The Differentiation Method in Rheology: IV. Characteristic Derivatives of Ideal Models in Couette Flow

1963 ◽  
Vol 3 (02) ◽  
pp. 177-184 ◽  
Author(s):  
J.G. Savins ◽  
G.C. Wallick ◽  
W.R. Foster
Keyword(s):  
Couette Flow ◽  
Poiseuille Flow ◽  
Integration Method ◽  
Flow Behavior ◽  
Preceding Paper ◽  
Applicable Range ◽  
Dual Differentiation ◽  
Viscoplastic Models ◽  
Basic Equations ◽  
Processing Techniques

Abstract The dual differentiation-integration method of rheological analysis is applied to Couette flow. Using machine processing techniques, a spectrum of characteristic derivative functions for a variety of ideal Generalized Newtonian and viscoplastic models has been developed: As for the case of Poiseuille flow the functions for Generalized Newtonian models as a class are strikingly different from the corresponding functions for the class of viscoplastic models. It is shown that this dual scheme of analysis is a highly sensitive analytic method for determining the applicable range of a rheological model. The unique characteristics of this function in the case of viscoplastics may lead to a more precise detection and evaluation of the yield point or yield stress in these materials. Introduction It has been shown that the dual differentiation- integration method of analysis is a discriminating and flexible method for interpreting flow behavior and determining the applicable range of a particular model from Poiseuille flow experiments. In the preceding paper the basic equations governing the Couette flow experiment were reviewed and the significance of changes in boundary conditions on data analysis in the case of the viscoplastic discussed. In this paper the dual method of analysis is applied to Couette flow using the suites of rheological models considered previously. THEORETICAL CONSIDERATIONS NEWTONIAN LIQUID f (p) = p......................(1) Substituting Eq. 1 in Eq. 4 of Ref. 3 and integrating yields Dv = p1........................(2) where Dv is the nominal shear rate at R1, viz:R2, and B is the radii ratio. Here R1 ............(3) ...................(4) ....................(5) GENERALIZED NEWTONIAN SYSTEMS Odd Power ..........(6) Integration after substitution of Eq. 6 in Eq. 4 of Ref. 3 yields ......(7) and hence, ...(8) ........(9) = .............(10) Series (General) ............(11) SPEJ P. 177^

A faster method for erosion and dilation of reservoir pore-complex images

1988 ◽  
Vol 25 (7) ◽  
pp. 1128-1131 ◽  
Author(s):  
J. R. Parker
Keyword(s):  
Flow Behavior ◽  
Reservoir Rock ◽  
Two Dimensional ◽  
Thin Sections ◽  
Reservoir Rocks ◽  
Image Processing Techniques ◽  
The Third ◽  
Computer Image Processing ◽  
Third Dimension ◽  
Processing Techniques

Studies of thin sections of reservoir rock have been conducted for some time with the goal of understanding flow behavior and estimating physical properties. These sections are essentially two dimensional, but it has always been assumed that the results obtained can be extrapolated to the third dimension. Computer image-processing techniques are often used in this sort of analysis because of the large amounts of data contained in a single digitized section image. One of the methods used to process these images is erosion–dilation, wherein layers of each pore are stripped off (erosion) and then replaced (dilation). This results in a smoothing of the pore perimeters and can be used to estimate pore radii, volume, and roughness. Because of the size of each image, erosion–dilation of images of the pore complex of reservoir rocks is a time-consuming process. A new method called global erosion is much faster, with no increase in memory requirement or decrease in accuracy. This should permit the processing of larger images or a greater number of small images than does the standard method.

scholarly journals Patterns in Wall-Bounded Shear Flows

2020 ◽  
Vol 52 (1) ◽  
pp. 343-367 ◽  
Author(s):  
Laurette S. Tuckerman ◽  
Matthew Chantry ◽  
Dwight Barkley
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Pipe Flow ◽  
Shear Flows ◽  
Plane Couette Flow ◽  
Plane Poiseuille Flow ◽  
Flow Focusing ◽  
Annular Pipe ◽  
Flow Plane

Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

Characterization of Air-Entrainment in a Plunging Water Jet System Using Image Processing: An Educational Approach

