Mathematical modelling of granulation: static and dynamic liquid bridges
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Date
2002
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Massey University
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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.
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Keywords
Liquid bridges
Citation
Rynhart, P. (2002), Mathematical modelling of granulation: static and dynamic liquid bridges, Research Letters in the Information and Mathematical Sciences, 3, 199-212