Theoretical, numerical and experimental study of capillary wetting rates on smooth vertical surfaces for liquids of varying Kapitsa numbers

When the surface of a liquid encounters a solid surface, a dynamic meniscus forms that traverses along the surface. This dynamic capillary wetting process plays a role in a wide range of technical applications and natural phenomena, such as liquid interaction with coatings on industrial materials, power generation system and atmospheric water harvesting technology. While wetting dynamics on flat horizontal surfaces and vertical curved surfaces are well studied, the precise mechanism of a wetting front advancing on a flat vertical surface remains partially understood. Predictive models for wetting dynamics in existing literature rely on specific empirical coefficients or simplified scaling laws, both of which reduce their applicability. In this presentation, the distinct wetting behavior of liquids with varying viscosity and surface tension is presented using a threshold based on the Kapitza number (Ka). For low Ka liquids, a semi-analytical framework is developed to account for key factors such as dynamic contact angle, and associated viscous friction related to the moving contact line. For high Ka liquids the semi-analytical framework does not provide a closed form solution and numerical simulations (using an interface tracking model, VOF) are required. The theoretical and numerical predictions are compared with our transient experimental measurements for both contact angle and wetting distance, with good agreement.