Moving Solid Boundaries In The FHP Model And Coarse-Grained Model Of A Molecular Pump

In this research, we used a Lattice Gas Cellular Automata model (LGCA) calledFHP to investigate the pumping properties of a molecular pump relying on a dynamicratchet mechanism. Molecular pumping is a hot research topic, and the theoreticalresults obtained in the course of this research could find promising applications inmodern biology and medicine involving micro?uidic devices (MEMS).The pumping mechanism relies on a simple channel connecting two reservoirsof ?uid. As the walls of the channel are driven in a periodic and asymmetric way("dynamic ratchet"), a pumping ?ow builds up inside the channel. A LGCA model(FHP-III), is used to investigate the in?uence of various parameters (i.e. the wettingproperties of the channel, the frequency of the walls'motion, the dimensions of thechannel and the degree of slip occurring at the walls) on the pumping properties of themechanism. LGCA models are particularly well adapted to simulating ?ows on smallscales, for they do not rely on the continuity assumption. Furthermore, they provide arather simple way to handle solid boundaries with complex shape and/or various degreeof slip.The non-steady Couette ?ow between infinite plane parallel plates was used asa benchmark to test an existing method dedicated to handling moving solid bound-aries. We found that this method leads to significantly erroneous velocity profiles, andprovided a solution to cure this problem. The results obtained with the new methodfit extremely well with the exact solution of the Couette ?ow. We also proposed anew method to handle solid boundaries with various degree of slip. Simulation resultsshow that the corresponding slip length does not depend on the shear stress at the solidboundary: the method can therefore be used to apply a first order slip boundary condi-tion at solid walls. Finally, we proposed a method to handle solid boundaries movingaccording to more general motion laws. This method ensures mass conservation andfurther ensures that momentum is transferred from the moving wall to the ?uid, ac- cording to the motion direction of the wall. This last method was used to performsimulations of the molecular pump.Numerical simulations of the dynamic ratchet pump confirmed that a directed?uid ?ow emerges inside the channel, resulting in a pumping effect. We found that thepumping efficiency of the mechanism strongly relies on the wetting properties of thechannel, the frequency of the walls'motion, the dimensions of the channel, and the de-gree of slip occurring at solid walls. Corresponding evolution laws were subsequentlyobtained. The pumping ?ow inside the channel can thus be controlled by appropriatelytuning these parameters.