Table of contents

We consider the general problem of matching rheological models to experiments. We introduce the concept of identifiability of models from a given set of experiments. To illustrate this in detail, we study two rheology models, the grade-two and Oldroyd 3-parameter models, and consider two hypothetical rheometers to see if the coefficients of the rheology models are identifiable from experimental measurements or not. For the Oldroyd models, we show that the coefficients can be estimated from experiments from the two rheometers. But for the grade-two model, it is not possible to distinguish the two nonNewtonian parameters, only their sum can be estimated, and thus the grade-two model is not identifiable by the two hypothetical rheometers. However, our results imply that a different rheometer may be able to do that.

We conduct a numerical study of viscoelectric and steric effects on an oscillatory electroosmotic flow (OEOF) and their impact on the mass transport of a passive solute through a hydrophobic microchannel. In many applications of electroosmosis, zeta potentials as high as 100–200 mV can be found; in such a situation, the Debye–Hückel approximation is no longer valid, and the steric effect must be considered because the crowding of finite-sized ions close to the microchannel walls. In addition to the previous effect, the local viscosity can be increased due to the viscoelectric effect for strong electric potentials induced in the electric double layer. Earlier works have studied the mass transfer caused by an OEOF; however, the combined effects' influence has not been considered. This research suggests that under an appropriate combination of the viscoelectric and steric effects, together with the microchannel hydrophobicity, the mass transport can be controlled and notably enhanced compared with the case where such effects are disregarded. An interesting behavior occurs for relatively high values of the steric factor ν, where there is a linear dependence between the mass transport $\tilde{Q}$ and the viscoelectric factor $\tilde{f}$; in contrast, for low values of ν, the relationship $\tilde{Q}-\tilde{f}$ is non-linear.

RANS simulations are performed for flow past rectangular cylinders with different elongation ratios (L/D= 1, 2, 4, 6, 8, 10, 12, 14 and 16) at Re= 22 000 using the k-ω SST turbulence model. As L/D increases from 1 to 6, stepwise increase of Strouhal number (St) exists, whereas an almost linear variation of St with respect to L/D can be found (St= 0.1618*L/D) at L/D⩾ 8. In the flow, two small secondary vortices beneath the shear layers are identified and the trailing-edge secondary vortex presents opposite rotational direction comparing with the leading-edge main vortex. Analysis of the shear layer and vortex characteristics is carried out to correlate with the wall normal stress and shear stress on the rectangular cylinder surfaces. Further, four coupling modes between leading-edge vortex (L-vortex) and trailing-edge vortex (T-vortex) among cylinders with different L/D are observed, named L-Vortex Mode (i.e. L/D= 1–2), L-T-Vortex Mode (i.e. L/D= 4–8), T-L-Vortex Mode (i.e. L/D= 10–14), and T-Vortex Mode (i.e. L/D ⩾ 16). When L/D > 4, the convective velocity of the L- and T-vortex is not sensitive to the L/D.

The article presents a three-dimensional numerical study of the large-amplitude, acoustically driven streaming flow in rectangular resonator for different frequencies of the acoustic wave and different temperature regime, isothermal and 60 K temperature difference between the top and bottom walls. The utilized numerical model was based on the Navier–Stokes compressible equations, the ideal gas model, and finite volume discretization. The oscillating wall of the resonator was modeled as a dynamically moving boundary of the numerical domain. The size of the resonators was adjusted to fit one period of the acoustic wave. The research revealed a stationary pair of streaming vortices in the resonator with a characteristic three-dimensional structure. Their intensity was much greater in the case of nonisothermal flow. The study of the impact of side walls on the intensity of streaming revealed its gradual decrease with approaching the walls, creating a quasiparabolic profile in the resonator. Interestingly, the relationship between the intensity of streaming and the frequency of the acoustic wave turned out to be not trivial and two maxima for different frequencies could be observed.

A monolithic mathematical framework for understanding the fluid–rigid–elastic structure interaction problem is proposed. A numerical method in a secondary formulation of the Navier–Stokes equations accompanying a technique for imposing the rigid boundaries is applied. The one-fluid formulation of the incompressible Navier–Stokes equation, containing the terms governing the elastic structure, is transformed into the vorticity-stream function formulation. The rigid structure is imposed in the flow field based on the velocity–vorticity kinematic relation and harmonic function theorem. The vorticity, level-set function, and left Cauchy–Green deformation tensor are updated utilizing three transport equations to investigate the evolution of the velocity field, elastic structure(s) configuration, and elastic stress tensor. The method is implemented to solve three challenging problems, and the results show its capabilities in proper imposing the rigid structures in the flow field and also the simultaneous modeling the rigid and elastic structure interactions with incompressible fluid flow.