We provide a mathematical analysis of the spectrum of the linear stability problem for one and two layer channel flows of the upper-convected Maxwell (UCM) and Oldroyd-B fluids at zero Reynolds number. For plane Couette flow of the UCM fluid, it has long been known (Gorodstov and Leonov, J. Appl. Math. Mech. (PMM) 31 (1967) 310) that, for any given streamwise wave number, there are two eigenval...

A complete mathematical description of oscillatory Couette flows within the framework of kinetic theory is not available in the literature. Motivated by this and their vast engineering applications, we present a parametric study of time-periodic oscillatory Couette flows using the unsteady direct simulation Monte Carlo ~DSMC! method. Computations are performed as a function of the Knudsen ~Kn! ...

Accurate evaluation of damping in laterally oscillating microstructures is challenging due to the complex flow behavior. In addition, device fabrication techniques and surface properties will have an important effect on the flow characteristics. Although kinetic approaches such as the direct simulation Monte Carlo (DSMC) method and directly solving the Boltzmann equation can address these chall...

We investigate MHD-Couette--Shercliff flows driven by lateral wall motion with turbulent transitions observed only at supercritical Re. Linearly, the Tollmien--Schlichting (TS) wave instability was isolated each for friction parameter H $\ensuremath{\gtrsim}$ 300 in MHD-Couette flow, and 1000 Shercliff flow. At low H, linear nonlinear growth led to saturation a traveling wave, where waves conjo...

A comparison is presented of growth rates obtained from numerical simulations and a linear analysis of the breakdown of streamwise streaks in plane Poiseuille and Couette ows. We nd agreement between results of the simulations and the stability analysis.

A novel methodology, based on the use of phosphorescence imaging, is applied to determine the local through-thickness velocity profile of lubricant in an elastohydrodynamic contact. The technique has spatial and temporal resolutions of 40 μm and 340 μs respectively and thus allows lubricant rheology to be investigated at conditions close to service conditions. The capability of the newly-develo...

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the p...

The purpose of this work is to examine the flow of a binary mixture including chemically inert incompressible Newtonian fluids in a duct of semicircular cross-section. Such a flow model has great significance not only of its own theoretical interest, but also for application to various engineering processes. The governing equations have been solved analytically using the finite Fourier sine and...

We study numerically shear banded flow in planar and curved Couette geometries. Our aim is to capture two recent observations in shear banding systems of roll cells stacked in the vorticity direction, associated with an undulation of the interface between the bands. Depending on the degree of cell curvature and on the material's constitutive properties, we find either (i) an instability of the ...

Experimental realizations of Taylor-Couette flow often include rigid end plates at bottom and top of the system. As a consequence of such end plates the bifurcation behavior of the basic laminar flow as well as the spatio-temporal properties of the emerging pattern, such as e.g. spiral vortex flow, can change. The latter point is in the focus of our present experimental study. The spatio-tempor...