Interaction between the oil droplet in water and wetted wall: Force model and motion law

Abstract

To investigate the force model and motion law of oil droplets in water near the wetted wall, oil droplets with R1 = 0.29–0.62 mm and oil films with R2 = 1–6 mm are solved numerically. In addition to buoyancy, flow resistance, and added mass force, the film-induced force triggered by the wetted wall constraint is also introduced into the force model. The drainage process is described using the Stokes–Reynolds equation, and the Young–Laplace equation is used to calculate the pressure within the water film. The results show that the force model can be coupled with the Stokes–Reynolds–Young–Laplace model equation to better describe the drainage dynamics near the wetted wall. The pressure distribution law is closely related to the shape of the water film, especially when the oil–water interface is in the shape of a dimple, which can lead to the formation of negative pressure zones within the water film. The maximum pressure first grows in an exponential, then logarithmic pattern and eventually approaches the equivalent Laplace pressure. Around the critical size, the direction of the film-induced force changes and the form of action switches between driving and drag forces. The film-induced force's dominant effect is strongest when the curvature radius of the oil film is comparable to the droplet size.