# Droplet impacts onto porous substrates: pre- and post-impact dynamics

Moreton, Gavin (2022) Droplet impacts onto porous substrates: pre- and post-impact dynamics. Doctoral thesis, University of East Anglia.

## Abstract

In physical settings such as droplets impacting onto soils, ink-jet printing, concrete and tarmac, the substrate plays a significant role in altering the flow. Such droplet impacts can lead to a penetration of fluid into the substrate in an unwanted or uncontrolled manner. Better modelling of the fluid mechanics during impact is crucial to a better understanding the fate of the liquid.

During droplet impact onto an impermeable plate the air acts as a cushioning layer. Moments before contact the air layer is thin and its pressure high. The high pressure deforms the drop’s free surface, forming an air bubble, which delays the droplet’s impact. Introducing a porous substrate allows air to enter the substrate and alter the approach to impact. After impact the liquid splashes along the substrate’s surface as a thin jet. Simultaneously, some liquid enters the substrate, slowing down the jet and increasing its thickness.

In chapters 2 and 3 we derive a mathematical model for an impact with an air cushioning layer onto an impermeable substrate, considering normal and oblique impacts with surface tension. Chapter 4 introduces a thin porous substrate. We couple the influence of the substrate through governing equations for the air and water, and we solve them numerically. Chapter 5 introduces deeper porous substrates: complex variable methods are used to couple the substrate behaviour with the gas and liquid governing equations. Chapter 6 begins to consider the post-impact dynamics. Here, for a drop meeting an impermeable substrate, Wagner theory is applied, and we solve the problem analytically with complex analytical methods. Chapter 7 introduces a porous substrate. We derive a model that couples the substrate behaviour with the spreading of the droplet and the motion of the jet along the substrate surface. Chapter 8 contains conclusions and open questions.

Item Type: Thesis (Doctoral) Faculty of Science > School of Mathematics Kitty Laine 05 Dec 2022 13:38 05 Dec 2022 13:38 https://ueaeprints.uea.ac.uk/id/eprint/89988