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<p>It is a well-established fact that vibration of a vessel in the vertical direction increases the settling velocity of large solid particles in yield-stress liquids obeying the Bingham model. In the present work, using the lattice Boltzmann method (LBM) we numerically show that in shear-thinning, yield-stress fluids obeying the Casson model the response of a circular solid particle settling in a finite-sized vibrating vessel is non-monotonic and exhibits four different settling regimes. Specifically, starting from a low dimensionless frequency of S = 0.8, the settling velocity of the particle progressively increases by vibrating the vessel until a critical frequency of S = 3.9 is reached. Beyond this critical frequency, the settling velocity of the particle starts decreasing until another critical frequency, roughly S = 4.7, is reached. Beyond this frequency, the settling velocity of the particle again increases up to roughly S = 7 beyond which it approaches an asymptotic value. By plotting the yielded zones and viscosity profiles it is shown that competition between yield stress effects with shear-thinning effects combined with the effects of the sidewalls is responsible for such complex settling behavior, not reported before. For particles that are already stuck in yield stress materials, our numerical results show that the amplitude needed to unblock such particles (at any given frequency) is larger for Casson fluid as compared with Bingham fluid. Since both fluid models have the same critical yield number, this finding highlights the importance of the rheological model adopted to represent particulate systems such as foodstuffs.</p> Graphical abstract <p>A solid particle settling in a vessel filled with viscoplastic fluids obeying the Casson model exhibits non-monotonic behavior depending on the frequency of the vessel (S) and yield stress of the fluid (Y). The non-monotonic effect is attributed to a competition between yielding (low frequencies), side-wall effects (intermediate frequencies) and shear-thinning (high frequencies).</p>

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Non-monotonic settling behavior of a circular solid particle immersed in a vibrating vessel filled with casson fluid

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • T. Rezaee,
  • M. Pourjafar-Chelikdani,
  • K. Sadeghy

摘要

It is a well-established fact that vibration of a vessel in the vertical direction increases the settling velocity of large solid particles in yield-stress liquids obeying the Bingham model. In the present work, using the lattice Boltzmann method (LBM) we numerically show that in shear-thinning, yield-stress fluids obeying the Casson model the response of a circular solid particle settling in a finite-sized vibrating vessel is non-monotonic and exhibits four different settling regimes. Specifically, starting from a low dimensionless frequency of S = 0.8, the settling velocity of the particle progressively increases by vibrating the vessel until a critical frequency of S = 3.9 is reached. Beyond this critical frequency, the settling velocity of the particle starts decreasing until another critical frequency, roughly S = 4.7, is reached. Beyond this frequency, the settling velocity of the particle again increases up to roughly S = 7 beyond which it approaches an asymptotic value. By plotting the yielded zones and viscosity profiles it is shown that competition between yield stress effects with shear-thinning effects combined with the effects of the sidewalls is responsible for such complex settling behavior, not reported before. For particles that are already stuck in yield stress materials, our numerical results show that the amplitude needed to unblock such particles (at any given frequency) is larger for Casson fluid as compared with Bingham fluid. Since both fluid models have the same critical yield number, this finding highlights the importance of the rheological model adopted to represent particulate systems such as foodstuffs.

Graphical abstract

A solid particle settling in a vessel filled with viscoplastic fluids obeying the Casson model exhibits non-monotonic behavior depending on the frequency of the vessel (S) and yield stress of the fluid (Y). The non-monotonic effect is attributed to a competition between yielding (low frequencies), side-wall effects (intermediate frequencies) and shear-thinning (high frequencies).