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Patterning surface textured plates with a viscoplastic fluid

Vanessa R. Kern1, Marcel Moura2, Pål E. S. Olsen1, and Andreas Carlson1,3,*

  • 1Mechanics Division, Department of Mathematics, University of Oslo, 0316 Oslo, Norway
  • 2PoreLab, the Njord Center, Department of Physics, University of Oslo, 0316 Oslo, Norway
  • 3Department of Medical Biochemistry and Biophysics, Umeå University, 901 87 Umeå, Sweden

  • *Contact author: acarlson@math.uio.no
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Phys. Rev. Fluids 11, 093301 – Published 28 September, 2026

DOI: https://doi.org/10.1103/1jz3-5j4d

Abstract

The deposition of a viscoplastic fluid onto a substrate can be achieved by moving apart two plates initially separated by a fluid-filled gap, where the footprint shape depends on the initiation of a fingering instability. Here, we present an approach for controlled deposition of a viscoplastic fluid by designing the macroscopic structure of the solid substrate. Through experiments in a lifted Hele-Shaw cell, we explore how slot, square, pyramid, and triangular patterns affect the dynamics of liquid deposition. The substrate structures directly control the symmetry and final shape of the deposited viscoplastic footprint, while having little systematic influence on the maximal normal adhesive force or on the force-gap scaling exponents once the total entrapped volume is accounted for through an effective initial gap. We develop a scaling description for the normal force of a Herschel–Bulkley fluid, showing that the measured force decay reflects a superposition of capillary, yield stress, and viscous contributions. For experiments producing stable patterning, the measured effective exponents are consistent with the theoretical range predicted by this model. Finally, we interpret the pattern-selection mechanism through a dynamical permeability analysis where the substrate texture creates an anisotropic permeability field whose angular maxima correlate with the preferred inward propagation directions of the invading air. Our results highlight a direct link between substrate geometry, interfacial dynamics, and the final deposited morphology, showing how millimetric deposition patterns can be programed using submillimetric surface structures.

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Phys. Rev. Fluids 11, 093301– Published 28 September, 2026
  • Received 30 June 2025
  • Accepted 17 July 2026
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