The effect of surface roughness on capillary rise in micro-grooves.

The capillary action is a unique feature of micro-grooves with numerous applications. This spontaneous flow eliminates the need for an extra pumping device to deliver a liquid. Capillary action depends on physical properties and features of the solid surface, as well as on thermophysical properties of the liquid. In this study, our previously proposed unifying capillary rise model is extended to include the effect of surface roughness. A new characteristic length scale is proposed that includes salient geometrical parameters, such as micro-grooves height, width, and surface roughness. Furthermore, it is shown that by using the proposed characteristic length scale, it can be determined whether the capillary action would occur in a given micro-groove and liquid. Various metallic and polymeric surfaces with a wide range of surface roughness are fabricated from aluminum, stainless-steel, natural graphite sheet, and 3D-printed stainless-steel and a polymer. A profilometer and sessile drop method are used to measure surface roughness and the contact angles, respectively. The present unifying model is compared against our measured data, and it is shown that it can predict the capillary rise in rough micro-grooves with less than a 10% relative difference. It is observed that the capillary height can be increased for a wetting surface by introducing surface roughness and by using optimal micro-groove cross-sections that are triangular as opposed to rectangular. The proposed compact, unifying model can be used to predict the capillary rise for any given micro-groove cross-section, and as a design tool for numerous industrial and biomedical applications, such as heat pipes, power electronic cooling solutions, sorption systems, medicine delivery devices, and microfluidics that utilize capillary micro-grooves.

A general form of capillary rise equation in micro-grooves.

Micro-grooves are a crucial feature in many applications, such as microelectro-mechanical systems, drug delivery, heat pipes, sorption systems, and microfluidic devices. Micro-grooves utilize capillary action to deliver a liquid, with no need for an extra pumping device, which makes them unique and desirable for numerous systems. Although the capillary action is well studied, all the available equations for the capillary rise are case-specific and depend on the geometry of the groove, surface properties, and the transport liquid. In this study, a unified non-dimensional model for capillary rise is proposed that can accurately predict the capillary rise for any given groove geometry and condition and only depends on two parameters: contact angle and characteristic length scale, defined as the ratio of the liquid-vapor to the solid-liquid interface. The proposed model is compared against data from the literature and can capture the experimental results with less than 10% relative difference. The effect of the grooves' height, width, and contact angle is investigated and reported. This study can be used for a unified approach in designing heat pipes, capillary-assisted evaporators for sorption systems, drug delivery micro-fluidic devices, etc.