Thesis
The simultaneous evaporation and imbibition of a droplet on a porous substrate
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2026
- Thesis identifier
- T18181
- Person Identifier (Local)
- 202169049
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- Mathematical models for the evolution of, and deposition from, a thin particle-laden droplet on three different porous substrates undergoing simultaneous evaporation and imbibition are formulated and analysed. In particular, analytical expressions for the evolution of the droplet, the flow within the droplet and the substrate, and for the transport and deposition onto the substrate of the particles, are obtained for droplets evolving in four different modes. While the physical mechanisms driving evaporation (namely, the diffusion-driven transport of vapour in the atmosphere away from the free surface of the droplet) and imbibition (namely, the pressure-driven transport of liquid in the substrate away from the base of the droplet) are rather different, perhaps rather unexpectedly, it is found that there are a number of qualitative and quantitative similarities as well as differences in the resulting behaviour of the droplet as it loses mass to its environment. For example, it is shown that a droplet undergoing pure imbibition on an infinitely thick, isotropic, flooded, porous substrate or a finitely thick, anisotropic, flooded, porous substrate in the constant contact radius (CR) mode never completely imbibes (i.e., it has an infinitely long lifetime), but if it evaporates (either with or without imbibition also occurring) then it has a finite lifetime, and increasing the strength of evaporation and/or imbibition shortens its lifetime. It is also shown that in the regime in which diffusion of particles is faster than axial advection but slower than radial advection of particles for an infinitely thick, isotropic, flooded, porous substrate, the final deposit of particles left behind on the substrate after the droplet has completely evaporated and/or imbibed is independent of both the nature and the strength of the physical mechanism(s) driving the mass loss from the droplet. On the other hand, for a finitely thick, anisotropic, dry or flooded, porous substrate, this is not the case. Not only are these results of theoretical interest, but they may also be potentially relevant to a wide variety of practical applications, including ink-jet printing, DNA chip manufacturing, and disease diagnostics, that would benefit from an improved ability to predict and/or control the final deposit pattern from a droplet undergoing simultaneous evaporation and imbibition.
- Advisor / supervisor
- Wilson, Stephen
- Resource Type
- DOI
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