Abstract
The stability of neutrally and non-neutrally buoyant particles immersed in a plane Poiseuille flow of a yield-stress fluid (Bingham fluid) is addressed numerically. Particles being carried by the yield-stress fluid can behave in different ways: they might (i) migrate inside the yielded regions or (ii) be transported without any relative motion inside the unyielded region if the yield stress is large enough compared to the buoyancy stress and the other stresses acting on the particles. Knowing the static stability of particles inside a bath of quiescent yield-stress fluid (Chaparian & Frigaard, J. Fluid Mech. , vol. 819, 2017, pp. 311–351), we analyse the latter behaviour when the yield-stress fluid Poiseuille flow is host to two-dimensional particles. Numerical experiments reveal that particles lose their stability (i.e. break the unyielded plug and sediment/migrate) with smaller buoyancy compared to the sedimentation inside a bath of quiescent yield-stress fluid, because of the inherent shear stress in the Poiseuille flow. The key parameter in interpreting the present results is the position of the particle relative to the position of the yield surface in the undisturbed flow (in the absence of any particle): the larger the portion of a particle located inside the undisturbed sheared regions, the more likely is the particle to be unstable. Yet, we find that the core unyielded plug can grow locally to some extent to contain the particles. This picture holds even for neutrally buoyant particles, although they are strictly stable when they are located wholly inside the undisturbed plug. We propose scalings for all cases.
Highlights
One of the interesting features of a yield-stress fluid is that it can hold particles/ bubbles of small buoyancy statically suspended
The stability of neutrally and non-neutrally buoyant particles immersed in yieldstress Poiseuille flows is investigated numerically in the present study: particles can be transported in the core unyielded region without any relative motion compared to the carrying adjacent fluid if the yield stress is large enough compared to the
This exceptional feature of yield-stress fluids was previously addressed in the case of particle sedimentation in a quiescent bath of yield-stress fluids, which resulted in reporting Yc∗ – the critical ratio of the yield stress to the buoyancy stress beyond which the particle does not move
Summary
One of the interesting features of a yield-stress fluid is that it can hold particles/ bubbles of small buoyancy statically suspended. This is practically important for many industries: from producing stable fresh concrete in the construction industry (Roussel 2006) to preventing sedimentation of drilling/rock cuttings in the oil and gas industry (Elgaddafi et al 2012). The complexity of particle dynamics in the yielded regions comes from various sources such as the nonlinearity of the fluid behaviour and particle–particle and particle–wall interactions, whereas in the core unyielded region particles might be trapped (which was evidenced experimentally by Merkak et al (2008, 2009) and Zade et al (2020)) because of the small stresses compared to the yield stress
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