On the importance of temporal floc size statistics and yield strength for population balance equation flocculation model.

Many aquatic environments contain cohesive sediments that flocculate and create flocs with a wide range of sizes. The Population Balance Equation (PBE) flocculation model is designed to predict the time-dependent floc size distribution and should be more complete than models based on median floc size. However, a PBE flocculation model includes many empirical parameters to represent important physical, chemical, and biological processes. We report a systematic investigation of key model parameters of the open-source PBE-based size class flocculation model FLOCMOD (Verney, Lafite, Claude Brun-Cottan and Le Hir, 2011) using the measured temporal floc size statistics reported by Keyvani and Strom (2014) at a constant turbulent shear rate S. Results show that the median floc size d50, in terms of both the equilibrium floc size and the initial floc growth, is insufficient to constrain the model parameters. A comprehensive error analysis shows that the model is capable of predicting three floc size statistics d16, d50 and d84, which also reveals a clear trend that the best calibrated fragmentation rate (inverse of floc yield strength) is proportional to the floc size statistics considered. Motivated by this finding, the importance of floc yield strength is demonstrated in the predicted temporal evolution of floc size by modeling the floc yield strength as microflocs and macroflocs giving two corresponding fragmentation rates. The model shows a significantly improved agreement in matching the measured floc size statistics.

Rheology of debris flow materials is controlled by the distance from jamming.

Debris flows are dense and fast-moving complex suspensions of soil and water that threaten lives and infrastructure. Assessing the hazard potential of debris flows requires predicting yield and flow behavior. Reported measurements of rheology for debris flow slurries are highly variable and sometimes contradictory due to heterogeneity in particle composition and volume fraction ([Formula: see text]) and also inconsistent measurement methods. Here we examine the composition and flow behavior of source materials that formed the postwildfire debris flows in Montecito, CA, in 2018, for a wide range of [Formula: see text] that encapsulates debris flow formation by overland flow. We find that shear viscosity and yield stress are controlled by the distance from jamming, [Formula: see text], where the jamming fraction [Formula: see text] is a material parameter that depends on grain size polydispersity and friction. By rescaling shear and viscous stresses to account for these effects, the data collapse onto a simple nondimensional flow curve indicative of a Bingham plastic (viscoplastic) fluid. Given the highly nonlinear dependence of rheology on [Formula: see text], our findings suggest that determining the jamming fraction for natural materials will significantly improve flow models for geophysical suspensions such as hyperconcentrated flows and debris flows.

The effect of a crosslinking chemical reaction on pattern formation in viscous fingering of miscible fluids in a Hele-Shaw cell.

Viscous fingering can occur in fluid motion whenever a high mobility fluid displaces a low mobility fluid in a Darcy type flow. When the mobility difference is primarily attributable to viscosity (e.g., flow between the two horizontal plates of a Hele-Shaw cell), viscous fingering (VF) occurs, which is sometimes termed the Saffman-Taylor instability. Alternatively, in the presence of differences in density in a gravity field, buoyancy-driven convection can occur. These instabilities have been studied for decades, in part because of their many applications in pollutant dispersal, ocean currents, enhanced petroleum recovery, and so on. More recent interest has emerged regarding the effects of chemical reactions on fingering instabilities. As chemical reactions change the key flow parameters (densities, viscosities, and concentrations), they may have either a destabilizing or stabilizing effect on the flow. Hence, new flow patterns can emerge; moreover, one can then hope to gain some control over flow instabilities through reaction rates, flow rates, and reaction products. We report effects of chemical reactions on VF in a Hele-Shaw cell for a reactive step-growth cross-linking polymerization system. The cross-linked reaction product results in a non-monotonic viscosity profile at the interface, which affects flow stability. Furthermore, three-dimensional internal flows influence the long-term pattern that results.

Saffman-Taylor Instability and the Inner Splitting Mechanism.

For viscously unstable, miscible Hele-Shaw displacements, we investigate the origin of the streamwise vorticity shown to be responsible for the inner splitting mechanism by Oliveira and Meiburg [J. Fluid Mech. 687 431 (2011)JFLSA70022-112010.1017/jfm.2011.367]. Towards this end, we compare 3D Navier-Stokes simulation results for neutrally buoyant, viscously unstable displacements and gravitationally unstable, constant viscosity ones. Only the former exhibit the generation of streamwise vorticity. The simulation results show that it is caused by the lateral displacement of the more viscous fluid by the less viscous one, with the variable viscosity terms playing a dominant role.

Miscible, porous media displacements with density stratification.

High accuracy, three-dimensional numerical simulations of miscible displacements with gravity override, in both homogeneous and heterogeneous porous media, are discussed for the quarter five-spot configuration. The influence of viscous and gravitational effects on the overall displacement dynamics is described in terms of the vorticity variable. Density differences influence the flow primarily by establishing a narrow gravity layer, in which the effective Peclet number is enhanced due to the higher flow rate. Although this effect plays a dominant role in homogeneous flows, it is suppressed to some extent in heterogeneous displacements. This is a result of coupling between the viscous and permeability vorticity fields. When the viscous wavelength is much larger than the permeability wavelength, gravity override becomes more effective because coupling between the viscous and permeability vorticity fields is less pronounced. Buoyancy forces of a certain magnitude can lead to a pinch-off of the gravity layer, thereby slowing it down.

Density-driven instabilities of variable-viscosity miscible fluids in a capillary tube.

A linear stability analysis is presented for variable-viscosity miscible fluids in an unstable configuration; that is, a heavier fluid placed above a lighter one in a vertically oriented capillary tube. The initial interface thickness is treated as a parameter to the problem. The analysis is based on the three-dimensional Stokes equations, coupled to a convection-diffusion equation for the concentration field, in cylindrical coordinates. When both fluids have identical viscosities, the dispersion relations show that for all values of the governing parameters the three-dimensional mode with an azimuthal wave number of one represents the most unstable disturbance. The stability results also indicate the existence of a critical Rayleigh number of about 920, below which all perturbations are stable. For the variable viscosity case, the growth rate does not depend on which of the two fluids is more viscous. For every parameter combination the maximum of the eigenfunctions tends to shift toward the less viscous fluid. With increasing mobility ratio, the instability is damped uniformly. We observe a crossover of the most unstable mode from azimuthal to axisymmetric perturbations for Rayleigh numbers greater than 10(5) and high mobility ratios. Hence, the damping influence is much stronger on the three-dimensional mode than the corresponding axisymmetric mode for large Rayleigh numbers. For a fixed mobility ratio, similar to the constant viscosity case, the growth rates are seen to reach a plateau for Rayleigh numbers in excess of 10(6). At higher mobility ratios, interestingly, the largest growth rates and unstable wave numbers are obtained for intermediate interface thicknesses. This demonstrates that, for variable viscosities, thicker interfaces can be more unstable than their thinner counterparts, which is in contrast to the constant viscosity result where growth rate was seen to decline monotonically with increasing interface thickness.