A material-invariant (frame indifferent) version of the Maxwell–Cattaneo law is proposed in which the relaxation rate of the heat flux is given by Oldroyd’s upper-convected derivative. It is shown ...that the new formulation allows for the elimination of the heat flux, thus yielding a single equation for the temperature field. This feature is to be expected from a truly frame indifferent description.
Rotating forms of suspension culture allow cells to aggregate into spheroids, prevent the de-differentiating influence of 2D culture, and, perhaps most importantly of all, provide physiologically ...relevant, in vivo levels of shear stress. Rotating suspension culture technology has not been widely implemented, in large part because the vessels are prohibitively expensive, labor-intensive to use, and are difficult to scale for industrial applications. Our solution addresses each of these challenges in a new vessel called a cell spinpod. These small 3.5 mL capacity vessels are constructed from injection-molded thermoplastic polymer components. They contain self-sealing axial silicone rubber ports, and fluoropolymer, breathable membranes. Here we report the two-fluid modeling of the flow and stresses in cell spinpods. Cell spinpods were used to demonstrate the effect of fluid shear stress on renal cell gene expression and cellular functions, particularly membrane and xenobiotic transporters, mitochondrial function, and myeloma light chain, cisplatin and doxorubicin, toxicity. During exposure to myeloma immunoglobulin light chains, rotation increased release of clinically validated nephrotoxicity cytokine markers in a toxin-specific pattern. Addition of cisplatin or doxorubicin nephrotoxins reversed the enhanced glucose and albumin uptake induced by fluid shear stress in rotating cell spinpod cultures. Cell spinpods are a simple, inexpensive, easily automated culture device that enhances cellular functions for in vitro studies of nephrotoxicity.
Static and dynamic light scattering experiments show that the mixed micelles of sodium dodecyl sulfate (SDS) and cocoamidopropyl betaine (CAPB) undergo a sphere-to-rod transition at unexpectedly low ...total surfactant concentrations, about 10 mM. The lowest transition concentration is observed at molar fraction 0.8 of CAPB in the surfactant mixture. The transition brings about a sharp increase in the viscosity of the respective surfactant solutions due to the growth of rodlike micelles. Parallel experiments with mixed solutions of CAPB and sodium laureth sulfate (sodium dodecyl-trioxyethylene sulfate, SDP3S) showed that the sphere-to-rod transition in SDP3S/CAPB mixtures occurs at higher surfactant concentrations, above 40 mM. The observed difference in the transition concentrations for SDS and SDP3S can be explained by the bulkier SDP3S headgroup. The latter should lead to larger mean area per molecule in the micelles containing SDP3S and, hence, to smaller spontaneous radius of curvature of the micelles (i.e., less favored transition from spherical to rodlike micelles). The static light scattering data are used to determine the mean aggregation number and the effective size of the spherical mixed SDS/CAPB micelles. From the dependence of the aggregation number on the surfactant concentration, the mean energy for transfer of a surfactant molecule from a spherical into a rodlike micelle is estimated.
Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that ...the wall's elastic compliance can be exploited towards new modalities of microscale mixing. While previous studies mainly focused on the local instability induced by the fluid–structure interactions (FSIs) in the system, we derive a one-dimensional (1-D) model to study the FSI's effect on the global instability. The proposed 1-D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analysed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a novel reduced 1-D wall deformation equation. Although a quantitative comparison with previous experiments is difficult, the behaviours of the proposed model show, qualitatively, agreement with the experimental observations, and capture several key effects. Specifically, we find the critical conditions under which the inflated base state of the 1-D FSI model is linearly unstable to infinitesimal perturbations. The critical Reynolds numbers predicted are in agreement with experimental observations. The unstable modes are highly oscillatory, with frequencies close to the natural frequency of the wall, suggesting that the observed instabilities are resonance phenomena. Furthermore, during the start-up from an undeformed initial state, self-sustained oscillations can be triggered by FSI. Our modelling framework can be applied to other microfluidic systems with similar geometric scale separation under different operating conditions.
•Fluid–structure interaction between a microchannel with a soft top wall and a power-law fluid flow is analyzed.•The coupled problem is reduced to the solution of a single nonlinear first-order ...ODE.•The theory applies to both thin and thick plate-like microchannel top walls.•The theoretical predictions are benchmarked against full two-way coupled 3D simulations in ANSYS.
We study fluid–structure interactions (FSIs) in a long and shallow microchannel, conveying a non-Newtonian fluid, at steady state. The microchannel has a linearly elastic and compliant top wall, while its three other walls are rigid. The fluid flowing inside the microchannel has a shear-dependent viscosity described by the power-law rheological model. We employ lubrication theory to solve for the flow problem inside the long and shallow microchannel. For the structural problem, we employ two plate theories, namely Kirchhoff–Love theory of thin plates and Reissner–Mindlin first-order shear deformation theory. The hydrodynamic pressure couples the flow and deformation problem by acting as a distributed load onto the soft top wall. Within our perturbative (lubrication theory) approach, we determine the relationship between the flow rate and the pressure gradient, which is a nonlinear first-order ordinary differential equation for the pressure. From the solution of this differential equation, all other quantities of interest in non-Newtonian microchannel FSIs follow. Through illustrative examples, we show the effect of FSI coupling strength and the plate thickness on the pressure drop across the microchannel. Through direct numerical simulation of non-Newtonian microchannel FSIs using commercial computational engineering tools, we benchmark the prediction from our mathematical theory for the flow rate–pressure drop relation and the structural deformation profile of the top wall. In doing so, we also establish the limits of applicability of our perturbative theory.
In this Letter, we address the long-range interaction between kinks and antikinks, as well as kinks and kinks, in φ^{2n+4} field theories for n>1. The kink-antikink interaction is generically ...attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the 2n/(n-1)th power of their separation, and we identify the general prefactor for arbitrary n. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of n=2 (φ^{8} model), n=3 (φ^{10} model), and n=4 (φ^{12} model).
•Closure for inter-phase heat transfer coefficient of a two-fluid model is proposed.•Shear and thermal gradients can aid each other to increase particle migration.•Identified origin and functional ...form of a thermo-rheological migration force.•Simulated heat transfer and flow of dense suspension in non-axisymmetric curvilinear geometry.
We develop a two-fluid model (TFM) for heat transfer in dense non-Brownian suspensions. Specifically, we propose closure relations for the inter-phase heat transfer coefficient and the thermal diffusivity of the particle phase based on calibration against experimental data. The model is then employed to simulate non-isothermal flow in an annular Couette cell. We find that, when the shear rate is controlled by the rotation of the inner cylinder, both the shear and thermal gradients are responsible for particle migration. Within the TFM framework, we identify the origin and functional form of a “thermo-rheological” migration force that rationalizes our observations. Furthermore, we apply our model to flow in eccentric Couette cells. Our simulations reveal that the system’s heat transfer coefficient is affected by both the classic shear-induced migration of particles and the newly identified thermo-rheological migration effect.
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