a numerical study of 3d electrokinetic flows through micromixers was performed. the micromixers considered here consisted of heterogeneous rectangular microchannels with prescribed patterns of zeta-potential at their walls. numerical simulation of electroosmotic flows within heterogeneous channels requires solution of the navier-stokes, ernest-plank and species concentration equations. it is kn...

Abstract In the present paper we utilize Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. particular, show practice that there exists a low-dimensional space allowing approximate solutions of equations. We also demonstrate it is possible process complexity depending only on dimension such but ...

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Starting from a minimal physical model of self-propelled hard rods on a substrate in two dimensions, we derive a modified Smoluchowski equation for the system. Self-propulsion enhances longitudinal diffusion and modifies the mean-field excluded volume interaction. From the Smoluchowski equation we obtain hydrodynamic equations for rod concentration, polarization and nematic order parameter. New...

1. Introduction Understanding concentrated colloidal dynamics in the presence of different pairwise interactions and external fields provides a basis to predict the temporal evolution of colloidal microstructures in diverse phenomena including suspension rheology and colloidal crystallization. However, a microscopic theory of concentrated colloidal dynamics does not yet exist that rigorously in...

We study the Doi model for suspensions of rod–like molecules. The Doi model couples a microscopic Fokker–Planck type equation (Smoluchowski equation) to the macroscopic Stokes equation. The Smoluchowski equation describes the evolution of the distribution of the rod orientations; it comes as a drift–diffusion equation on the sphere at every point in physical space. For sufficiently high macrosc...

{ This paper studies a stochastic particle method for the numerical treatment of Smoluchowski equation governing the coagulation of particles in a host gas. Convergence in probability is established for the Monte Carlo estimators, when the number of particles tends to in nity. The deterministic limit is characterized as the solution of a discrete in time version of the Smoluchowski equation. Un...

Using tools of nonequilibirum mechanics, we study a model of self-propelled hard rods on a substrate in two dimensions to quantify the interplay of self-propulsion and excluded-volume effects. We derive of a Smoluchowski equation for the configurational probability density of self-propelled rods that contains several modifications as compared to the familiar Smoluchowski equation for thermal ro...