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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Delaying viscous fingering patterns during fluid detachment.

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Updated: Jul 5, 2025

Challenges in Rheological Characterization of Highly Concentrated Suspensions — A Case Study for Screen-printing Silver Pastes
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Detachment forces during parallel-plate gap separation mediated by a simple yield-stress fluid.

Vítor Hugo de Oliveira Pereira1, Wilson Barros2

  • 1Departamento de Física, Universidade Federal de Pernambuco (UFPE), Cidade Universitária, 50670-901, Recife, Pernambuco, Brazil.

The European Physical Journal. E, Soft Matter
|January 23, 2024
PubMed
Summary

This study reveals how yield-stress fluids behave under traction, showing instability at small gaps and stable flow at larger ones. We isolated viscosity, capillarity, and yield stress contributions to traction force.

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Area of Science:

  • Fluid mechanics
  • Rheology
  • Soft matter physics

Background:

  • Yield-stress fluids exhibit complex flow behaviors.
  • Understanding traction forces is crucial for industrial applications.

Purpose of the Study:

  • To monitor and analyze the normal traction force response of yield-stress fluids.
  • To investigate the influence of confinement geometry and initial gap on fluid behavior.
  • To differentiate and quantify contributions of viscosity, capillarity, and yield stress to traction force.

Main Methods:

  • Experimental setup involving two circular parallel plates separated at constant velocity.
  • Visual inspection for Saffman-Taylor instability and fingering patterns.
  • Application of the Herschel-Bulkley model to analyze traction force scaling.

Main Results:

  • Saffman-Taylor instability observed at narrow initial gaps, characterized by fingering patterns.
  • Stable circular symmetry maintained at larger initial gaps, indicating absence of instability.
  • Cascade of traction force contributions allowed isolation of viscosity, capillarity, and yield stress effects.

Conclusions:

  • The study successfully isolated and quantified individual force contributions in yield-stress fluids.
  • Instability is a key factor influencing fluid behavior and traction forces at small scales.
  • The Herschel-Bulkley model effectively describes traction force scaling across different regimes.