We numerically investigate viscoelastic phase separation in polymer solutions under shear using a time-dependent Ginzburg-Landau model. The gross variables in our model are the polymer volume fraction and a conformation tensor. The latter represents chain deformations and relaxes slowly on the rheological time giving rise to a large viscoelastic stress. The polymer and the solvent obey two-flui...

The cross-stream migration of a deformable drop in a unidirectional shear flow of a second-order fluid is considered. Expressions for the particle velocity due to the separate effects of deformation and viscoelastic rheology are obtained. The direction and magnitude of migration are calculated for the particular cases of Poiseuille flow and simple shear flow and compared with experimental data.

Previous experimental measurements and linear stability analyses of curvilinear shearing flows of viscoelastic fluids have shown that the combination of streamwise curvature and elastic normal stresses can lead to flow destabilization. Torsional shear flows of highly elastic fluids with closed streamlines can also accumulate heat from viscous dissipation resulting in nonuniformity in the temper...

It has been well-known for over six decades that the addition of minute amounts of long polymer chains to organic solvents, or water, can lead to significant turbulent drag reduction. This discovery has had many practical applications such as in pipeline fluid transport, oil well operations, vehicle design and submersible vehicle projectiles, and more recently arteriosclerosis treatment. Howeve...

This paper presents a numerical simulation of the developing flow and heat transfer of a viscoelastic fluid in a rectangular duct. In fully developed flow of a viscoelastic fluid in a non-circular duct, secondary flows normal to the flow direction are expected to enhance the rate of heat and mass transfer. On the other hand, properties such as viscosity, thermal conductivity, specific heat and ...

The objective of present research is to examine the thermal radiation effect in three-dimensional mixed convection flow of viscoelastic fluid. The boundary layer analysis has been discussed for flow by an exponentially stretching surface with convective conditions. The resulting partial differential equations are reduced into a system of nonlinear ordinary differential equations using appropria...

This letter describes the flow kinematics and stability of thin fluid sheets produced by impinging obliquely aligned laminar jets of a series of viscoelastic wormlike micelle solutions. As the velocity of the impinging jets is increased, the sheets of viscoelastic fluid grow larger and eventually become unstable. High speed imaging reveals a transition through a series of striking new flow stru...

In the present work, the effect of fluid’s elasticity was investigated on the hydrodynamic instability of Blasius flow. To determine the critical Reynolds number as a function of the elasticity number, a two-dimensional linear temporal stability analysis was invoked. The viscoelastic fluid is assumed to obey the Walters’ B fluid model for which base flow velocity profiles were fortunately avail...

We establish an analog of the Beale–Kato–Majda criterion for singularities of smooth solutions of the system of PDE arising in the Oldroyd model for ideal viscoelastic flow. It is well known that smooth solutions of the initial value problem associated with Euler’s equations { ∂tu+ (u · ∇)u = −∇p ∇ · u = 0 , (x, t) ∈ R 3 × (0, T ) (1.1) exist for some finite time T > 0. Here u = u(x, t) ∈ R and...