Lattice-Boltzmann Method for Non-Newtonian Fluid Flows

We study an ad hoc extension of the Lattice-Boltzmann method that allows the simulation of non-Newtonian fluids described by generalized Newtonian models. We extensively test the accuracy of the method for the case of shear-thinning and shear-thickening truncated power-law fluids in the parallel plate geometry, and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution. Finally, we also tested the method in the reentrant-flow geometry, in which the shear-rate is no-longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points. In this geometry, we also found excellent agreement with the solutions obtained by standard finite-element methods, and the agreement improves with higher lattice resolution

Two-dimensional hydrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic fluid flow through porous media

The behaviour of two dimensional binary and ternary amphiphilic fluids under flow conditions is investigated using a hydrodynamic lattice gas model. After the validation of the model in simple cases (Poiseuille flow, Darcy's law for single component fluids), attention is focussed on the properties of binary immiscible fluids in porous media. An extension of Darcy's law which explicitly admits a viscous coupling between the fluids is verified, and evidence of capillary effects are described. The influence of a third component, namely surfactant, is studied in the same context. Invasion simulations have also been performed. The effect of the applied force on the invasion process is reported. As the forcing level increases, the invasion process becomes faster and the residual oil saturation decreases. The introduction of surfactant in the invading phase during imbibition produces new phenomena, including emulsification and micellisation. At very low fluid forcing levels, this leads to the production of a low-resistance gel, which then slows down the progress of the invading fluid. At long times (beyond the water percolation threshold), the concentration of remaining oil within the porous medium is lowered by the action of surfactant, thus enhancing oil recovery. On the other hand, the introduction of surfactant in the invading phase during drainage simulations slows down the invasion process -- the invading fluid takes a more tortuous path to invade the porous medium -- and reduces the oil recovery (the residual oil saturation increases).Comment: 48 pages, 26 figures. Phys. Rev. E (in press

Interface Roughening in a Hydrodynamic Lattice-Gas Model with Surfactant

Using a hydrodynamic lattice-gas model, we study interface growth in a binary fluid with various concentrations of surfactant. We find that the interface is smoothed by small concentrations of surfactant, while microemulsion droplets form for large surfactant concentrations. To assist in determining the stability limits of the interface, we calculate the change in the roughness and growth exponents $\alpha$ and $\beta$ as a function of surfactant concentration along the interface.Comment: 4 pages with 4 embedded ps figures. Requires psfig.tex. Will appear in PRL 14 Oct 199

Three dimensional hysdrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic flow through porous media

We report the results of a study of multiphase flow in porous media. A Darcy's law for steady multiphase flow was investigated for both binary and ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager reciprocity were shown to be a good approximation of the simulation data. The dependence of the relative permeability coefficients on water saturation was investigated and showed good qualitative agreement with experimental data. Non-steady state invasion flows were investigated, with particular interest in the asymptotic residual oil saturation. The addition of surfactant to the invasive fluid was shown to significantly reduce the residual oil saturation.Comment: To appear in Phys. Rev.

Tumour cell thrombospondin-1 regulates tumour cell adhesion and invasion through the urokinase plasminogen activator receptor

We have previously shown that platelet-produced thrombospondin-1 up-regulates the urokinase plasminogen activator and its receptor and promotes tumour cell invasion. Although tumour cells produce thrombospondin-1 in vivo, they produce only minimal amounts of thrombospondin-1 in vitro. To determine the effect of tumour cell-produced thrombospondin-1 in the regulation of the plasminogen/plasmin system and tumour cell invasion, we studied THBS-1 -transfected MDA-MB-435 breast cancer cells that overexpress thrombospondin-1. The role of urokinase plasminogen receptor in thrombospondin-1-mediated adhesion and invasion was studied by antisense inhibition, enzymatic cleavage and antibody neutralization. Tumour cell adhesion to collagen and laminin was evaluated. Tumour cell invasion was studied in a modified Boyden chamber collagen invasion assay. Tumour cell thrombospondin-1 induced a 2–7 fold increase in urokinase plasminogen activator receptor and cell-associated urokinase plasminogen activator expression and a 50–65% increase in cell-associated urokinase plasminogen activator and plasmin activities. Furthermore, tumour cell thrombospondin-1 promoted tumour cell invasion and decreased tumour cell adhesion through up-regulation of urokinase plasminogen activator receptor-controlled urokinase plasminogen activator and plasmin activities. We conclude that tumour cell-produced thrombospondin-1 may play a critical role in the regulation of tumour cell adhesion and tumour cell invasion. © 2000 Cancer Research Campaig

