Hydrodynamics of colloids in a narrow channel

Abstract

dimensional reaction-diffusion systems are investigated. The two-component models which satisfy some specified conservation laws are considered. It is found that three-states lattice gases with a single local conservation law can be classified into two families, one where the function is degenerate, i.e., takes the same value for two different states, another where the conserved quantity is a linear nondegenerate function of the occupation variable. This two groups of families are investigated in this work. For the first group, the hydrodynamic equation is obtained nonlinear and therefore admits shock solutions. For the second group, for open systems with different boundary fugacities, a complete list of models where the shock performs a biased random walk on the lattice is found. <br /> As the second approach, a simulation method is used to model a suspension of colloidal particles in a narrow channel. To this end, a hybrid simulation scheme which couples a Molecular Dynamics simulation method to a MPC fluid, which is a coarse-grained model to describe fluid dynamics, is used. Then, the motion of colloidal particles in the presence of the gravitational force (sedimentation) is considered. The dependence of the sedimentation velocity of colloidal particles on volume fraction is discussed. The results which obtained for sedimentation velocity of colloids as a function of volume fraction are compared with the case without hydrodynamic interactions. The Reynolds numbers for a range of gravitational force are determined. A linear increase of the sedimentation velocity of colloids as a function of gravitational force is obtained. The formation of the zig-zag shape in the chain of sedimenting colloidal particles in the channel is noticed. A systematic behaviour of the average distances between successive col- loids in the presence of the external force is showed. This behaviour is discussed being as a sign for developing a density discontinuity in the system.<br /> The current density of colloidal particles is determined and existing shock solutions of the system in the two approaches, are discussed.