Estimation of drag force acting on spheres by slow flow and its application to a microfluidic device

Abstract

The present study deals with the problem of determining drag force acting on spherical particles by slow flow through the particles in random arrays. Effective-medium theories using simplified models such as EM-I, EM-II, EM-III, and EM-IV are presented to predict the drag on the spheres in random arrays. These predictions are compared with numerical simulations. The EM-IV model in which the volume exclusion effect near the representative sphere is taken into account in defining the effective-medium is found to compare very well with the numerical simulations up to the volume fraction of spheres O=0.5. In addition, Carman’s correlation is given for comparison. This empirical correlation is shown to be in good agreement with the simulation results beyond Φ=0.4. Therefore, it is found that selective use of EM-IV and Carman’s correlation depending on Φ is practically the best way to obtain accurate predictions of the drag for full range ofO Finally, the estimations are compared with the previous experimental results for the gas pressure drop across a micropacked bed reactor. The comparison shows a reasonable agreement between the experimental results and the estimations by Carman’s correlation.