Numerical and Theoretical Investigations of Flow in a Microcone and Plate Viscometer

Abstract

The slip flow of fluid in a microcone-plate viscometer has been considered. The first-order slip boundary condition is applied. A slip flow primary solution corresponding to unidirectional flow has been obtained. By ignoring all the convective terms and assuming a small gap angle, another closed-form solution called zeroth-order solution for slip flow is obtained. Previous investigations of the flow in the cone and plate did not consider the slip conditions at the solid-fluid interfacial boundary. Slip flow is also numerically studied in a microcone and plate viscometer. The accuracy of the two solutions is assessed by comparing their results with numerical solutions obtained by solving the full Navier–Stokes equation. The primary solution does not completely describe the flow in microcone and plate, and some deviations are found. On the other hand, the zeroth-order solution perfectly predicted the slip and no-slip flow in the inner region. A slip factor that takes into account spatial distribution yields a perfect match between the zeroth-order solution and numerical solution. On the other hand, analytical zeroth-order solution for outer region does not agree with the numerical work, and we should rely on the numerical solution. Taking a realistic range of slip length resulting from actual devices, numerical and theoretical results show that the differences in viscosity measurements between considering slip and no-slip are significant.