scholarly journals Numerical Simulation of Drop Formation in Power-Law Fluids

2018 ◽  
Vol 34 (6) ◽  
pp. 3153-3156
Author(s):  
Fahime Hoseinzade ◽  
Hamid Reza Ghorbani
Keyword(s):  
Newtonian Fluid ◽  
Power Law ◽  
Drop Size ◽  
Two Dimensions ◽  
Orifice Diameter ◽  
Fluid Flow Rate ◽  
Power Law Model ◽  
Motion Equations ◽  
Power Law Fluids ◽  
Submerged Orifice

The purpose of this work was the study of the formation process of Newtonian drop in a continuous non-Newtonian fluid. This process was numerically studied by entering liquid into a submerged orifice in a cylindrical vessel. The simulations were carried out using SOLA-VOF method. In this code, the complete motion equations were predicted two dimensions and using finite difference method. In addition, power law model was used to simulate a non-Newtonian fluid. In this research, the effects of orifice diameter and Newtonian fluid flow rate were studied on the formation of the drop, size and its formation time.

scholarly journals Flow of power-law liquids in a Hele-Shaw cell driven by non-uniform electro-osmotic slip in the case of strong depletion

2016 ◽  
Vol 807 ◽  
pp. 235-257 ◽  
Author(s):  
Evgeniy Boyko ◽  
Moran Bercovici ◽  
Amir D. Gat
Keyword(s):  
Power Law ◽  
Asymptotic Approximation ◽  
Approximate Solutions ◽  
Two Dimensions ◽  
Analysis And Design ◽  
Power Law Fluids ◽  
Wall Depletion ◽  
Strong Depletion ◽  
Characteristic Pressure ◽  
Hele Shaw Cell

We analyse flow of non-Newtonian fluids in a Hele-Shaw cell, subjected to spatially non-uniform electro-osmotic slip. Motivated by their potential use for increasing the characteristic pressure fields, we specifically focus on power-law fluids with wall depletion properties. We derive a $p$-Poisson equation governing the pressure field, as well as a set of linearized equations representing its asymptotic approximation for weakly non-Newtonian behaviour. To investigate the effect of non-Newtonian properties on the resulting fluidic pressure and velocity, we consider several configurations in one and two dimensions, and calculate both exact and approximate solutions. We show that the asymptotic approximation is in good agreement with exact solutions even for fluids with significant non-Newtonian behaviour, allowing its use in the analysis and design of microfluidic systems involving electrokinetic transport of such fluids.

Non-Newtonian Lubrication Theory for Rough Surfaces: Application to Rigid and Elastic Rollers

1982 ◽  
Vol 24 (3) ◽  
pp. 147-154 ◽  
Author(s):  
P. Sinha ◽  
J. B. Shukla ◽  
C. Singh ◽  
K. R. Prasad
Keyword(s):  
Surface Roughness ◽  
Elastic Deformation ◽  
Newtonian Fluid ◽  
Power Law ◽  
Reynolds Equation ◽  
Stochastic Theory ◽  
Power Law Model ◽  
Pure Rolling ◽  
Lubrication Characteristics ◽  
Rigid Surfaces

To predict the consequences of the interaction of the lubricant rheology with surface roughness, the stochastic theory of lubrication for Newtonian fluid is modified to take into account the non-Newtonian behaviour of the lubricant, by considering the power law model. Generalized forms of the Reynolds equation for two types of roughness arrangements, viz., longitudinal and transverse, are derived. These equations are subsequently used to study the lubrication characteristics of infinitely long rough roller bearings, and two particular cases, namely pure rolling (rigid surfaces) and rolling with elastic deformation, are discussed.

