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.  for the particle distribution in suspensions is coupled with the Volume of Fluid method  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for monodisperse solid particles in the flow – pictures a to c illustrate the simulation of finite length substrate withdrawn out of coating vessel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  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.
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.
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