Friction Law for Bingham Fluid Flow in Channels of Arbitrary Cross-Section Shapes

In many biomedical and industrial technological applications it is necessary to drive fluids that exhibit plastic or elasto-plastic behaviour. Particularly for cases in which fast results are demanded, or only small fluid samples are available, micro-channels are used. These normally have cross-section geometries determined by the manufacturing procedures and may be of square, rectangular, triangular and other shapes. In order to obtain the expected results, such as protein separation, particle concentrations, and the like, the rate of flow and time-dependent pattern of it must be carefully determined. In this paper it is presented an analytically rigorous method for calculating the friction coefficient in channels of arbitrary cross-section contours for plastic flow that may be conveniently described by the Bingham model. Results are presented for a variety of shapes and for different values of the yield stress.