Mathematical modelling of granulation: static and dynamic liquid bridges

Abstract

Liquid bridges are important in a number of industrial applications, such as the granulation of pharmaceuticals, pesticides, and the creation of detergents and fine chemicals. This paper concerns a mathematical study of static and dynamic liquid bridges. For the static case, a new analytical solution to theYoung-Laplace equation is obtained, in which the true shape of the liquid bridge surface is able to be written in terms of known mathematical functions. The phase portrait of the differential equation governing the bridge shape is then examined. For the dynamic case of colliding spheres, the motion of the bridge is derived from mass conservation and the Navier-Stokes equations. The bridge surface is approximated as a cylinder and the solution is valid for low Reynolds number (Re 1). As the spheres approach, their motion is shown to be damped by the viscosity of the liquid bridge.