Brownian dynamics of fully confined suspensions of rigid particles without Green's functions

We introduce a Rigid-Body Fluctuating Immersed Boundary (RB-FIB) method to perform large-scale Brownian dynamics simulations of suspensions of rigid particles in fully confined domains, without any need to explicitly construct Green's functions or mobility operators. In the RB-FIB approach, discretized fluctuating Stokes equations are solved with prescribed boundary conditions in conjunction with a rigid-body immersed boundary method to discretize arbitrarily shaped colloidal particles with no-slip or active-slip prescribed on their surface. We design a specialized Split-Euler-Maruyama temporal integrator that uses a combination of random finite differences to capture the stochastic drift appearing in the overdamped Langevin equation. The RB-FIB method presented in this work only solves mobility problems in each time step using a preconditioned iterative solver and has a computational complexity that scales linearly in the number of particles and fluid grid cells. We demonstrate that the RB-FIB method correctly reproduces the Gibbs-Boltzmann equilibrium distribution and use the method to examine the time correlation functions for two spheres tightly confined in a cuboid. We model a quasi-two-dimensional colloidal crystal confined in a narrow microchannel and hydrodynamically driven across a commensurate periodic substrate potential mimicking the effect of a corrugated wall. We observe partial and full depinning of the colloidal monolayer from the substrate potential above a certain wall speed, consistent with a transition from static to kinetic friction through propagating kink solitons. Unexpectedly, we find that particles nearest to the boundaries of the domain are the first to be displaced, followed by particles in the middle of the domain.

Design of surface hierarchy for extreme hydrophobicity

An extreme water-repellent surface is designed and fabricated with a hierarchical integration of nano- and microscale textures. We combined the two readily accessible etching techniques, a standard deep silicon etching, and a gas phase isotropic etching (XeF2) for the uniform formation of double roughness on a silicon surface. The fabricated synthetic surface shows the hallmarks of the Lotus effect: durable super water repellency (contact angle>173 degrees) and the sole existence of the Cassie state even with a very large spacing between roughness structures (>1:7.5). We directly demonstrate the absence of the Wenzel's or wetted state through a series of experiments. When a water droplet is squeezed or dropped on the fabricated surface, the contact angle hardly changes and the released droplet instantly springs back without remaining wetted on the surface. We also show that a ball of water droplet keeps bouncing on the surface. Furthermore, the droplet shows very small contact angle hysteresis which can be further used in applications such as super-repellent coating and low-drag microfludics. These properties are attributed to the nano/micro surface texture designed to keep the nonwetting state energetically favorable.

Immersed finite element method and its applications to biological systems

This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid-structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid-structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility.