An evaluation of interface capturing methods in a VOF based model for multiphase flow of a non-Newtonian ceramic in tape casting

The aim of the present study is to evaluate the different interface capturing methods as well as to find the best approach for flow modeling of the ceramic slurry in the tape casting process. The conventional volume of fluid (VOF) method with three different interpolation methods for interface capturing, i.e. the Geometric Reconstruction Scheme (GRS), High Resolution Interface Capturing (HRIC) and Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM), are investigated for the advection of the VOF, both for Newtonian and non-Newtonian cases. The main purpose is to find the best method for the free surface capturing during the flow of a ceramic slurry described by a constitutive power law equation in the tape casting process. First the developed model is tested against well-documented and relevant solutions from literature involving free surface tracking and subsequently it is used to investigate the flow of a La_0.85Sr_0.15MnO₃ (LSM) ceramic slurry modeled with the Ostwald de Waele power law. Results of the modeling are compared with corresponding experimental data and good agreement is found.     

A Comparison of Simple Rheological Parameters and Simulation Data for Zymomonas mobilis Fermentation Broths with High Substrate Loading in a 3-L Bioreactor

Traditionally, as much as 80% or more of an ethanol fermentation broth is water that must be removed. This mixture is not only costly to separate but also produces a large aqueous stream that must then be disposed of or recycled. Integrative approaches to water reduction include increasing the biomass concentration during fermentation. In this paper, experimental results are presented for the rheological behavior of high-solids enzymatic cellulose hydrolysis and ethanol fermentation for biomass conversion using Solka Floc as the model feedstock. The experimental determination of the viscosity, shear stress, and shear rate relationships of the 10 to 20% slurry concentrations with constant enzyme concentrations are performed with a variable speed rotational viscometer (2.0 to 200 rpm) at 40 °C. The viscosities of enzymatic suspension observed were in range of 0.0418 to 0.0144, 0.233 to 0.0348, and 0.292 to 0.0447 Pa s for shear rates up to 100 reciprocal seconds at 10, 15, and 20% initial solids (w/v), respectively. Computational fluid dynamics analysis of bioreactor mixing demonstrates the change in bioreactor mixing with increasing biomass concentration. The portion-loading method is shown to be effective for processing high-solids slurries.     

Numerical study of the vortex-induced electroosmotic mixing of non-Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.     

Performance modeling and analysis of blood flow in elastic arteries

The effect of magnetic field has been examined on rheological models of blood. One. of them is the Power Law model and the other is the generalized Maxwell model. It is noticed that the magnetic field has a significant effect on the flow phenomena. The investigation shows that the model considered here is capable of taking into account the rheological properties affecting the blood flow and hemodynamic features, which may be important for medical doctors to predict diseases for individuals on the basis of the pattern of flow for an elastic artery in the presence of a transverses magnetic field. The effects of a magnetic field have been used to control the flow, which may be useful in certain hypertension cases, etc.     

A generalization of Reiner's mathematical model for wet sand

In this paper we modify the constitutive relation derived by Reiner (1945), to describe dilatancy in wet sand, by suggesting that the shear viscosity would depend on the shear rate and the volume fraction. We then look at the flow of a saturated densely packed bed of particles (with liquid in the pores) between two horizontal flat plates. We obtain exact solutions for a very special case.     

On the Stagnation Point Flow of a Special Class of Non-Newtonian Fluids

Abstract

The two-dimensional boundary layer equations for a class of non-Newtonian fluids, for which the apparent viscosity can be expressed as a polynomial in the second scalar invariant of the rate of strain tensor, have been derived. These equations have been employed to analyse the flow near a stagnation point over a stationary impermeable wall. The non-Newtonian effects on the boundary layer velocity profile and the wall skin friction have been studied, and compared with the corresponding Newtonian fluid. The fluid velocity in the boundary layer has been shown to be retarded by the non-Newtonian effect while the skin friction increases proportionate to it.     

THE VORTEX BLOB METHOD AS A SECOND-GRADE NON-NEWTONIAN FLUID

We show that a certain class of vortex blob approximations for ideal hydrodynamics in two dimensions can be rigorously understood as solutions to the equations of second-grade non-Newtonian fluids with zero viscosity and initial data in the space of Radon measures M (R ²). The solutions of this regularized PDE, also known as the isotropic Lagrangian averaged Euler or Euler-α equations, are geodesics on the volume preserving diffeomorphism group with respect to a new weak right invariant metric. We prove global existence of unique weak solutions (geodesics) for initial vorticity in M (R ²) such as point-vortex data, and show that the associated coadjoint orbit is preserved by the flow. Moreover, solutions of this particular vortex blob method converge to solutions of the Euler equations with bounded initial vorticity, provided that the initial data is approximated weakly in measure, and the total variation of the approximation also converges. In particular, this includes grid-based approximation schemes as are common in practical vortex computations.