Simultaneous evaporation and imbibition of a droplet on a fully flooded porous substrate

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Craig, David and Wray, Alexander W. and Sefiane, Khellil and Wilson, Stephen K. (2026) Simultaneous evaporation and imbibition of a droplet on a fully flooded porous substrate. Physical Review Fluids. ISSN 2469-990X (In Press) (https://doi.org/10.1103/jxdz-7h5w)

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Abstract

A mathematical model for the evolution of, and deposition from, a thin particle-laden droplet on an infinitely thick, isotropic, fully flooded, porous substrate with interconnected pores undergoing simultaneous evaporation and imbibition is formulated and analysed. In particular, analytical expressions for the evolution of the droplet, as well as for 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 flow of vapour in the atmosphere away from the free surface of the droplet) and imbibition (namely, the pressure-driven flow 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 in the constant contact radius 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, 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. Not only are these results of theoretical interest, but they are also 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.

ORCID iDs

Craig, David, Wray, Alexander W. ORCID logoORCID: https://orcid.org/0000-0002-3219-8272, Sefiane, Khellil and Wilson, Stephen K. ORCID logoORCID: https://orcid.org/0000-0001-7841-9643;
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