(180z) Numerical Simulation of Drying Process of Polymer Solution Inkjet-Droplets for Predicting Film Configuration

Numerical Simulation of Drying Process of Polymer Solution Inkjet-Droplets for Predicting Film Configuration

Jun FUKAI*, Kazuki Kubo, Jing Hong WANG and Koichi NAKASO

Department of Chemical Engineering, Graduate School of Engineering, Kyushu University, Motooka 744, Nishi-ku, Fukuoka, 819-0395 Japan

*Corresponding author: jfukai@chem-eng.kyushu-u.ac.jp

Keywords: inkjet printing, drying process, polymer solution droplet, numerical

1 Introduction

Inkjet printings are expected to be used as an alternative manufacturing process of color filters of displays, organic EL displays etc. A basic process of this method is that solution/suspension droplets depositing on a substrate are dried, to form thin films. The most industrial applications require forming flat films on substrates. However, it is not easy to make such films because, in general, a ring structure develops on the periphery of the film due to solute/particle transport during the drying process. A lot of experimental studies were reported to prevent the films from forming ring structure. Several theoretical models were also developed to predict the film configuration. However, the applicable conditions of these models are limited because of several assumptions. It is thus required to develop a theoretical model which is applied to wide operating conditions.

The final purpose of this study is to numerically predict film configuration with modeling transport phenomena caused in a droplet as accurately as possible. As the first step, a mathematical model considering the fluid dynamics, heat transfer and mass transfer in a polymer solute droplet was proposed in this study. The model was numerically solved using a Lagrangian finite element method. The characteristic drying behaviors and film configuration found in the calculations were reported.

2 Mathematical model

2.1 Governing equations

Computational domain consists of a sessile droplet and substrate. A proposed mathematical model considers local evaporation rates of solvent from the free surface, a decrease of the droplet volume due to the evaporation, thermal and solutal Marangoni forces on free surface, stress balance between droplet and vapor phases, temperature drop due to evaporation latent heat etc. On two-dimensional axis symmetric coordinate, the equations of continuity, motion, energy and solute mass were numerically solved using a Lagrangian finite element method. In the iteration of time step, the finite elements were automatically regenerated when they largely distorted.

 A reason for using Lagrangian method is that the boundary conditions on the free surface is directly reflected to the discritized equations, leading to accurate simulations compared to conventional Euler methods such tracking method and level set method.

Generally the contact line of the solution droplet deposited on a substrate recedes to some degree, and subsequently stops due to the self-pinning mechanism. The self-pinning was assumed to happen when the solute concentration at the contact line reaches a threshold value.

2.2 Physical properties

The density, viscosity and surface tension of the solution were given as functions of solute concentration and temperature on the basis of the measured value. Mass diffusion coefficient was estimated using Wilke-Chang’s equation. The other physical properties were cited from physical properties handbooks, and assumed constants. The local evaporation rate on the free surface was calculated using the equation reported by H. Hu et al. (J. Phys. Chem. B, 106, 1334 (2002))

3 Results

Polystyrene/Anisole droplets were chosen. The initial droplet diameter was 30 mm. The initial contact angle was 30¢ª.

3.1 Drying process

The model predicted oscillation of free surface, whose period and amplitude were the order of 10²ms and 10^-1 mm respectively, due to Marangoni instability. The amplitude of the oscillation decreased with decreasing the evaporation rate. This Marangoni instability had been experimentally found by P. Kavehpour et al. (Colloids and Surfaces A, 206, 409(2002)). This is the first research which numerically predicts this instability as far as the authors’ best knowledge.

The temperature profile developed horizontally. It was not influenced by Marangoni convective flow during the whole process. Namely, the conduction dominated the heat transfer in the droplet. The solute concentration profile was concentrically developed from the free surface at the initial stage, and subsequently disturbed due to the convective flow. Self-pinning occurred immediately after deposition, and decreased the contact angle as the drying advanced. Unfortunately, the lateral flow which must be deduced by self-pinning was not obviously found in the calculated velocity field because the effect of oscillation on the velocity was emphasized. However, the solute was concentrated near the contact line. This high solute concentration leads to a ring structure on the periphery of the formed film.

3-2 Film configuration

The calculations continued until 94-97 vol.% of the solvent evaporated. At this instant, the ring structure developed on the periphery of the films. The model also predicted that the film shape was shifted from ring-like to dot-like as evaporation rate artificially decreased. These results qualitatively agree with the experimental results. 

4. Conclusion

The numerical techniques should be still modified to achieve accurate predictions. However, the model predicted characteristic behaviors of the droplet which had been experimentally known.