Journal of Non-Newtonian Fluid Mechanics最新文献

The stability conditions of a two-dimensional gravity-driven flow of a thin layer of a power-law fluid flowing over a heated, uneven, inclined porous surface are investigated. A two-sided model is employed to account for the bottom filtration in the porous layer. The governing equations are reduced under the long-wave approximation and the cross-stream dependence is eliminated by means of the Integral Boundary Layer technique. Floquet–Bloch theory is used to investigate at linear level how the porous bottom waviness influences the thermocapillarity stability of the flow in a shear-thinning fluid. Differently from the even case, the linear stability analysis suggests that for flow over sufficiently wavy undulations the thermocapillarity may stabilize the equilibrium flow, depending on the values of dimensionless governing numbers and parameters. This stabilizing phenomenon is enhanced by the shear-thinning rheology of the fluid while it is reduced by the permeability of the layer. Numerical simulations, performed solving the reduced nonlinear model through a second order Finite Volume scheme, confirm the results of the linear stability analysis.

We investigate numerically the influence of thixotropic effects on the impact of a drop onto a thin film, a fundamental process in many technical systems. Direct numerical simulations are performed with a Volume-of-Fluid (VOF) method based multiphase flow solver whose capabilities are expanded in order to enable simulations of a thixotropic liquid. The thixotropic behavior is modeled by a rate kinetic equation for the structural integrity of the assumed microstructure of the liquid. The corresponding structural parameter is described by an additional VOF-variable. After a validation of the implementations, we vary systematically the two parameters of the thixotropic model for a selected impact scenario in order to identify thixotropic effects during the impact and on the overall impact morphology. The two parameters are the mutation number $Mu=t_{\text{exp}}/t_{\theta }$ as the ratio of the experimental time scale to the time scale of the structural rebuilding and the parameter $\beta$, which describes the effectivity of the shear-induced structural disintegration. The parameter study leads to a regime map with three different regimes. For $Mu>10$, the liquid behaves purely shear-thinning. High shear rates during the early stages of the impact lead to a low apparent viscosity at the crown base and to an enhanced crown growth. For $Mu<0.1$, the liquid behaves irreversible thixotropic or rheodestructing, respectively. Structural rebuilding is negligible and every deformation leads to a further disintegration of the microstructure. In this regime, a thin region of disintegrated microstructure develops within the liquid, spanning from the location of high shear stresses at the bottom into the crown rim. In between these two regimes, purely thixotropic effects become significant. A complex microstructure develops during the impact, in which features of both regimes occur combined, leading to a pronounced viscosity gradient along the crown wall. A comparison of the resulting maximum crown heights reveals that various combinations of $Mu$ and $\beta$ values can lead to the same maximum crown height whereas the crown shapes prior to this point in time can be very different.

The effect of sinusoidal vibration is numerically investigated on the dynamical behavior of a cluster of 50 identical non-Brownian circular solid particles randomly distributed in a circular envelope. The cluster is immersed in a finite vessel filled with an inelastic viscoplastic fluid obeying the Casson model. The solid particles are modeled using the improved smoothed-profile method (iSPM) whereas the flow of the continuous phase is modeled using the lattice Boltzmann method (LBM). An in-house LBM-iSPM code, modified for Casson fluid, is used to study the effect of sinusoidal vibration on disaggregating the cluster. We have deliberately ignored the gravitational term in the equations of motion so that the sole effect of vibration on the cluster response can better be investigated. Numerical results suggest that vibration can disaggregate the cluster with its efficiency depending on the fluid's yield stress. For any given yield stress, vibration can disperse the cluster provided the frequency and/or amplitude of the forced oscillation are larger than a threshold. The secondary flow formed in the channel during the transient phase is shown to be the main cause of the cluster's fluid-mediated dispersion. It is shown that the system reaches equilibrium when the secondary flow is vanished through dissipation. Vibration is predicted to become more effective in disaggregating clusters the larger the size of the particles or the smaller their number density.

An experimental study of the turbulent dynamics of emulsification in a cross-slot microfluidic device is presented. The continuous phase contains a minute amount of an inelastic polymer (xanthan). The Reynolds numbers are sufficiently large (up to 16000) so the drag reduction phenomenon is observed during the emulsification process. The statistics of droplet sizes in the resulting emulsions are measured ex-situ by means of digital microscopy in a wide range of Reynolds numbers and polymer concentrations in the continuous phase. Integral measurements of the statistics of the pressure drops in the micro-channel allow one to systematically map the drag reduction states. Corresponding to each state, the space–time dynamics of the emulsification process are assessed by means of in-situ high speed imaging of the interface between the two fluids which further allows one to extract the characteristic time and space scales associated to the dynamics of the interface. Various dynamic regimes of the microscopic emulsification process are mapped in terms of the Reynolds number and shear thinning rheology of the continuous phase.