2011 ◽  
Author(s):  
Arman Molki ◽  
Lyes Khezzar ◽  
Afshin Goharzadeh
Keyword(s):  
Image Processing ◽  
Free Surface ◽  
Flow Behavior ◽  
Air Entrainment ◽  
Experimental Setup ◽  
Water Mixture ◽  
Educational Approach ◽  
Image Processing Techniques ◽  
Processing Techniques

This paper outlines a proposed experimental setup and image processing techniques using MATLAB for the characterization of the average dynamic behavior of the air/water mixture under the free surface of water penetrated by a plunging jet. The proposed setup focuses on the dynamics of air entrainment below the free surface and the identification of the major regimes related to the entrainment process of bubbles in water, namely: (a) no-entrainment, (b) incipient entrainment, (c) intermittent entrainment, and (d) continuous entrainment. The experimental setup allows students to observe the flow behavior below the free liquid surface and determine the penetration depth of the bubble plumes using image processing techniques in MATLAB. The focal point of the experiment is image analysis for qualitative and quantitative characterization of the bubble plume.

The Differentiation Method in Rheology: I. Poiseuille-Type Flow

1962 ◽  
Vol 2 (03) ◽  
pp. 211-215 ◽  
Author(s):  
J.G. Savins ◽  
G.C. Wallick ◽  
W.R. Foster
Keyword(s):  
Integral Equation ◽  
Data Analysis ◽  
Integration Method ◽  
Flow Behavior ◽  
Rheological Parameters ◽  
Flow Properties ◽  
Ideal Model ◽  
Rheological Analysis ◽  
Differentiation Method ◽  
General Method

Abstract A comprehensive review of the salient features of the differentiation method of rheological analysis in Poiseuille flow from its inception circa 1928 is presented. Here no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical parameters are required in the data-analysis process. In contrast, the integration method involves interpreting flow properties in terms of a particular ideal model. It is shown that, although both methods represent modes of solution of the same integral equation, being relatively bias-free, the differentiation method offers a more discriminating procedure for rheological analysis. The application to problems involving plane Poiseuille flow is also described. Introduction In most instances, the approach to the problem of interpreting the rheological properties of various compositions as they ate affected by changes in chemical or physical environment, as saying the characteristics of a particular constituent of a suspension, analyzing flow behavior in terms of interactions between components in a system, to cite but a few examples, has been in terms of what Hersey terms the integration method. Briefly, it consists of interpreting flow properties in terms of a particular ideal model. The usual practice of the integration method is to choose a model with a minimum number of parameters because, other things being equal, it is desirable to use the simplest model which will describe the behavior of a real material and yet be mathematically tract able for the requirements of data analysis. This expression is then substituted into an equation which relates observed kinematical and dynamical quantities, such as volume flux Q and pressure gradient J, and angular velocity and torque T, in a capillary and concentric cylinder apparatus, respectively. The rheological parameters appear on integrating, in an expression relating the pairs of observable quantities such as those just given. In many instances a particular model provides a good representation of rheological behavior over a reasonable range of compositional and environmental changes. just as often, however, it is obvious that the interpretation of rheological changes by the integration method is not providing realistic information about changes in flow behavior. A more general method of interpreting rheological data for a given material is to make no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical quantities, e.g., flow rate and pressure drop in capillary flow or angular velocity and torque in a rotational viscometer. This general method Hersey terms the differentiation method. Instead of integrating, one differentiates the integral equation with respect to one of the limits, i.e., one of the boundary conditions; the resulting expression contains the same observable quantities just given, their derivatives, and the rheological function evaluated at that boundary. By obtaining these derivatives from experimental ‘data, graphically or by a computer routine, they can be substituted into the differential equation and a graphical form of the function derived. THEORY OF THE DIFFERENTIATION METHOD FOR POISEUILLE-TYPE FLOWS In this introductory paper, two flow cases which are important in viscometry are considered (one for the first time) from the differentiation method of analysis, flow in a cylindrical tube and flow between fixed parallel surfaces of infinite extent, the basic integral equations being formulated in a manner analogous to the way they originally appeared in the literature. In addition, the following ideal conditions will be assumed:an absence of anomalous wall effects,isotropic behavior everywhere, andsteady laminar flow conditions. SPEJ P. 211^

