A Compressible Turbulence Model for Pressure—Strain

This work focuses on the performance and validation of compressible turbulence models for the pressure-strain correlation. Considering the Launder Reece and Rodi (LRR) incompressible model for the pressure-strain correlation, Adumitroaie et al., Huang et al., and Marzougui et al., used different modeling approaches to develop turbulence models, taking into account compressibility effects for this term. Two numerical coefficients are dependent on the turbulent Mach number, and all of the remaining coefficients conserve the same values as in the original LRR model. The models do not correctly predict the compressible turbulence at a high-speed shear flow. So, the revision of these models is the major aim of this study. In the present work, the compressible model for the pressure-strain correlation developed by Khlifi−Lili, involving the turbulent Mach number, the gradient, and the convective Mach numbers, is used to modify the linear mean shear strain and the slow terms of the previous models. The models are tested in two compressible turbulent flows: homogeneous shear flow and the newly developed plane mixing layers. The predicted results of the proposed modifications of the Adumitroaie et al., Huang et al., and Marzougui et al., models and of its universal versions are compared with direct numerical simulation (DNS) and experiment data. The results show that the important parameters of compressibility in homogeneous shear flow and in the mixing layers are well predicted by the proposal models.

Chemical production on a deforming substrate

The interplay between chemical reaction and substrate deformation is discussed by adapting Ranz's formulation for scalar mixing to the case of a reactive mixture between segregated reactants, initially separated by an interface whose thickness may not be vanishingly small. Experiments in a simple shear flow demonstrate the existence of three regimes depending on the Damköhler number $Da=t_s/t_c$ where $t_s$ is the mixing time of the interface width and $t_c$ is the chemical time. Instead of treating explicitly the chemical cross-term, we rationalize these different regimes by globalizing it as a production term involving a flux which depends on the rate at which the reaction zone is fed by the reactants, a formulation valid for $Da>1$ . For $Da<1$ , the reactants interpenetrate before they react, giving rise to a ‘diffusio-chemical’ regime where chemical production occurs within a substrate whose width is controlled by molecular diffusion.

Dynamics of Individual Red Blood Cells Under Shear Flow: A Way to Discriminate Deformability Alterations

In this work, we compared the dynamics of motion in a linear shear flow of individual red blood cells (RBCs) from healthy and pathological donors (Sickle Cell Disease (SCD) or Sickle Cell-β-thalassemia) and of low and high densities, in a suspending medium of higher viscosity. In these conditions, at lower shear rates, biconcave discocyte-shaped RBCs present an unsteady flip-flopping motion, where the cell axis of symmetry rotates in the shear plane, rocking to and fro between an orbital angle ±ϕ observed when the cell is on its edge. We show that the evolution of ϕ depends solely on RBC density for healthy RBCs, with denser RBCs displaying lower ϕ values than the lighter ones. Typically, at a shear stress of 0.08 Pa, ϕ has values of 82 and 72° for RBCs with average densities of 1.097 and 1.115, respectively. Surprisingly, we show that SCD RBCs display the same ϕ-evolution as healthy RBCs of same density, showing that the flip-flopping behavior is unaffected by the SCD pathology. When the shear stress is increased further (above 0.1 Pa), healthy RBCs start going through a transition to a fluid-like motion, called tank-treading, where the RBC has a quasi-constant orientation relatively to the flow and the membrane rotates around the center of mass of the cell. This transition occurs at higher shear stresses (above 0.2 Pa) for denser cells. This shift toward higher stresses is even more remarkable in the case of SCD RBCs, showing that the transition to the tank-treading regime is highly dependent on the SCD pathology. Indeed, at a shear stress of 0.2 Pa, for RBCs with a density of 1.097, 100% of healthy RBCs have transited to the tank-treading regime vs. less than 50% SCD RBCs. We correlate the observed differences in dynamics to the alterations of RBC mechanical properties with regard to density and SCD pathology reported in the literature. Our results suggest that it might be possible to develop simple non-invasive assays for diagnosis purpose based on the RBC motion in shear flow and relying on this millifluidic approach.

Flow driven vesicle unbinding under mechanosensitive adhesion

Ligand receptor based adhesion is the primary mode of interaction of cellular blood constituents with the endothelium. These adhered entities also experience shear flow imposed by the blood which may...

Thermally Fluctuating, Semiflexible Sheets in Simple Shear Flow

We perform Brownian dynamics simulations of semiflexible colloidal sheets with hydrodynamic interactions and thermal fluctuations in shear flow. As a function of the ratio of bending rigidity to shear energy...

Oblique instability of a stratified oscillatory boundary layer

The instability and dynamics of a vertical oscillatory boundary layer in a container filled with a stratified fluid are addressed. Past experiments have shown that when the boundary oscillation frequency is of the same order as the buoyancy frequency, the system is unstable to a herringbone pattern of oblique waves. Prior studies assuming the basic state to be a unidirectional oscillatory shear flow were unable to account for the oblique waves. By accounting for confinement effects present in the experiments, and the ensuing three-dimensional structure of the basic state, we are able to numerically reproduce the experimental observations, opening the door to fully analysing the impacts of stratification on such boundary layers.