Study on the characteristics of a rimming flow

Abstract

Coating flows are among an important class of flows commonly found in manufacturing process. The special case of a continuous coating flow inside a rotating horizontal circular cylinder, referred to as rimming flow, and the particle segregation phenomena in this rimming flow show diverse patterns depending on the controllable parameters. In this research we found that as the controllable parameters are varied, there appear transient states between uniformly particle-dispersed and distinctly particle-segregated states. To distinguish between the states, we studied the effects of rotating speed, fluid filling fraction and fluid viscosity and represented the parameters’ range of the states by means of the modified Jeffreys number β which scales the importance between viscous and gravitational force. Steady, two-dimensional velocity fields and free surface shapes of the rimming flow have been investigated by solving full Navier-Stokes equations using Galerkin finite element analysis without approximations applied in most previous theoretical and numerical studies of this phenomenon. Changes in the free surface shapes and velocity and pressure field are shown according to the capillary number and the dimensionless parameter β. Three distinct patterns are observed and classified into homogenous film, bump, and fluid pool states. The variation of the arc length of the meniscus according to β is investigated and the abrupt increase of it is observed in the transition from the homogeneous film state to the bump state. It is shown numerically that the capillary number also plays an important role in the transition between states. The shape of the free surface changes from bump to homogenous film state as the capillary number decreases. Our computational result agrees well with those obtained experimentally with respect to the free surface shape for filling fraction as high as 0.35. Using the constitutive equations for the viscoelastic fluid and particle-suspension, pat...