The flow of suspensions through tubes. III. Collisions of small uniform spheres

1964 ◽  
Vol 282 (1391) ◽  
pp. 569-591 ◽  
Keyword(s):  
Steady State ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Collision Frequency ◽  
Reynolds Numbers ◽  
Tube Axis ◽  
Rigid Spheres ◽  
Liquid Drops ◽  
Net Migration ◽  
Dilute Suspensions

Two-body interactions of small rigid and deformable spheres in dilute suspensions undergoing Poiseuille flow at Reynolds numbers less than 10 –3 were studied and found to be similar to those previously observed in Couette flow. Two-body collisions between rigid spheres were symmetrical and reversible, the paths of approach and recession being curvilinear and mirror images of one another, except near the wall. The measured collision frequency agreed well with a theory based on rectilinear approach and recession, whereas the measured steady-state number of doublets was twice that predicted by the theory. The discrepancy was in part due to the existence of non-sepa­rating doublets, the orbits of which were also studied. In contrast, collisions between liquid drops were unsymmetrical, thus providing a mechanism for net migration of drops towards the tube axis in addition to the axial migration previously observed with single deformed drops.

scholarly journals Basic Flows of Generalized Second Grade Fluids Based on a Sisko Model

2017 ◽  
Vol 22 (4) ◽  
pp. 1019-1033
Author(s):  
A. Walicka
Keyword(s):  
Couette Flow ◽  
Poiseuille Flow ◽  
Equations Of Motion ◽  
Plane Channel ◽  
Second Grade ◽  
Sisko Fluid ◽  
Coaxial Cylinders ◽  
Solutions Of Equations ◽  
Simple Flows ◽  
Second Grade Fluids

Abstract The present investigation is concerned with basic flows of generalized second grade fluids based on a Sisko fluid. After formulation of the general equations of motion three simple flows of viscoplastic fluids of a Sisko type or fluids similar to them are considered. These flows are: Poiseuille flow in a plane channel, Poiseuille flow in a circular pipe and rotating Couette flow between two coaxial cylinders. After presentation the Sisko model one was presented some models of fluids similar to this model. Next it was given the solutions of equations of motion for three flows mentioned above.

The Velocity Distribution for Ferromagnetic Fluids

2013 ◽  
Vol 860-863 ◽  
pp. 1506-1509
Author(s):  
Ming Jun Li ◽  
Kai Fu Liang
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Magnetic Fluids ◽  
Free Electrons ◽  
Boundary Layer Equations ◽  
Ferromagnetic Fluids

The magnetic fluids are assumed non-conductive with few free electrons existing, then the boundary layer equations are obtained for two special non-conductive ferromagnetic fluids, i.e. non-conductive Poiseuille flow and Couette flow, and the velocity distribution are found to be parabolic.

Stability of plane Poiseuille–Couette flow in a fluid layer overlying a porous layer

2017 ◽  
Vol 826 ◽  
pp. 376-395 ◽  
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Couette Flow ◽  
Porous Layer ◽  
Poiseuille Flow ◽  
Fluid Layer ◽  
Maximum Velocity ◽  
Stability Characteristic ◽  
Layer System ◽  
Neutral Curves ◽  
Layer Mode ◽  
The Stability

This paper performs a linear stability analysis to investigate the stability of plane Poiseuille–Couette flow in a fluid layer overlying a porous medium saturated with the same fluid. The effect of superimposed Couette flow on the associated Poiseuille flow in such a two-layer system is explored carefully. The result shows that the presence of Couette flow may destabilize the Poiseuille flow at small depth ratio $\hat{d}$, defined by the ratio of the depth of the fluid layer to the depth of the porous layer, and induce a tri-modal structure to the neutral curves. At moderate $\hat{d}$, the Couette component generally produces a stabilization effect on the flow. When the velocity of the upper moving wall is large enough, a bi-modal behaviour of the neutral curves appears and a shift of instability mode occurs from the long-wave fluid-layer mode to the porous-layer mode with higher wavenumber. These stability characteristics are remarkably different from those of the plane Poiseuille–Couette flow in a single fluid layer in that the flow becomes absolutely stable when the wall velocity is over 70 % of the maximum velocity of the Poiseuille component of flow. The stability of pure Couette flow in such a two-layer system is also studied. It is found that the flow is still absolutely stable with respect to infinitesimal disturbances, which is the same as the stability characteristic of a single-layer plane Couette flow.

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