1,244 research outputs found
Shock Formation in a Multidimensional Viscoelastic Diffusive System
We examine a model for non-Fickian "sorption overshoot" behavior in diffusive polymer-penetrant systems. The equations of motion proposed by Cohen and White [SIAM J. Appl. Math., 51 (1991), pp. 472–483] are solved for two-dimensional problems using matched asymptotic expansions. The phenomenon of shock formation predicted by the model is examined and contrasted with similar behavior in classical reaction-diffusion systems. Mass uptake curves produced by the model are examined and shown to compare favorably with experimental observations
Slippage and Migration in Taylor-Couette Flow of a Model for Dilute Wormlike Micellar Solutions
Submitted to J. Non-Newt Fluid Mechanics, June 2005In this paper we explore a model, most appropriate for dilute or semi-dilute worm-like micellar solutions, in an axisymmetric circular Taylor-Couette geometry. This study is a natural continuation of earlier work on rectilinear shear flows. The model, based on a bead-spring microstructure with nonaffine motion, reproduces the pronounced plateau in the stress strain-rate flow curve as observed in laboratory measurements of steady shearing flows. We also carry out a linear stability analysis of the computed steady state solutions. The results show shear-banding in the form of sharp changes in velocity gradients, spatial variations in number density, and in
alignment or stretching of the micelles. The velocity profiles obtained in numerical
solutions show strong qualitative agreement with those of laboratory experiments.NSF Collaborative Research Projec
The Onset of Stationary and Oscillatory Convection in a Horizontal Porous Layer Saturated with Viscoelastic Liquid Heated and Soluted From Below: Effect of Anisotropy
The onset of double diffusive stationary and oscillatory convection in a viscoelastic Oldroyd type fluid saturated in an anisotropic porous layer heated and soluted from below is studied. The flow is governed by the extended Darcy model for Oldroyd fluid. Stability analysis based on the method of perturbations of infinitesimal amplitude is performed using the normal mode technique. The analysis examines the effect of the Darcy Rayleigh number, the solutal Darcy the Rayleigh number, the relaxation time, the retardation time and the Lewis number. Important conclusions include the destabilizing effect of the relaxation time, the Darcy Rayleigh number and the Lewis number and the stabilizing effect of the solutal Darcy Rayleigh number, the retardation time and anisotropy parameter. Some of the results are generalization of the previous findings for isotropic porous medium
Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer
The nonlinear stability of thermal convection in a layer of an Oldroyd-B
fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is
used to describe the flow in a layer of an anisotropic porous medium. The results of the
linear instability theory are delineated. The thresholds for the stationary and oscillatory
convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The
stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the
cubic Landau equations. It shows that these solutions always bifurcate supercritically.
The heat transfer is estimated in terms of the Nusselt number for the stationary and
oscillatory modes. The result shows that, when the ratio of the thermal to mechanical
anisotropy parameters increases, the heat transfer decreases
Thermal Convection in a Couple-Stress Fluid in the Presence of Horizontal Magnetic Field with Hall Currents
The thermal stability of a couple-stress fluid is considered to include the effects of uniform horizontal magnetic field and Hall currents. The analysis is carried out within the framework of linear stability theory and normal made technique. For the case of stationary convection, magnetic field has stabilizing effect whereas Hall currents are found to have destabilizing effect on the system. The couple stress, however, has dual character in contrast to its stabilizing effect in the absence of Hall currents. Oscillatory modes are not allowed in the system. Graphs in each case have been plotted by giving numerical values to the parameters, depicting the stability characteristics
Energy-stable linear schemes for polymer-solvent phase field models
We present new linear energy-stable numerical schemes for numerical
simulation of complex polymer-solvent mixtures. The mathematical model proposed
by Zhou, Zhang and E (Physical Review E 73, 2006) consists of the Cahn-Hilliard
equation which describes dynamics of the interface that separates polymer and
solvent and the Oldroyd-B equations for the hydrodynamics of polymeric
mixtures. The model is thermodynamically consistent and dissipates free energy.
Our main goal in this paper is to derive numerical schemes for the
polymer-solvent mixture model that are energy dissipative and efficient in
time. To this end we will propose several problem-suited time discretizations
yielding linear schemes and discuss their properties
Age-dependent transient shear banding in soft glasses
We study numerically the formation of long-lived transient shear bands during
shear startup within two models of soft glasses (a simple fluidity model and an
adapted `soft glassy rheology' model). The degree and duration of banding
depends strongly on the applied shear rate, and on sample age before shearing.
In both models the ultimate steady flow state is homogeneous at all shear
rates, consistent with the underlying constitutive curve being monotonic.
However, particularly in the SGR case, the transient bands can be extremely
long lived. The banding instability is neither `purely viscous' nor `purely
elastic' in origin, but is closely associated with stress overshoot in startup
flow.Comment: 4 pages, 3 figure
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