scholarly journals Chemotaxis in shear flow: Similarity solutions of the steady‐state chemoattractant and bacterial distributions

AIChE Journal ◽  
2019 ◽  
Vol 65 (10) ◽  
Author(s):  
Suin Shim ◽  
Howard A. Stone ◽  
Roseanne M. Ford
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Similarity Solutions ◽  
Flow Similarity

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

Elastic recovery of immiscible blends 1. Analysis after steady state shear flow

1999 ◽  
Vol 38 (1) ◽  
pp. 65-72 ◽  
Author(s):  
I. Vinckier ◽  
P. Moldenaers ◽  
J. Mewis
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Elastic Recovery ◽  
Immiscible Blends

The effect of weak Brownian rotations on particles in shear flow

1971 ◽  
Vol 46 (4) ◽  
pp. 685-703 ◽  
Author(s):  
L. G. Leal ◽  
E. J. Hinch
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Probability Distribution ◽  
Shear Flow ◽  
Equilibrium Distribution ◽  
Steady State Probability ◽  
Bulk Properties ◽  
Closed Orbits ◽  
Basic Equations

Axisymmetric particles in zero Reynolds number shear flow execute closed orbits. In this paper we consider the role of small Brownian couples in establishing a steady-state probability distribution for a particle being on any particular orbit. After presenting the basic equations, we derive an expression for the equilibrium distribution. This result is then used to calculate some bulk properties for a suspension of such particles, and these predicted properties are compared with available experimental observation.

Micro-mechanics of electrostatically stabilized suspensions of cellulose nanofibrils under steady state shear flow

Soft Matter ◽  
2016 ◽  
Vol 12 (6) ◽  
pp. 1721-1735 ◽  
Author(s):  
F. Martoïa ◽  
P. J. J. Dumont ◽  
L. Orgéas ◽  
M. N. Belgacem ◽  
J.-L. Putaux
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Cellulose Nanofibrils ◽  
Oxidized Cellulose ◽  
Cellulose Nanofibril ◽  
Aqueous Suspensions

In this study, we characterized and modeled the rheology of TEMPO-oxidized cellulose nanofibril (NFC) aqueous suspensions with electrostatically stabilized and unflocculated nanofibrous structures.

scholarly journals Rheology of a suspension of elastic particles in a viscous shear flow

2011 ◽  
Vol 687 ◽  
pp. 209-237 ◽  
Author(s):  
Tong Gao ◽  
Howard H. Hu ◽  
Pedro Ponte Castañeda
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Effective Viscosity ◽  
Circular Cross Section ◽  
Solid Particles ◽  
Simple Shear Flow ◽  
Arbitrary Lagrangian Eulerian ◽  
Viscous Shear ◽  
Elastic Particles ◽  
Steady State Solutions

AbstractIn this paper we consider a suspension of elastic solid particles in a viscous liquid. The particles are assumed to be neo-Hookean and can undergo finite elastic deformations. A polarization technique, originally developed for analogous problems in linear elasticity, is used to establish a theory for describing the finite-strain, time-dependent response of an ellipsoidal elastic particle in a viscous fluid flow under Stokes flow conditions. A set of coupled, nonlinear, first-order ODEs is obtained for the evolution of the uniform stress fields in the particle, as well as for the shape and orientation of the particle, which can in turn be used to characterize the rheology of a dilute suspension of elastic particles in a shear flow. When applied to a suspension of cylindrical particles with initially circular cross-section, the theory confirms the existence of steady-state solutions, which can be given simple analytical expressions. The two-dimensional, steady-state solutions for the particle shape and orientation, as well as for the effective viscosity and normal stress differences in the suspension, are in excellent agreement with direct numerical simulations of multiple-particle dispersions in a shear flow obtained by using an arbitrary Lagrangian–Eulerian (ALE) finite element method (FEM) solver. The corresponding solutions for the evolution of the microstructure and the rheological properties of suspensions of initially spherical (three-dimensional) particles in a simple shear flow are also obtained, and compared with the results of Roscoe (J. Fluid Mech., vol. 28, 1967, pp. 273–293) in the steady-state regime. Interestingly, the results show that sufficiently soft elastic particles can be used to reduce the effective viscosity of the suspension (relative to that of the pure fluid).

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