Velocity gradient

About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.

Dilute polystyrene solutions in extensional flows: Birefringence and flow modification

Abstract: The coil—stretch transition in dilute polymer solutions has been studied using four- and two-roll mills to generate two-dimensional extensional flows. Flow birefringence measurements give the polymer conformation in the flow, while velocity gradient measurements using homodyne light scattering reveal the effects of the polymer on the flow field. When the polymers become sufficiently extended there is a distinct onset of measurable decreases in the velocity gradients. A necessary condition for this occur is a very high level of domain overlap between the extended molecules. If we estimate this by the volume concentration of circumscribed spheres, φeff (i.e., the sphere diameter equals the extended length of the polymer), the onset of an effect of polymer on the flow does not occur until φeff ≈ 4000–6000. Nevertheless, our measurements show that dilute polymer solutions do inhibit the development of large strain rates in regions of persistent extensional flow. The present flow birefringence measurements also extend previous studies to a wider range of flow types, thus providing new information that can be used in the evaluation of molecular models for polymer flow dynamics. In the present paper, we compare experimental data with predictions from the elastic dumbbell model with various combinations of a nonlinear spring, conformation-dependent anisotropic friction (including strain-inefficient rotation), and internal viscosity.

Active and hibernating turbulence in minimal channel flow of newtonian and polymeric fluids.

Abstract: Turbulent channel flow of drag-reducing polymer solutions is simulated in minimal flow geometries. Even in the Newtonian limit, we find intervals of "hibernating" turbulence that display many features of the universal maximum drag reduction asymptote observed in polymer solutions: weak streamwise vortices, nearly nonexistent streamwise variations, and a mean velocity gradient that quantitatively matches experiments. As viscoelasticity increases, the frequency of these intervals also increases, while the intervals themselves are unchanged, leading to flows that increasingly resemble maximum drag reduction.

Radiative Convective Nanofluid Flow Past a Stretching/Shrinking Sheet with Slip Effects

Abstract: Steady two-dimensional laminar mixed convective boundary-layer slip nanofluid flow in a Darcian porous medium due to a stretching/shrinking sheet is studied theoretically and numerically. A thermal radiative effect is incorporated in the model. The governing transport, partial differential equations, along with the boundary conditions, are transformed into a dimensionless form and then, via a linear group of transformation, a system of coupled similarity differential equations is derived. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth–fifth-order numerical quadrature method from Maple symbolic software. The effects of the controlling parameters (namely, stretching/shrinking, velocity slip, thermal slip, mass slip, Darcy number, radiation conduction, buoyancy ratio parameter, and Lewis number) on the dimensionless velocity, temperature, nanoparticle volume fraction, velocity gradient, temperature gradient, and nanoparticle volume fraction gradient are shown in graphi...

Analytical modeling of material flow in equal channel angular extrusion (ECAE)

Abstract: We provide analytical forms for the plastic deformation and velocity gradients associated with a single pass of equal channel angular extrusion (ECAE). Three cases of plastic deformation are considered: ideal simple shear, a plastic deformation zone (PDZ) in the shape of a central fan of angle β m , and a two-part PDZ consisting of a central fan in the ‘upper’ region and a low intensity shear deformation in the ‘lower’ region. The analysis for simple shear considers a general die angle Φ , whereas the other two cases only consider Φ =90°. The tensors for deformation and velocity gradients completely describe the deformation, such as the directions and magnitudes of material stretching and rotations. From this analysis, one can calculate deformation and texture evolution. Texture evolution during flow through the central fan zone involves continuous rotation of the texture components causing the texture developed at the end of the extrusion to be rotated relative to the ideal simple shear case. The analysis of the two-part zone suggests inhomogeneity in texture evolution, in which features of the initial texture are retained and rotated in the lower region, while they are nearly erased in the upper region. These analytical flow patterns for a single pass can be repeatedly applied for any number of passes of any ECAE route.