In the present work, the effect of a fluid's yield stress is investigated on the hydroelastic instability in pressuredriven flow through a two-dimensional channel lined with a highly-compliant polymeric gel. Having assumed that the fluid obeys the Herschel-Bulkley model with the gel obeying the two-parameter Mooney-Rivlin model, analytical basic solutions were obtained for the fluid and solid sides at vanishingly-small Reynolds numbers. The stability of the basic solutions so-obtained was then investigated when subjected to infinitesimally-small, normal-mode perturbations. Having dropped all nonlinear perturbation terms, an eigenvalue problem was obtained which was numerically solved using the shooting method. The effect of the fluid's yield stress was then examined on the growth rate of the most unstable modes. Based on the numerical results obtained in this work, it is concluded that the yield stress has a destabilizing effect on pressure-driven flows of Bingham fluids in two-dimensional channels lined with compliant gels. For Herschel-Bulkley fluids, the effect of yield stress can be stabilizing or destabilizing depending on the power-law exponent (i.e., the degree of the fluid's shear-thinning). gel to obey the hyperelastic Mooney-Rivlin model, to the best of our knowledge, for the first time. This robust solid model better fits rheological data for soft polymeric gels, and so it is expected that more meaningful results could be obtained using this model. 12) Like Gkanis and Kumar 5) , we intend to focus on the creeping flow case only both because of its industrial implications in microfluidic field and also because it excludes complications which might arise through the rise of Tollmien-Schlichting (TS) waves. At this extreme, Gkanis and Kumar 5) have shown that for pressure-driven flow of Newtonian fluids in compliant channels, there are two types of instability for Re = 0: i) a finite-wavelength mode which becomes unstable for sufficiently thick solids, and (ii) a short-wavelength mode which arises due to the discontinuity of the first normal stress difference at the interface. It would be interesting to see how these modes are affected by a fluid's yield stress. To achieve its objectives, the work is organized as follows. In the next section we present the governing equations for the solid and the fluid side. We then proceed with obtaining the basic solution for each phase. The linearized equations governing the stability of the basic state are then introduced. The numerical method of solution is briefly described followed by presenting the numerical results. The work is summarized by highlighting its major findings. GOVERNING EQUATIONSWe consider the pressure-driven flow of a viscoplastic fluid in planar Poiseuille flow, as shown in Fig. 1. As can be seen in this figure, the upper and lower plates are lined with a complaint layer made of a soft polymeric gel having a thickness of HR with 2R representing the height of the channel. Assuming that the width of the channel is much larger than its height, we w...

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Five carbonaceous nano-additives (graphite, graphene, carbon black, carbon nanotubes, and diamond) had different impacts on the sinterability, microstructural evolution, and properties of titanium carbide. In this research, the sintering by spark plasma was employed to produce the monolithic TiC and carbon-doped ceramics under the sintering parameters of 1900 ºC, 10 min, 40 MPa. The carbon black additive had the best performance in densifying the TiC, thanks to its fine particle size, as well as its high chemical reactivity with TiO2 surface oxide. By contrast, the incorporation of nano-diamonds resulted in a considerable decline in the relative density of TiC owing to the graphitization phenomenon, together with the gas production at high temperatures. Although carbon precipitation from the TiC matrix occurred in all samples, some of the added carbonaceous phases promoted this phenomenon, while the others hindered it to some extent. Amongst the introduced additives, carbon black had the most contribution to grain refining, so that a roughly halved average grain size was attained in comparison with the undoped specimen. The highest values of hardness (3233 HV0.1 kg), thermal conductivity (25.1 W/mK), and flexural strength (658 MPa) secured for the ceramic incorporated by 5 wt% nano carbon black.

This study investigates the effects of inertia on the hydroelastic instability of a pressure-driven Herschel-Bulkley fluid passing through a two-dimensional channel lined with a polymeric coating. The no-viscous hyperelastic polymeric coating is assumed to follow the two-constant Mooney-Rivlin model. In this work, analytical basic solutions are determined for both the polymeric gel and the fluid at very low Reynolds numbers. Next, the basic solutions are subjected to infinitesimally-small, normal-mode perturbations. After eliminating the nonlinear terms, two 4-th order differential equations are obtained. The equations with appropriate boundary conditions are then numerically solved using the shooting method. The results of the solution show that the inertia terms in the perturbed equations destabilize the pressure-driven Herschel-Bulkley fluid flow. The investigation reveals that the elastic parameter has a stabilizing effect on the flow. Also, based on the obtained results, the yield stress, depending on the power-law index, has a stabilizing or destabilizing effect on the flow. Since in this work the inertia terms are included in the pertinent governing equations, therefore, the results of this study are much more realistic and reliable than previous works in which inertia terms were absent. In addition, unlike the previous works, the present study considers both the shear-thinning and shear-thickening types of fluids. Hence, the results of this work embrace all the fluids which obey the Herschel-Bulkley model.