Institute of Natural and Mathematical Sciences
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Item Solution of the Young-Laplace equation for three particles(Massey University, 2003) Rynhart, P.R.; McLachlan, R.; Jones, J.R.; McKibbin, R.This paper presents the solution to the liquid bridge profile formed between three equally sized spherical primary particles. The particles are equally separated, with sphere centres located on the vertices of an equilateral triangle. Equations for the problem are derived and solved numerically for given constant mean curvature H0, contact angle , and inter-particle separation distance S. The binding force between particles is calculated and plotted as a function of liquid bridge volume for a particular example. Agreement with experiment is provided.Item Mathematical modelling of granulation: static and dynamic liquid bridges(Massey University, 2002) Rynhart, PatrickLiquid 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.