(61e) Direct Numerical Simulation of Viscous Forces Due to Liquid Bridge Formed Between Two Moving Particles

In many particulate processes in
chemical engineering fields, liquid is often added to dry powder to improve
powder characteristics and ease powder handling. Examples of such processes include
wet agglomeration, particle coating and catalytic reaction. When relatively
small amount of liquid is dispersed in powder, liquid bridges are formed
between primary particles and bonding forces are exerted on the particles, i.e.
surface tension and viscous forces. In particular, viscous forces can
significantly influence the powder behaviour in a process since liquid
viscosity can vary many orders of magnitude depending on the applications.
Therefore, it is of paramount importance to accurately estimate the viscous
forces in order to understand the process.

Several viscous force models are
proposed in literature based on (a) the solutions of the Reynolds lubrication
equation and (b) asymptotic solutions of the Stokes equations. It is shown that
these models can estimate viscous forces comparable to experimental
measurements when the inter-particle separation distance is sufficiently small.
However, the accuracy decreases drastically when the separation distance
increases. Therefore, there is a need to derive more accurate viscous force
models.

In the present work, liquid bridges
between particles are directly simulated using the Volume of Fluid (VOF) method
with dynamic mesh as shown in Figure 1. It can be observed that the pressure
distribution obtained from simulation is in good agreement with that obtained
from the solution of the Reynolds lubrication equation when the separation
distance is small (Figure 1a), whilst the difference becomes significant when
the separation distance becomes large (Figure 1b). The forces exerted on the
particles obtained from the simulations are then used to derive an improved
viscous force model.

Figure 1
Pressure distribution between particles; (a) small separation distance case and
(b) large separation distance case. Dashed line presents the solution of the
Reynolds lubrication equation (J. Colloid Interface Sci., 231, pp 26-31,
2000).

Keywords

Viscous force; Liquid bridge; Direct Numerical Simulation;
Volume of Fluid (VOF) method