Numerical simulation of the hydrodynamics of yield stress fluids during dip coating

Abstract

1 The dip coating of yield stress fluids was simulated at Bingham number below 1. 2 The effects of individual physical parameters and the lifting speed on the flow inside the bath were studied. 3 The relationship between flow region, velocity and shear stress of fluids in the bath were established. 4 The dimensionless film thickness can be well described by the Bingham number. The literature has treated the dip coating of yield stress fluids with the Bingham number ( B i = τ c / K γ ˙ n , where τ c , K , γ ˙ and n are the yield stress, consistency factor, shear rate and power-law exponent, respectively.) being larger than 1, and has ignored the influence of shear-dependent component ( K γ ˙ n ). This work simulated the dip-coating process for various simple yield stress fluids with Bi numbers below 1, and showed the importance of yield stress and shear-dependent component for the hydrodynamics inside the bath as well as the film thickness. The yielded-unyielded boundaries as well as the profiles of flow velocity and shear stress were theoretically determined under final steady state. The main flow characteristics of drainage in the meniscus were captured. Under the negligible effect of surface tension on the film coating, a semi-empirical model of film thickness considering drainage effect is proposed with good prediction performance.