Flows of Dehaven Fluid in Symmetrically Curved Capillary Fissures and Tubes

Abstract

In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of DeHaven type fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. variable cross-section, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. Each example is concluded with a presentation of the formulae for the velocity flow on the outer surface of a thin porous layer. Upon introduction of hindrance factors, these formulae may be presented in the most general forms.