Numerical Investigation of Power-Law Fluid Flows and Heat Transfer inside of Curved Duct under Aiding Thermal Buoyancy

2018 ◽  
Vol 16 ◽  
pp. 84-95 ◽  
Author(s):  
Fayçal Bouzit ◽  
Houssem Laidoudi ◽  
Bilal Blissag ◽  
Mohamed Bouzit ◽  
Abdellah Guenaim
Keyword(s):  
Heat Transfer ◽  
Numerical Investigation ◽  
Power Law ◽  
Flow Behavior ◽  
Two Dimensions ◽  
Thermal Buoyancy ◽  
Curved Duct ◽  
Ansys Cfx ◽  
Power Law Fluids ◽  
Power Law Index

This paper deals with a numerical investigation in order to predict correctly the combined effects of aiding thermal buoyancy and rheological flow behavior of power-law fluids on downward flow and heat transfer rate inside of 180° curved duct. The governing equations involving the momentum, continuity and the energy are solved in two-dimensions using the package called ANSYS-CFX. The computational results are depicted and discussed for the range of conditions as:Re= 40 to 1000,Ri= 0 to-1 andn= 0.4 to 1.2 at fixed value of Prandt number ofPr= 1. To interpret the found results, the flow structure and temperature field are shown in form of streamlines and isotherm contours. The average Nusselt number of the inner and outer walls of curved channel is calculated to determine the role of Reynolds number, Richardson number and power-law index. It is found that increase in strength of aiding buoyancy creates a counter rotating region in angle of 90 degrees of the duct.

Pressure Transient Behavior of Non-Newtonian/Newtonian Fluid Composite Reservoirs

1981 ◽  
Vol 21 (02) ◽  
pp. 271-280 ◽  
Author(s):  
O. Lund ◽  
Chi U. Ikoku
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Media ◽  
Newtonian Fluid ◽  
Power Law ◽  
Well Test ◽  
Well Test Analysis ◽  
Partial Differential ◽  
Test Analysis ◽  
Power Law Fluids

Abstract Pressure transient theory of flow of non-Newtonian power-law fluids in porous media is extended to non-Newtonian/Newtonian fluid composite reservoirs. This paper examines application of non-Newtonian and conventional (Newtonian) well test analysis techniques to injectivity and falloff tests in wells where different amounts of non-Newtonian fluids have been injected into the reservoir to displace the in-situ Newtonian fluid (oil and/or water). Early time pressure data can be analyzed by non-Newtonian well test analysis methods. Conventional semilog methods may be used to analyze late time falloff data. The location of the non-Newtonian fluid front can be estimated from well tests using the radius of investigation equation for power-law fluids. An equation for calculating shear rates and apparent viscosities for power-law fluids in reservoirs is presented. An example problem is used to illustrate observations and solution techniques. Introduction Recent studies have proposed new well test analysis techniques for interpreting pressure data obtained during injectivity and falloff testing in reservoirs containing slightly compressible non-Newtonian, power-law fluids. The first papers proposing well test analysis methods for non-Newtonian fluid injection wells were published in 1979. Odeh and Yang1 derived a partial differential equation for flow of power-law fluids through porous media. They used a power-law function relating the viscosity to the shear rate. The power-law viscosity function was coupled with the variable viscosity diffusivity equation and a shear rate relationship proposed by Savins2 to give the new partial differential equation. An approximate analytical solution was obtained. The solution provided new plotting techniques for analyzing injection and falloff test data. The utility of the new methods was demonstrated on field tests. They also derived the steady-state flow equation and an expression for the radius of investigation. Isochronal testing was discussed. McDonald3 presented a numerical study using the power-law flow equation of Odeh and Yang. He presented different numerical techniques of solving the equation and compared results with the analytical results of Odeh and Yang. He found that a finer grid was required for finite difference simulation of power-law fluids than for black-oil fluids. A partial differential equation for radial flow of non-Newtonian power-law fluids through porous media was published by Ikoku and Ramey4,5 in 1979. Coupling the non-Newtonian Darcy's law with the continuity equation, the rigorous partial differential equation was derived:Equation 1

A Comparison of Differential and Integral Descriptions of the Annular Flow of a Power-Law Fluid

