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In the present work, spontaneous imbibition of shear-dependent fluids is numerically investigated in a two-layered, rectangular/fan-shaped, paper-based diagnostic kit using the modified Richards equation. It is shown that the average velocity at the test line of the kit is strongly influenced by the absorbent pad's microstructure with its contact angle playing a predominant role. Assuming that the test fluid is shear-thinning, a generalized version of the Richards equation, valid for power-law fluids, was used to investigate the effect of shear-thinning on the quasi-steady regime. The shear-thinning behavior of the test fluid is predicted to shorten the duration of the constant-velocity regime on the nitrocellulose membrane used as the test cell. By manipulating the contact angle and/or choosing appropriate microstructure for the absorbent pad, it is still possible to establish a constant velocity regime at the test line for nearly five minutes even for such fluids. A comparison between our numerical results and published numerical results obtained using simplistic theories has revealed the key role played by the transition, partially-saturated zone near the advancing front during the liquid imbibition. The general conclusion is that use should preferably be made of robust models such as Richards equation for the design of lateral-flow, paper-based assays.

Taylor-Couette instability of thixotropic fluids obeying Moore model is numerically investigated for the case in which the inner cylinder is rotating and the outer cylinder is fixed. A linear temporal stability analysis is invoked in which infinitesimally-small perturbations, represented by normal modes, are superimposed to the base flow and their time evolution is followed in order to detect the onset of instability. An eigenvalue problem is obtained which is solved numerically using finitedifference scheme coupled with the ''polyeig'' function of the Matlab software. The neutral instability curve is plotted as a function of the thixotropic parameters of the Moore model for a broad range of parameters. Based on the results obtained in this work, it is concluded that the viscosity ratio in the Moore model has a destabilizing effect on circular Couette flow. On the other hand, an increase in the breakdown-to-buildup ratio in the Moore model is predicted to have a stabilizing or destabilizing effect on circular Couette flow depending on the gap size and also the magnitude of the thixotropy ratio.

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