scholarly journals Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows

1998 ◽  
Vol 36 (3) ◽  
pp. 269-298 ◽  
Author(s):  
M. A. Bees ◽  
N. A. Hill ◽  
T. J. Pedley
Keyword(s):  
Shear Flows ◽  
Orientation Distribution ◽  
Steady Shear ◽  
Analytical Approximations ◽  
Dipolar Particles

scholarly journals Characterising shear-induced dynamics in flowing complex fluids using differential dynamic microscopy

Soft Matter ◽  
2021 ◽  
Vol 17 (39) ◽  
pp. 8838-8849
Author(s):  
James A. Richards ◽  
Vincent A. Martinez ◽  
Jochen Arlt
Keyword(s):  
Shear Flows ◽  
Complex Fluids ◽  
Steady Shear ◽  
Concentrated Emulsion ◽  
Microscopic Dynamics

We show how DDM measures microscopic dynamics in oscillatory or steady shear flows and use the technique to explore the yielding of a concentrated emulsion.

scholarly journals A General Numerical Method for Analyzing the Linear Stability of Stratified Parallel Shear Flows

2014 ◽  
Vol 31 (12) ◽  
pp. 2795-2808 ◽  
Author(s):  
Tim Rees ◽  
Adam Monahan
Keyword(s):  
Stability Analysis ◽  
Numerical Method ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Analytical Approximations ◽  
Onset Of Turbulence ◽  
Parallel Shear Flows ◽  
Critical Layers ◽  
The Stability ◽  
Stability Results

Abstract The stability analysis of stratified parallel shear flows is fundamental to investigations of the onset of turbulence in atmospheric and oceanic datasets. The stability analysis is performed by considering the behavior of small-amplitude waves, which is governed by the Taylor–Goldstein (TG) equation. The TG equation is a singular second-order eigenvalue problem, whose solutions, for all but the simplest background stratification and shear profiles, must be computed numerically. Accurate numerical solutions require that particular care be taken in the vicinity of critical layers resulting from the singular nature of the equation. Here a numerical method is presented for finding unstable modes of the TG equation, which calculates eigenvalues by combining numerical solutions with analytical approximations across critical layers. The accuracy of this method is assessed by comparison to the small number of stratification and shear profiles for which analytical solutions exist. New stability results from perturbations to some of these profiles are also obtained.

Note on the rheology of a dilute suspension of dipolar spheres with weak Brownian couples

1972 ◽  
Vol 56 (4) ◽  
pp. 803-813 ◽  
Author(s):  
E. J. Hinch ◽  
L. G. Leal
Keyword(s):  
Rheological Properties ◽  
Applied Field ◽  
Asymptotic Form ◽  
Present Note ◽  
Orientation Distribution ◽  
Dipole Axis ◽  
Brownian Rotation ◽  
Bulk Stress ◽  
Dilute Suspension ◽  
Dipolar Particles

A problem of theoretical interest in suspension rheology is the calculation of bulk rheological properties for a dilute suspension of spherical dipolar particles in the presence of weak Brownian rotation, when the applied field is perpendicular to the local vorticity of the bulk flow. In the present note, we determine the asymptotic form for the orientation distribution of the dipole axis in the limit of weak Brownian motion and use this distribution to determine the corresponding rheological properties of the suspension. The bulk stress is then discussed in terms of an effective viscosity for shear flow.

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