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<p>A simplified model is derived for pressure-driven flow between adjacent surfaces of materials modeled as seemingly viscoplastic or truly viscoplastic. The material response to external forces is traditionally described by constitutive relations in which the extra stress tensor <b>S</b> is expressed as a function of the symmetric part of the velocity gradient <b>D</b>. However, for viscoplastic materials, <b>S</b> cannot, in general, be written as a function of <b>D</b>, whereas <b>D</b> can be expressed in terms of <b>S</b>. Motivated by this observation, a model based on constitutive relations of the form <b>D</b> = <i>f</i>(<b>S</b>) is proposed, leading to a system of first-order partial differential equations. A local Poiseuille law is also formulated, and a reduced-dimensional equation for the pressure is derived. Explicit velocity profiles are obtained for selected cases.</p>

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Modeling pressure-driven flow between adjacent surfaces of viscoplastic and seemingly viscoplastic materials

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月8日

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  • Andreas Almqvist,
  • Evgeniya Burtseva,
  • Kumbakonam Rajagopal,
  • Peter Wall

摘要

A simplified model is derived for pressure-driven flow between adjacent surfaces of materials modeled as seemingly viscoplastic or truly viscoplastic. The material response to external forces is traditionally described by constitutive relations in which the extra stress tensor S is expressed as a function of the symmetric part of the velocity gradient D. However, for viscoplastic materials, S cannot, in general, be written as a function of D, whereas D can be expressed in terms of S. Motivated by this observation, a model based on constitutive relations of the form D = f(S) is proposed, leading to a system of first-order partial differential equations. A local Poiseuille law is also formulated, and a reduced-dimensional equation for the pressure is derived. Explicit velocity profiles are obtained for selected cases.