This article introduces a method to determine the Kolmogorov rheological scales for turbulent flow in Viscoelastic Oldroyd-B fluids. The findings reveal a noteworthy characteristic wherein the Kolmogorov rheological length is consistently smaller than that observed in Newtonian cases. Moreover, this length diminishes with an increase in the prominence of elastic effects. Leveraging these rheological scales, a detailed friction equation for turbulent flow in Oldroyd-B fluids is derived. The resultant friction relationship exhibits a high degree of agreement with existing theories. Notably, it delineates the Maximum Drag Reduction (MDR) scenario for the studied case ($\beta$=0.9). Additionally, the investigation delves into the onset of drag reduction effects, shedding light on the transitional phases in viscoelastic fluid flows.

In this work, we propose a functionalised bi-viscous lubrication model to study the material properties of concentrated non-Brownian suspensions and explore the possible confinement-induced non-Newtonian effects of the lubricant in the rheological response of this type of suspensions. From tribological studies, it is well-known that even macroscopically Newtonian liquids under strong confinement might exhibit properties which deviate significantly from their bulk behaviour. When two surfaces separated by an extremely small gap (still large compared to the molecular size) are sheared, strong shear-thinning of the lubricant viscosity at low shear-rates is observed, in spite of its Newtonian-like bulk response. This is connected to a significant increase of the zero-shear-rate viscosity under extreme confinement. We start from an effective lubrication algorithm recently proposed and develop a new gap-size-dependent interparticle bi-viscous lubrication model, able to capture qualitatively the main phenomenology of confined lubricants. We solve the lubrication interaction between particles iteratively via a semi-implicit splitting scheme. Since the handling of lubrication is made implicitly here, the method copes efficiently with large increases of the inter-particle effective viscosities, which would otherwise lead to simulation blow-up or the use of vanishing time-steps in standard explicit schemes. We analyse the rheological response of the suspension systematically in terms of model parameters. In contrast to pure Newtonian lubrication interactions, distinct shear-thinning and shear-thickening regimes in the relative suspension viscosity are observed, which are discussed in terms of particle microstructure coupled with the complex rheology of the confined lubricant. In addition, normal-stress response is negative in both $N_1$ and $N_2$, which is difficult to achieve with standard contact frictional models.

Helical static mixers are used widely for mixing of non-Newtonian fluid flows in the laminar regime. We study flows of three viscoelastic constitutive models (sPTT, FENE-P, and Giesekus) in the helical static mixer using computational fluid dynamics. These three models have similarities in steady viscometric flows in that they all exhibit shear thinning and their planar extensional viscosities can be matched, but their responses can differ in complex geometries. We observe flow distribution asymmetries at the element intersections for all three models, which hinders the mixing performance of the device. These have previously been observed with the constant shear viscosity FENE-CR model. The asymmetry behaves similarly between the sPTT and Giesekus models, however the FENE-P model behaves in a distinct manner; beyond a critical degree of elasticity, the asymmetry sharply changes direction. This was also observed previously with the FENE-CR model. These results suggest that shear thinning and second-normal stress differences (present in the Giesekus model) do not significantly influence mixing performance in the range of conditions studied. We show that increasing the aspect (length/diameter) ratio of the mixer elements mitigates the poor mixing caused by elasticity. Overall, this study provides insight into the behaviour of these well-used constitutive models in complex, industrially-relevant flows.

The increase in viscosity under shear known as shear thickening (ST) is an inherent property of a wide variety of dense particulate suspensions. Recent studies indicate that ST systems formed by fractal particles are promising candidates for various practical applications. However, ST in fractal systems remains poorly explored. Here we experimentally study the ST behavior in suspensions of hydrophilic fumed silica (FS) particles in glycerol. Remarkably, unlike non-fractal systems, we observe a strong dependence of the onset stress for ST on the volume fraction of fractal objects and a reversible weakening of the ST response that depends strongly on the particle volume fraction as well as the properties of the FS system. Using in-situ boundary imaging, we map out the spatio-temporal flow properties during ST for different FS systems. We find that the fractal nature and structural properties like the internal branching of the particles can qualitatively explain the complex ST phase diagram of these systems.

Few simulations currently explore the dynamics of microswimmers swimming through viscoelastic environments. In this study, we employ a direct-forcing fictitious domain method to investigate the collective behavior of spherical squirmers within viscoelastic fluids at low Reynolds numbers. Our findings reveal clear differences between pusher and puller swimmers: puller swimmers exhibit a tendency to aggregate into clusters, particularly noticeable in suspensions with high concentrations, which increases the average speed of the swimmers. Through an analysis of the cluster-size distribution function, we observe the larger-scale clusters of puller swimmers with increasing concentration. Moreover, the presence of fluid elasticity significantly reduces both the average swimming speed of squirmers and the fluid’s kinetic energy.