1969 ◽  
Vol 9 (03) ◽  
pp. 311-315
Author(s):  
G.C. Wallick ◽  
J.G. Savins
Keyword(s):  
Shear Rate ◽  
Newtonian Fluid ◽  
Power Law ◽  
Flow Problem ◽  
Axial Flow ◽  
Past Experience ◽  
Radial Coordinate ◽  
Power Law Model ◽  
Power Law Fluid ◽  
Model Parameter

Abstract Some physical processes may be described mathematically in both differentialand integral equation form. Formulation choice for numerical solution often isbased upon personal preference rather than upon problem characteristics. Wecompare differential and integral methods for the numerical description of thesteady-state flow of a non-Newtonian, power-law fluid through an annulus. Forthis application, our data indicate that the integral formulation is superiorboth in solution accuracy and computational efficiency. Our integral solutionmethod is a generalization of an earlier analytic solution that was restrictedto integer values of the power-law model parameter N. The new method ispower-law model parameter N. The new method is more directly applicable inpractical applications and is valid for all N, integer and non-integer. Introduction In many instances differential and integral equations may be used with equalvalidity for the mathematical description of a physical precess. The choice ofmethods often is dictated more by the past experience and predilection of theanalyst than past experience and predilection of the analyst than by the natureof the problem. Yet the efficiency and efficacy of the solution process may bestrongly dependent upon the problem formulation selected. As an example of thisprocedural dichotomy we will consider the numerical description of thesteady-state isothermal axial flow of an incompressible time independentnon-Newtonian fluid through the annular spacing between two fixed concentriccylinders of radii Ri and R, R greater than Ri.* We assume that the cylindersare infinite in length (no end effects) and that the flow is produced by theapplication of a constant pressure gradient in the axial z-direction. This flowproblem has been treated by a number of investigators, and has practicalapplication, e.g., flow of drilling fluids, extrusion of molten plastics, etc. Fredrickson and Bird have shown that, subject to the above assumptions, theflow equation may be written in the form ...........(1) where J = -dp/dz= constant p represents the pressure, the radial coordinate, and = z pressure, the radial coordinate, and = z represents the shearingstress. We seek a solution of Eq. 1 subject to the adherence boundaryconditions ...........(2) where v = vz is the axial flow velocity. For this flow problem it can beshown that .............(3) where is the shear-dependent viscosity function, and that the shear rate maybe expressed in the forms ..............(4) The minus sign is used in Eq. 4 to insure that and always have the samesign, greater than 0. In principle, the flow problem outlined here may besolved for any non-Newtonian fluid for which the shear-dependent viscosityfunction can be established as a known analytic function of the rate of shearfrom an investigation of any of the viscometric flows. However, it isconvenient for our purpose to use the particular viscometric function .............(5) which is referred to as the power-law model. The parameters n and Kcharacterize the relationship between shear rate and shear stress for a powerlaw liquid. The parameter n is a measure of the departure from Newtonianbehavior. If n less than 1, the flow behavior is of the "shearthinning" type; if n greater than 1, it is of the "shearthickening" category.

Thermal Transport Characteristics of Non-Newtonian Electroosmotic Flow in a Slit Microchannel

2011 ◽  
Author(s):  
Ashkan Babaie ◽  
Arman Sadeghi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Power Law ◽  
Electroosmotic Flow ◽  
Chemical Species ◽  
Biological Applications ◽  
Power Law Model ◽  
Sample Collection ◽  
Fluid Delivery ◽  
Flow Parameters ◽  
Power Law Fluids ◽  
Thermal Features

Electroosmosis has many applications in fluid delivery at microscale, sample collection, detection, mixing and separation of various biological and chemical species. In biological applications, most fluids are known to be non-Newtonian. Therefore, the study of thermal features of non-Newtonian electroosmotic flow is of great importance for scientific communities. In the present work, the fully developed electroosmotic flow of power-law fluids in a slit microchannel is investigated. The related equations are transformed into non-dimensional forms and necessary changes are made to adapt them for non-Newtonian fluids of power-law model. Results show that depending on different flow parameters like Debye-Hu¨ckel or related viscous dissipation and Joule heating parameters, non-Newtonian characteristics of the flow may lead to significant deviations from Newtonian flow behaviors.

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