Modulation of elasto-inertial transitions in Taylor–Couette flow by small particles

Particle suspensions in non-Newtonian liquid matrices are frequently encountered in nature and industrial applications. We here study the Taylor–Couette flow (TCF) of semidilute spherical particle suspensions (volume fraction $\leq 0.1$ ) in viscoelastic, constant-viscosity liquids (Boger fluids). We describe the influence of particle load on various flow transitions encountered in TCF of such fluids, and on the nature of these transitions. Particle addition is found to delay the onset of first- and second-order transitions, thus stabilising laminar flows. It also renders them hysteretic, suggesting an effect on the nature of bifurcations. The transition to elasto-inertial turbulence (EIT) is shown to be delayed by the presence of particles, and the features of EIT altered, with preserved spatio-temporal large scales. These results imply that particle loading and viscoelasticity, which are known to destabilise the flow when considered separately, can on the other hand compete with one another and ultimately stabilise the flow when considered together.

A comparison of the performance of depth-integrated ice-dynamics solvers

In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continen- tal scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet. Under simplified conditions with constant viscosity, the maximum stable timestep of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum timestep that is independent of resolution, like the SSA solver. Analysis indicates that the L1L2-SIA solver should behave similarly, but in practice, the complexity of its implementation can make it difficult to maintain stability. In realistic simulations of the Greenland ice sheet with a non-linear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of ∆x = 4 km, the DIVA solver runs approximately 15 times faster than the Hybrid and L1L2-SIA solvers. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself.

Regularity of Weak Solutions to the Inhomogeneous Stationary Navier–Stokes Equations

One of the most intriguing issues in the mathematical theory of the stationary Navier–Stokes equations is the regularity of weak solutions. This problem has been deeply investigated for homogeneous fluids. In this paper, the regularity of the solutions in the case of not constant viscosity is analyzed. Precisely, it is proved that for a bounded domain Ω⊂R2, a weak solution u∈W1,q(Ω) is locally Hölder continuous if q=2, and Hölder continuous around x, if q∈(1,2) and |μ(x)−μ0| is suitably small, with μ0 positive constant; an analogous result holds true for a bounded domain Ω⊂Rn(n>2) and weak solutions in W1,n/2(Ω).

Effects of (MHD) and wall properties oscillatory flow for williamson fluid with constant viscosity through porous channel

In this research, the williamson flow with heat transfer through the tube of compliant wall properties with slip at boundaries is analyzed analytically. An approximated theoretical model is constructed of springbacked flexible compliant walls pipe, chosen to move as sinusoidal wave

Numerical Modeling of a Short-Dwell Coater for Bio-Based Coating Applications

Computational fluid dynamics (CFD) simulations were used for the evaluation of critical issues associated with coating processes with the aim of developing and optimizing this important industrial technology. Four different models, namely, the constant viscosity, shear thinning, Oldroyd-B viscoelastic, and Giesekus models, were analyzed and compared in a short-dwell coater (SDC) using a bio-based coating material. The simulation results showed that the primary vortex formations predicted by the viscoelastic models were highly dependent on the flow Deborah number, resulting in uneven stress distribution over the coated surface. For the viscoelastic models, the dominance of elastic forces over viscous forces gave rise to significant normal stress difference, primarily along the surface of the substrate paper. The shear-thinning phenomena predicted by the Giesekus model, however, tended to relax the stress development in contrast to the Oldroyd-B model. The observations indicate that a reduced coating velocity or modification of the coating material with a reduced relaxation time constant can significantly enhance the uniformity and thickness of the coating over the coated surface under controlled conditions.