(6ar) Simulation of Concentrated Suspensions in Thin Film Processing

Simulation
of concentrated suspensions in thin film processing

Mahyar Javidi¹,
Andrew N. Hrymak²

Department of Chemical and Biochemical Engineering, University
of Western Ontario, London, ON, Canada

Keywords: coating, film, suspension, solid particle

Particle-laden flows are important in
a wide range of industrial fields, such as oil and gas refinement, paper
manufacturing, waste water treatment, biological and polymer processes where
transport and manipulation of suspensions occur [1, 2]. In addition, the
capability of developing a thin uniform suspension layer with evenly
distributed particles is essential in many applications. In coating processes
of suspensions, the particle distribution pattern can enhance the performance
of the final product by changing the bulk and surface characteristics. In this
work, the behavior of suspensions in a dip/free coating process is
investigated. Specifically, the adherence of a thin film on a substrate surface
in vertical withdrawal from a pool of liquid with dispersed solid particles.

In the current study, the dynamics of
concentrated suspension flow is modeled based on the density of solid particles
in the system, where macroscopic methods are used for tracking the volume
fraction of particles in the flow. In modeling the dispersions in dip
coating, a nonlinear constitutive equation of Phillips et al. [3] for the
particle distribution in suspensions is coupled with the Volume of Fluid method
[4] for capturing the free surface. The model is incorporated into a finite
volume method formulation to simulate shear-induced particle migration in
non-homogenous shear flows of suspensions in the dip coating process.

Numerical
simulation enables one to predict the film thickness and validate with
experimental results in a range of solid particle volume concentration from 0.1
to 0.4 and withdrawal velocities of 5 and 15 cm/s. Simulation of free coating
for a cylindrical substrate (e.g. fiber, wire) in the dispersion can be seen in
Fig. 1 for the initial particle volume fraction of 0.4.

Fig. 1. Dip coating for monodisperse solid particles in the flow ?
pictures a to c illustrate the simulation of finite length substrate withdrawn
out of coating vessel  

For calculating the dispersions flow, a viscosity
model is implemented in OpenFOAM for the formulation of the stress tensor. The
viscosity in the system is approached as a function of the particle volume
fraction in the suspending medium. In the current study, the viscosity of
concentrated suspensions is approximated by the Krieger [5] correlation which
is valid for all volume fractions, applied in the simulations.

The numerical simulation for dip coating of
dispersions has been developed in three dimensions. A finite length cylinder
with 6.5 cm length and 1.58 mm radius, has been used as a coating substrate. At
the initial condition of the simulation, the substrate is in a semi immersed
condition with up to 6 cm of cylinder immersed in the coating liquid and 0.5 cm
of the cylinder is out of the coating fluid. The substrate is withdrawn at the
speed of 0.05 and 0.15 cm/s from a coating bath with a range of (10-40 vol%) of
dispersed polystyrene particles in mineral oil.

The final condition of coated substrate is shown in
Fig 3a, where the substrate is completely withdrawn out of the coating bath. In
Fig 3a, points 1 cm to 7.5 cm show the 6.5 cm substrate with the coating film.
The coating thickness measured at every 0.5 cm along the cylinder substrate
length and the coating thickness results presented in Fig 3b-d. The positions
on the substrate in Fig 3b-d associate with the values shown by a ruler beside
the simulation images.

            
  a                               b                                                         

   c    d

Fig. 3. The
coating thickness are presented along the substrate length withdrawn from
coating bath, the simulation results (a) with associated positions on the cylinder
and for mineral oil with (b) 10%, (c) 20% and (d) 40% of dispersed polystyrene particles

For this work, the moving mesh method is applied
where the substrate and mesh moves with the withdrawal velocity. The zero
gradient boundary condition has been set for the base of the coating bath, and
zero velocity has been set for the bath wall. The contact angle between the
bath wall and coating fluid, and the contact angle between substrate and
coating liquid is measured using the goniometer and its value which is 18ͦ,
applied in boundary conditions of the system. This work investigates a
simulation approach to investigate suspension flows and to identify possible
limitations and solutions within this simulation methodology.

References

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K. Lin, M. Mata & A.L. Bertozzi, J. Phys D 240, 1661-1673(2011)

2.   S. R. Subia, M. S. Ingber, L. A. Mondy, S. A.
Altobelli & A. L. Graham, J. Fluid Mech 373, 193-219 (1998)

3.   R.J. Phillips, R. C. Armstrong, R. A. Brown, A.
L. Graham & J. R. Abbott, Phys Fluids A 4, 30-40 (1992)

4. C. W. Hirt, B. D. Nicols, J. Comp. Phys. 39, 201-225 (1981)

5. I. M. Krieger,
Adv. Colloid Interface Sci., 3, 111-136 (1972)