Capillary and priming pressures control the penetration of yield-stress fluids through non-wetting 2D meshes

TL;DR

This work tackles the challenge of forcing yield-stress fluids into non-wetting 2D meshes by performing quasi-static experiments that couple controlled pressure forcing with direct visualization. It demonstrates that penetration through hydrophobic meshes is dominated by capillary forces, with the threshold set by the maximum Laplace pressure $\Delta P_{L,max}$, while a newly identified priming pressure $\Delta P_p$ governs the local invasion pattern. The yield stress $\sigma_y$ contributes a smaller, secondary pressure $\Delta P_\sigma_y$, but its primary effect is to control whether penetration manifests as bursts through single pores or as collective coalescence across multiple pores, via a predictive criterion involving a critical yield $\sigma_y^c$. The findings introduce a plastocapillary framework, enabling design strategies for homogeneous penetration at minimal pressure and offering insights for applications in filtration, textiles, coatings, and civil engineering. The work thus provides a quantitative, geometry-driven picture of capillarity- and yield-stress–mediated imbibition in non-wetting 2D meshes with potential extension to more complex porous media.

Abstract

Forcing hydrophilic fluids through hydrophobic porous solids is a recurrent industrial challenge. If the penetrating fluid is Newtonian, the imposed pressure has to overcome the capillary pressure at the fluid-air interface in a pore. The presence of a yield-stress, however, makes the pressure transfer and the penetration significantly more complex. In this study, we experimentally investigate the forced penetration of a water based yield-stress fluid through a regular hydrophobic mesh under quasi-static conditions, combining quantitative pressure measurements and direct visualisation of the penetration process. We reveal that the penetration is controlled by a competition between the yield-stress and two distinct pressures. The capillary pressure, that dictates the threshold at which the yield-stress fluid penetrates the hydrophobic mesh, and a priming pressure, that controls how the fluid advances through it. The latter corresponds to a pressure drop ensuing a local capillary instability, never reported before. Our findings shine a new light on forced imbibition processes, with direct implications on their fundamental understanding and practical engineering.

Figures (16)

• Figure 1: (a) Quasi-static experimental setup. (b) and (c) Side-view and top-view diagrams, respectively, of the woven polyamide meshes (diagrams provided by the manufacturer). Definition of key dimensions: pore size $m$, fiber diameter $d$, and mesh thickness $e$.
• Figure 2: Snapshots from an experiment with mesh 3 and a fluid with a yield stress of 66Pa, showing the progression of the fluid-air interface. The camera focus is on the hydrophobic mesh, for which we can observe some side pores filled with glue. (a) The fluid approaches the mesh. The ring light forms a central circular reflection on the fluid front. (b) The fluid contacts the mesh at the center. The pores here show a small white reflection at the edges, indicating initial contact. At this step, the compressor pressure is $\Delta P_{\mathrm{comp}} = \Delta P_{\mathrm{contact}}$, the initial flowing pressure required to bring the yield stress fluid to the tip of the syringe. (c) The fluid contacts the entire mesh. (d) The fluid starts to advance into the pores, as the light reflections shift to square shapes in the pore centers. (e) The fluid lightly protrudes through the pores, forming circular reflection patterns. (f) As we increase the applied pressure, drops expand through the pores, nearing neighboring drops. The circled area indicates where the first breakthrough will occur. (g) Neighbouring drops touch and begin coalescing, accelerating the dynamics. (h) to (j) Successive coalescences quickly connect multiple pores, forming clusters as the fluid penetrates.
• Figure 3: Main. Laplace pressure as a function of the immersion angle $\alpha$, for $\theta=90^{\circ}$, $m=71µm$ and $\ell=33µm$. The maximum pressure $\Delta P_{L,\mathrm{max}}$ is reached at the critical immersion angle $\alpha_c$. The priming pressure $\Delta P_p$ is defined as $\Delta P_p= \Delta P_{L,\mathrm{max}} - \Delta P_L(180^{\circ})$. Inset. Definition of the parameters: $\alpha$ is the immersion angle, $\theta$ is the contact angle on a single fiber, $m$ the pore size, $\ell$ the pore depth.
• Figure 4: Experimentally measured penetration pressure $\Delta P_{\mathrm{pen}}$ as a function of theoretical maximum Laplace pressure $\Delta P_{L,\mathrm{max}}$, obtained with water (blue squares) and dilute Carbopol suspension without yield stress (red triangles). The symbol positions corresponds to the mean value measured for at least 4 measurements in each condition, and the height of the errorbars to the associated standard deviation. The dotted line corresponds to $\Delta P_{\mathrm{pen}} = \Delta P_{L,\mathrm{max}}$.
• Figure 5: Penetration pressure $\Delta P_{\mathrm{pen}}$ as a function of yield stress $\sigma_y$, for the five meshes used. Each point represents the average value for a set of parameters ($\sigma_y$, $m$, $e$) over 2 to 10 experiments. The lighter-colored areas indicating the corresponding standard deviations.