InterPore2025

Evaporation and absorption of surfactant-laden droplets on unsaturated porous media

22 May 2025, 09:05

15m

Oral Presentation (MS16) Fluid Interactions with Thin Porous Media MS16

Speaker

Xiaoxing Li (Eindhoven University of Technology)

Description

Understanding the evaporation and absorption of surfactant-laden droplets on porous media is challenging and important for many industrial applications, such as inkjet printing. Fast penetration of the droplets is desirable to minimize the time droplets remain on the paper, thereby preventing the coalescence of droplets, which is an undesirable outcome in inkjet printing. The addition of surfactants can alter the surface energy of the liquid-gas interface in the paper, possibly accelerating the penetration rate of droplets(1,2). Surfactants can also suppress the coffee-ring effects in the droplet, resulting in a more uniform deposition ink pattern, further improving the inkjet printing quality(3,4). Therefore, understanding the imbibition of surfactant-laden ink into paper is critical for optimizing inkjet printing. The complexity and visualization difficulty of porous media, and the interaction between fluid dynamics and surfactants make this a challenging problem.

The evaporation of surfactant-laden droplets on a fibrous thin paper sheet is a complex process, involving spontaneous droplet evaporation, water imbibition into pores causing an unsaturated porous medium, and surfactant transport in both the droplet and the porous medium, as illustrated in Figure 1. We use both theoretical and numerical methods to explore this process. The mathematical model for flow in droplets is based on lubrication theory. For the calculation of the vapor concentration, which determines the evaporation flux, an analytical method is used. For the droplet absorption process, the Richards equation is used, where it should be noted that we do not describe the flow on the scale of the pores, but rather use properties averaged over a number of pores. For the surfactant transport process, a mass conservative convection-diffusion-adsorption model is employed, including adsorption at both the liquid-air and liquid-solid interfaces.

We first simulate one-dimensional (1D) absorption of surfactant-laden ink into unsaturated porous media to investigate the influence of parameters, such as porosity, Peclet number (Pe), Damköhler number (Da), and maximum adsorbed surfactant concentration, on the absorption dynamics. This analysis also allows us to study the similarities and differences compared to saturated flow models. Then we extend our study to two-dimensional (2D) problems assuming axial symmetry in cylindrical coordinates, incorporating droplet dynamics and liquid-air interface adsorption in unsaturated regions. This extension contribute to advancing our understanding of complex dynamics involved in surfactant-laden droplet absorption in porous media.

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