Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.

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Modelization of dispersion of swimming bacteria in Poiseuille flow

10.5194/egusphere-egu21-7183 ◽

2021 ◽

Author(s):

Akash Ganesh ◽

Romain Rescanieres ◽

Carine Douarche ◽

Harold Auradou

Keyword(s):

Shear Rate ◽

Numerical Simulations ◽

Poiseuille Flow ◽

Dispersion Coefficient ◽

Equations Of Motion ◽

Critical Shear Rate ◽

Uniform Shear ◽

Simple Boundary ◽

Swimming Bacteria ◽

Local Shear

We study the shear-induced migration of dilute suspensions of swimming bacteria (modelled as Active elongated Brownian Particles or ABPs) subject to plane Poiseuille flow in a confined channel. By incorporating very simple boundary conditions, we perform numerical simulations of the 3D equations of motion describing the change in position and orientation of the particles. We investigate the effects of confinement, of non-uniform shear and of aspect ratio of the particles on the overall dynamics of the ABPs population.We particularly study the coupling between the local shear and the change in the orientation of the particles. We thus perform numerical simulations on both the case where the change in the orientation of the ABPs is purely diffusive (decoupled case) and the case where their orientation is coupled to the shear flow (coupled case). We observe that the decoupled case exhibits a Taylor dispersion i.e.&#160; the effective dispersion coefficient of the ABPs along the direction of the flow is proportional to the square of the imposed shear at all shears.&#160;However, for all the coupled cases we observe a transition from a Taylor to an active-Taylor regime at a critical shear rate, indicating the effect of shear coupling on the orientation dynamics of the particles. This critical shear rate is directly correlated to the degree of confinement. The change in the dispersion coefficient along the direction of the flow as function of the shear rate is in qualitative agreement with previous studies[1].&#160;To further understand these results, we also investigate the change in the dispersion coefficient in the other two directions along with the effect of the shape of the particles. We believe that this study should enhance our understanding of dispersion of bacteria through porous media, on surfaces etc. where shear flows are ubiquitous.&#160;[1] Sandeep Chilukuri, Cynthia H.Collins, and Patrick T. Underhill. Dispersionof flagellated swimming microorganisms in planar poiseuille flow.Physics offluids, 27, (031902):1 &#8211;17, 2015

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Patterns in Wall-Bounded Shear Flows

Annual Review of Fluid Mechanics ◽

10.1146/annurev-fluid-010719-060221 ◽

2020 ◽

Vol 52 (1) ◽

pp. 343-367 ◽

Cited By ~ 19

Author(s):

Laurette S. Tuckerman ◽

Matthew Chantry ◽

Dwight Barkley

Keyword(s):

Numerical Simulations ◽

Couette Flow ◽

Poiseuille Flow ◽

Pipe Flow ◽

Shear Flows ◽

Plane Couette Flow ◽

Plane Poiseuille Flow ◽

Flow Focusing ◽

Annular Pipe ◽

Flow Plane

Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

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Taylor–Couette–Poiseuille flow with a weakly permeable inner cylinder: absolute instabilities and selection of global modes

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.437 ◽

2018 ◽

Vol 849 ◽

pp. 741-776

Author(s):

Nils Tilton ◽

Denis Martinand

Keyword(s):

Numerical Simulations ◽

Poiseuille Flow ◽

Radial Flow ◽

Temporal Frequency ◽

Outer Cylinder ◽

Global Mode ◽

Permeable Membrane ◽

Global Modes ◽

Taylor Couette ◽

Base Flows

Variations in the local stability of the flow in a Taylor–Couette cell can be imposed by adding an axial Poiseuille flow and a radial flow associated with one or both of the cylinders being permeable. At a given rotation rate of the inner cylinder, this results in adjacent regions of the flow that can be simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for studying global modes of instability. To this end, building on the existing stability analysis in absolute modes developing over axially invariant base flows, we consider the case of axially varying base flows in systems for which the outer cylinder is impermeable, and the inner cylinder is a weakly permeable membrane through which the radial flow is governed by Darcy’s law. The frameworks of linear and nonlinear global modes are used to describe the instabilities and assess the results of direct numerical simulations using a dedicated pseudospectral method. Three different axially evolving set-ups are considered. In the first, fluid injection occurs along the full inner cylinder. In the second, fluid extraction occurs along the full inner cylinder. Besides its fundamental interest, this set-up is relevant to filtration devices. In the third, fluid flux through the inner cylinder evolves from extraction to injection as cross-flow reversal occurs. In agreement with the global mode analyses, the numerical simulations develop centrifugal instabilities above the predicted critical rotation rates and downstream of the predicted axial locations. The global mode analyses do not fully explain, however, that the instabilities observed in the numerical simulations take the form of axial stacks of wavepackets characterized by jumps of the temporal frequency.

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Numerical simulations on the dynamics of trains of particles in a viscoelastic fluid flowing in a microchannel

Meccanica ◽

10.1007/s11012-019-00985-6 ◽

2019 ◽

Vol 55 (2) ◽

pp. 317-330 ◽

Cited By ~ 3

Author(s):

Gaetano D’Avino ◽

Pier Luca Maffettone

Keyword(s):

Numerical Simulations ◽

Viscoelastic Fluid

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