Numerical modeling and verification of gas flow through a network of crossed narrow v-grooves

Abstract

The gas flow through a network of crossing thin micro-machined channels has been successfully modeled and simulated. The crossings are formed by two sets of v-grooves that intersect as two silicon wafers are bonded together. The gas is distributed from inlets via a manifold of channels to the narrow v-grooves. The narrow v-grooves could work as a particle filter. The fluidic model is derived from the Navier–Stokes equation and assumes laminar isothermal flow and incorporates small Knudsen number corrections and Poiseuille number calculations. The simulations use the finite element method. Several elements of the full crossing network model are treated separately before lumping them together: the straight v-grooves, a single crossing in an infinite set and a set of exactly four crossings along the flow path. The introduction of a crossing effectively corresponds to a virtual reduction of the length of the flow path, thereby defining a new effective length. The first and last crossings of each flow path together contribute to a pressure drop equal to that from three ordinary crossings. The derived full network model has been compared to previous experimental results on several differently shaped crossed v-groove networks. Within the experimental errors, the model corresponds to the mass flow and pressure drop measurements. The main error source is the uncertainty in v-groove width which has a profound impact on the fluidic behavior.