by performing boundary integral simulations of two simple problems: the lift of a single red blood cell in shear flow near a wall, and the binary collisions of red blood cells in shear flow. We then estimate the concentration profile of a red blood cell suspension by developing a kinetic master equation that balances these lift and collisional processes. We expect this theory to be qualitative, as we neglect screening and multi-body interactions that could be important in concentrated systems. Nevertheless, we find that the theory reasonably matches fully-resolved, numerical simulations of red blood cell suspensions in Couette flow, especially near the wall where the cell-free layer is. Scaling theories for the cell-free layer thickness agree well with in vitro experiments. The coarse-grained theories we develop are an order of magnitude faster than large-scale numerical simulations, although we do gain computational efficiency at the expense of some accuracy. Project 3: We examine the dynamics of vesicles in extensional flows, which are hyperbolic flow patterns that commonly manifest themselves in flow through contractions and rising/suction flows. When vesicles are placed in these flows, they undergo three sets of instabilities that are in many ways different than standard droplets: a) ``dumbbell'' -- the initially symmetric vesicle transitions to an unsteady, asymmetric dumbbell, b) ``burst'' -- the vesicle extends symmetrically without bound, c)``pearling'' -- a series of beads develops in the central thread of the vesicle after the ``burst'' transition. We develop a mathematical framework (simulations and theory) to elucidate the major physics behind each of these shape transitions. For the ``dumbbell'' transition, we also perform preliminary experiments to verify the existence of this instability. We find that many of these shape transitions can be recast as a modified Rayleigh-Plateau instability. However, membrane incompressibility causes many interesting results that are different from droplets (such as asymmetric shapes and the weak dependence of the vesicle's stability on the viscosity contrast between inner and outer fluids). Furthermore, bending of the phospholipid bilayer can give rise to permanent buckled states under compression. Our simulations and scaling analyses for the three shape transitions discussed above agree well with the stability criterion from published experimental data.