Liquid Wicking in Hierarchical Microstructures

The aim of this work is to model the flow of liquid as it spreads through a structured cavity (‘wicking’), as described schematically in Figure 1. The problem was posed by Analog Devices in the context of the 118th European Study Group with Industry, which was held in UCD in July 2018. The aim of the modelling exercise is to find the optimum structure morphology/size/porosity/materials for wicking/routing of liquid inside a cavity under various temperature and environment conditions? Wicking of surfaces has many applications in the fields of biology, sensing and integrated chip cooling. As such, the existing literature on the subject is extensive. Therefore, the first objective of this report is to carry out a detailed literature review (Section 2), wherein we outline how the answers to many of the questions posed by Analog Devices can be answered by methods from the existing literature. Further refinements of this approach could be carried out, if any of the questions are not answered in this report. In this existing literature, the fluid that permeates the substrate is assumed to come from an infinite reservoir. Therefore, in section 3 we examine how including the finite volume of the liquid drop that permeates into the substrate affects the spreading dynamics. Additionally, we have also examined lubrication theory as a way of providing a very detailed and mathematically consistent description of wetting on rough surfaces, which we describe below in Section 4. Finally, our conclusions are presented in Section 5.