A Two-Threshold Model for Scaling Laws of Non-Interacting Snow Avalanches

The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity driven systems, we introduce a two-threshold 2-d cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceeding the lattice system breakdown are power law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power law exponents observed for land-, rock- or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.Comment: accepted PR

Diet, nutrition, obesity and their role in arthritis

Obesity and poor nutrition, individually and together, have created costly musculoskeletal disease epidemic in the United States. Processed food, with abundant empty calories, has contributed greatly to our dietary woes. Much of the food consumed today is packed with calories but refined to the point that essential nutrients are lacking. Even worse, processed food may have ingredients added that are detrimental to good health. Abundant research has documented a close relationship between obesity, poor diet and orthopaedic problems. Dietary supplements have been proven to provide both disease prevention and therapeutic benefits. Unfortunately, many weight loss programs and methods are ineffective and possibly dangerous. Additionally, the FDA does not regulate the nutritional supplement industry and product quality is high variable. It is imperative that physicians treating patients with musculoskeletal complaints understand these disease producing relationships and have a network in place to refer patients to reputable weight loss entities and for high quality nutritional supplements

Responses of phosphorus limited Lake Michigan phytoplankton to factorial enrichments with nitrogen and phosphorus

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109907/1/lno19741930409.pd

Kinematics of chromodynamic multicomponent lattice Boltzmann Simulation with a large density contrast

The utility of an enhanced chromodynamic, color gradient or phase-field multicomponent lattice Boltzmann (MCLB) equation for immiscible fluids with a density difference was demonstrated by Wen et al. [Phys. Rev. E 100, 023301 (2019)] and Ba et al. [Phys. Rev. E 94, 023310 (2016)], who advanced earlier work by Liu et al. [Phys. Rev. E 85, 046309 (2012)] by removing certain error terms in the momentum equations. But while these models' collision scheme has been carefully enhanced by degrees, there is, currently, no quantitative consideration in the macroscopic dynamics of the segregation scheme which is common to all. Here, by analysis of the kinetic-scale segregation rule (previously neglected when considering the continuum behavior) we derive, bound, and test the emergent kinematics of the continuum fluids' interface for this class of MCLB, concurrently demonstrating the circular relationship with—and competition between—the models' dynamics and kinematics. The analytical and numerical results we present in Sec. V confirm that, at the kinetic scale, for a range of density contrast, color is a material invariant. That is, within numerical error, the emergent interface structure is isotropic (i.e., without orientation dependence) and Galilean-invariant (i.e., without dependence on direction of motion). Numerical data further suggest that reported restrictions on the achievable density contrast in rapid flow, using chromodynamic MCLB, originate in the effect on the model's kinematics of the terms deriving from our term F1i in the evolution equation, which correct its dynamics for large density differences. Taken with Ba's applications and validations, this result significantly enhances the theoretical foundation of this MCLB variant, bringing it somewhat belatedly further into line with the schemes of Inamuro et al. [J. Comput. Phys. 198, 628 (2004)] and the free-energy scheme [see, e.g., Phys. Rev. E. 76, 045702(R) (2007), and references therein] which, in contradistinction to the present scheme and perhaps wisely, postulate appropriate kinematics a priori