Flow pattern transition,pressure gradient,hold-up predictions in gas/non-Newtonian power-law fluid stratified flow

This work focuses on gas/non-Newtonian power-law fluid stratified pipe flow. Two different theoretical approaches to obtain pressure gradient and hold-up predictions are presented: the steady fully developed two-fluid model and the pre-integrated model. The theoretical predictions are compared with experimental data available for horizontal and for slightly downward inclined air/shear thinning fluid stratified flow taken from literature. The predictions of the pre-integrated model are validated showing a good agreement when compared with experimental data. The criteria for the transition from the stratified flow pattern are applied to gas/non-Newtonian stratified flow. The neutral stability analysis (smooth/wavy stratified flow) and the well-posedness (existence region of stratified flow) of governing equations are carry out. The predicted transition boundaries are obtained using the steady fully developed two-fluid model and the pre-integrated model, where the shape factors and their derivatives are accounted for. A comparison between the predicted boundaries and experimental flow pattern maps is presented and shows a good agreement. A comment on the shear stress modeling by the pre-integrated model is provided.     

Simulation of non-Newtonian ink transfer between two separating plates for gravure-offset printing

The inks used in gravure-offset printing are non-Newtonian fluids with higher viscosities and lower surface tensions compared to Newtonian fluids. This paper examines the transfer of a non-Newtonian ink between two parallel plates when the top plate is moved upward with a constant velocity while the bottom plate is held fixed. Numerical simulations were carried out using the Carreau model to explore the behavior of a non-Newtonian ink in gravure-offset printing. The volume of fluid (VOF) model was adopted to demonstrate the stretching and break-up behaviors of the ink. The results indicate that the ink transfer ratio is greatly influenced by the contact angle, especially the contact angle at the upper plate (α). For lower values of α, oscillatory or unstable behavior of the position of minimum thickness of the ink between the two parallel plates during the stretching period is observed. This oscillation gradually diminishes as the contact angle at the upper plate is increased. Moreover, the number of satellite droplets increases as the velocity of the upper plate is increased. The surface tension of the conductive ink shows a positive impact on the ink transfer ratio to the upper plate. Indeed, the velocity of the upper plate has a significant influence on the ink transfer in gravure-offset printing when the Capillary number (Ca) is greater than 1 and the surface tension dominates over the ink transfer process when Ca is less than 1.     

The Effect of Double Dispersion on Natural Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

The effect of power law index parameter of the non-Newtonian fluid on free convection heat and mass transfer from a vertical wall is analyzed by considering double dispersion in a non-Darcy porous medium with constant wall temperature and concentration conditions. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. In this case a similarity solution is possible. The variation of heat and mass transfer coefficients with the governing parameters such as power law index, thermal and solutal dispersion parameters, inertia parameter, buoyancy ratio, and the Lewis number is discussed for a wide range of values of these parameters.     

Conserved dynamics and interface roughening in spontaneous imbibition: A critical overview

Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties of the imbibition front, with particular attention to the conservation law associated to the fluid, to problems arising from the actual structure of the embedding medium, and to external influences such as evaporation and gravity. Our main conclusion is that the scaling of moving interfaces includes many crossover phenomena, with competition between the average capillary pressure gradient and its fluctuations setting the maximal lengthscale for roughening. We discuss the physics of both pinned and moving interfaces and the ability of the existing models to account for their properties. Received 17 February 1999 and Received in final form 24 November 1999     

Weak solutions to the generalized Navier–Stokes equations with mixed boundary conditions and implicit obstacle constraints

This paper is concerned with the investigation of a generalized Navier–Stokes equation for non-Newtonian fluids of Bingham-type (GNSE, for short) involving a multivalued and nonmonotone slip boundary condition formulated by the generalized Clarke subdifferential of a locally Lipschitz superpotential, a no leak boundary condition, and an implicit obstacle inequality. We obtain the weak formulation of (GNSE) which is a generalized quasi-variational–hemivariational inequality. By introducing an Oseen model as an auxiliary (intermediated) problem and employing Kakutani-Ky Fan theorem for multivalued operators as well as the theory of nonsmooth analysis, an existence theorem to (GNSE) is established.     

Group properties and exact solutions for two-dimensional flow of a non-newtonian fluid

The Group Properties and the associated Lie Algebra are developed for the equations of motion of the unsteady two-dimensional flow of a non-Newtonian fluid in cartesian coordinates. Then by using the full one-parameter infinitesimal transformation group and its subgroups a number of exact solutions are obtained.     

On viscoelastic effects in non-Newtonian steady flows through porous media

This paper presents a mathematical model for describing approximately the viscoelastic effects in non-Newtonian steady flows through a porous medium. The rheological behaviour of power law fluids is considered in the Maxwell model of elastic behaviour of the fluids. The equations governing the steady flow through porous media are derived and an analytical solution of these equations in the case of a simple flow system is obtained. The conditions for which the viscoelastic effects may become observable from the pressure distribution measurements are shown and expressed in terms of some dimensionless groups. These have been found to be relevant in the evaluation of viscoelastic effects in the steady flow through porous media.     

A unified compatibility method for exact solutions of non-linear flow models of Newtonian and non-Newtonian fluids

Criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations. Necessary and sufficient compatibility conditions are derived which can be used to construct exact solutions of higher order ordinary differential equations subject to lower order equations. We provide the connection to generalized groups through conditional symmetries. Using this approach of compatibility and generalized groups, new exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived. The ansatz approach for obtaining exact solutions for non-linear flow models of Newtonian and non-Newtonian fluids is unified with the application of the compatibility and generalized group criteria.     

Instability of two streaming conducting and dielectric bounded fluids in porous medium under time-varying electric field

In this paper, we consider the instability of the interface between two superposed streaming conducting and dielectric fluids of finite depths through porous medium in a vertical electric field varying periodically with time. A damped Mathieu equation with complex coefficients is obtained. The method of multiple scales is used to obtain an approximate solution of this equation, and then to analyze the stability criteria of the system. We distinguish between the non-resonance case, and the resonance case, respectively. It is found, in the first case, that both the porosity of porous medium, and the kinematic viscosities have stabilizing effects, and the medium permeability has a destabilizing effect on the system. While in the second case, it is found that each of the frequency of the electric field, and the fluid velocities, as well as the medium permeability, has a stabilizing effect, and decreases the value of the resonance point, while each of the porosity of the porous medium, and the kinematic viscosities has a destabilizing effect, and increases the value of the resonance point. In the absence of both streaming velocities and porous medium, we obtain the canonical form of the Mathieu equation. It is found that the fluid depth and the surface tension have a destabilizing effect on the system. This instability sets in for any value of the fluid depth, and by increasing the depth, the instability holds for higher values of the electric potential; while the surface tension has no effect on the instability region for small wavenumber values. Finally, the case of a steady electric field in the presence of a porous medium is also investigated, and the stability conditions show that each of the fluid depths and the porosity of the porous medium ɛ has a destabilizing effect, while the fluid velocities have stabilizing effect. The stability conditions for two limiting cases of interest, the case of purely fluids), and the case of absence of streaming, are also obtained and discussed in detail.     

Generalized Wall Functions for Rough Walls Based on Data Assimilation

We present a systematic identification method for the development of equivalent boundary conditions for turbulent flow simulation over rough walls in engineering applications where the typical roughness involved is known for a given application. After parameterizing the roughness and sampling of the parameter space, numerical simulations or experiences are used to generate a database which is used to identify the coefficients of a polynomial reduced-order model. These laws are parameterized by an a priori length scale for which we propose a new a posteriori criterion.