We introduce a mesoscale technique for simulating the structure and rheology of block-copolymer melts and blends in hydrodynamic flows. The technique couples dynamic self-consistent field theory with continuum hydrodynamics and flow penalization to simulate polymeric fluid flows in channels of arbitrary geometry. We demonstrate the method by studying phase separation of an ABC triblock copolyme...

We present exact and analytically accurate results for the problem of a flexible polymer chain in shear flow. Under such a flow the polymer tumbles, and the probability distribution of the tumbling times tau of the polymer decays exponentially as approximately exp(-alphatau/tau_{0}) (where tau_{0} is the longest relaxation time). We show that for a Rouse chain this nontrivial constant alpha can...

Interior stagnation point flows of viscoelastic liquids arise in a wide variety of applications including extensional viscometry, polymer processing and microfluidics. Experimentally, these flows have long been known to exhibit instabilities, but the mechanisms underlying them have not previously been elucidated. We computationally demonstrate the existence of a supercritical oscillatory instab...

The effect of stress diffusivity is examined in both the Oldroyd-B and FENE-P models of a viscoelastic fluid in the low Reynolds (Stokes) limit for a 2D periodic time-dependent flow. A local analytic solution can be obtained when assuming a flow of the form u =Wi (x, y), whereWi is the Weissenberg number. In this case the width of the birefringent strand of the polymer stress scales with the ad...

This paper deals with peristaltic flow of a Johnson–Segalman fluid in an asymmetric channel under long-wavelength and lowReynolds number considerations. The channel asymmetry is caused due to the peristaltic wave train on the walls having different amplitudes and phase. A series solution for small Weissenberg number is obtained for the stream function, axial velocity, axial pressure gradient an...

We evaluate the stabilized three-field stress-velocity-pressure Galerkin/LeastSquares finite element formulation for viscoelastic fluids, using a benchmark problem of Oldroyd-B flow past a cylinder at various Weissenberg numbers. To address the issue of weak consistency exhibited by low-order velocity interpolations in the context of stabilized formulations, we also employ velocity gradient rec...

The industrial process of coating flat surfaces with polymeric substances is numerically simulated by solving the full equations of motion for a flow through a contraction with a moving boundary. The four-constant Oldroyd constitutive equation is used to represent the viscoelastic fluid. Some adjustments to existing finite-difference methods are made in such a way as to avoid singular iterative...

The unsteady two-dimensional stagnation point flow of the Walters B’ fluid impinging on an infinite plate in the presence of a transverse magnetic field is examined and solutions are obtained. It is assumed that the infinite plate at y 0 is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations a...