(381b) Hydrodynamics of Extended Rods on Curved Fluid Membranes

Transport and organization of cytoskeletal filaments on curved fluid-like interfaces are key to many cellular processes, including the transport of membrane-bound proteins. We present the first slender-body formulation and calculation of the translational, including motions in parallel and perpendicular directions, and rotational drag coefficients of rods on spherical membranes surrounded by two Newtonian fluids. The drag coefficients are solved numerically as a function of the rod’s length, L, and its ratio with the following length-scales: 2D membrane to the interior (I) and exterior (E) 3D bulk fluid viscosity ratios, l_I=η_m/η_I, l_E=η_m/η_E, and the membrane radius, R. Different asymptotic regimes are identified and compared against the planar membrane results. We find that when the confinement of flows on spherical membrane causes the translational drag perpendicular to the rod's alignment to increase superlinearly with the rod’s length, while the rotational motion exhibit purely local drag and the drag in parallel direction shows the familiar logarithmic correction observed in 3D slender-body formulation. We, then, extend our calculations to the case where the interior fluid geometry is a shell with a thickness substantially smaller than the membrane radius: H/R «1, as a model for studying the dynamics of particles on membrane-coated rigid beads. We compute the drag coefficients as a function of L, l_I, l_E, R and H and explore the different asymptotic regimes. Through asymptotic analysis we show that this problem is analogous to modeling the flow on the membrane using Brinkman equation, where the permeability is κ=Hl_I. Finally, we show that the confinement effects at H/R «1 cause the parallel, perpendicular and rotational drag coefficients to scale superlinearly with the rod’s length, with the scaling exponent being largest in the perpendicular direction and weakest in the parallel direction.