Non Newtonian Fluid

10 Key excerpts on "Non Newtonian Fluid"

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  eBook - ePub

  Recent Developments in Theoretical Fluid Mechanics

  Winter School, Paseky, 1992

  • G P Galdi, J. Necas(Authors)
  • 2023(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  K.R. Rajagopal

  Mechanics of Non–Newtonian Fluids

  1. Introduction

  This series of four lectures is intended to be an introduction to the mechanics of non-Newtonian fluids. It is meant to merely provide a nodding acquaintance to the burgeoning area of non-Newtonian fluid mechanics. The terminology non-Newtonian fluids can apply to a wide range of materials with widely disparate material structure, the main shared characteristic being the inability of the classical linearly viscous Newtonian model to capture the behavior of these fluids. Polymeric liquids, biological fluids, slurries, suspensions, liquid crystals are but some of the materials which belong to the class of non-Newtonian fluids. .

  The departure from Newtonian behavior manifests itself in these materials in many ways. Here we shall discuss the various features exhibited by non-Newtonian fluids. The main points of deviance from Newtonian behavior are:

  1. The ability to shear thin or shear thicken,
  2. The ability to creep,
  3. The ability to relax stresses,
  4. The presence of normal stress differences in simple shear flows,
  5. The presence of yield stress.

  A non-Newtonian fluid may possess just one or all of the above characteristics. We shall discuss each of these characteristics briefly.

  (i) Shear thinning or shear thickening

  Figure 1.

  Let us first consider a simple shear flow. In the case of a Newtonian fluid, the relation between the shear stress and shear rate is linear. However, in certain fluids this relationship can be non-linear. We could define a generalized apparent viscosity for these materials, which is the ratio of the shear stress to the shear rate. Materials in which the derivative of the generalized viscosity with respect to the shear rate is negative are called shear thinning fluids. If the derivative of the generalized viscosity to the shear rate is positive, such fluids are called shear thickening fluids. There are examples of both kinds of fluids.

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  The Finite Element Method in Heat Transfer and Fluid Dynamics

  • J. N. Reddy, D.K. Gartling(Authors)
  • 2010(Publication Date)
  • CRC Press

    (Publisher)

  6 Non-Newtonian Fluids 6.1 Introduction In Chapters 4 and 5 we studied the Þ nite element models of Newtonian ß uids (i.e., ß uids whose constitutive behavior is linear). Fluids that are not described by the Newtonian constitutive relations are commonly encountered in a wide variety of industrial processes. For example, such materials include motor oils, high molecular weight liquids such as polymers, slurries, pastes, and other complex mixtures. The processing and transport of such ß uids are central problems in the chemical, food, plastics, petroleum, and polymer industries. Non-Newtonian behavior manifests itself in a number of di ff erent ways. Most such ß uids exhibit a shear rate dependent viscosity, with “shear thinning” (i.e., decreasing viscosity with increasing shear rate) being the most prevalent behavior. Other phenomena associated with the elasticity and memory of the ß uid, such as recoil, are also observed in many situations. Di ff erences in the normal stress components occur in many ß ows and lead to such well-known e ff ects as rod climbing or the Weissenberg e ff ect, and the curvature of the free surface in an open channel ß ow. A comprehensive list and discussion of these and other non-Newtonian e ff ects is given in the book by Bird et al. [1]. For the present discussion non-Newtonian ß uids can conveniently be separated into two distinct categories: (1) inelastic ß uids or ß uids without memory, and (2) viscoelastic ß uids, in which memory e ff ects are signi Þ cant. The distinction is an important one from both a physical and computational point of view. Basically, inelastic ß uids can be viewed as generalizations (in some sense) of the Newtonian ß uid. The viscosity function for such materials depends on the rate of deformation of the ß uid and thus allows “shear thinning” e ff ects to be modeled.

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  eBook - PDF

  Multiphase Flow Handbook

  • Efstathios Michaelides, Clayton T. Crowe, John D. Schwarzkopf, Efstathios Michaelides, Clayton T. Crowe, John D. Schwarzkopf(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  It is difficult to imagine modern life without such materials. Think of the range of processed foodstuffs we consume every day, personal- and health-care products used routinely, cleaning aids and polishing waxes, etc., all of which fill the aisles of modern supermarkets, for instance. All modern technologies, including modern transportation (in terms of smart materials of construction or advanced fuels), entertainment industry (films, DVDs), medicine, environment, energy generation and conservation, etc., all exploit non-Newtonian characteristics in one form or the other at some stage during the course of their manufacture or application. The extraction of oil from rocks via polymer flooding, the soft gels used to make optical lenses, and the next generation of aviation fuels, all hinge on successfully imparting the desirable rheological characteristics to achieve the satisfactory product quality. Indeed, so widespread is the non-Newtonian fluid behavior that it would be no exaggeration to say that the Newtonian fluid behavior is more of an exception rather than the rule! Consequently, over the past 50–75 years or so, this branch of fluid mechanics has begun to receive systematic attention, albeit it is still in its embryonic stage (Boger and Walters, 1992, Tanner and Walters, 1998, Denn, 2004). Undoubtedly, significant advances 21.1 Introduction 21.2 Newtonian and Non-Newtonian Fluids 21.3 Rigid Nondeformable Particles 21.4 Fluid Spheres 21.5 Other Effects 21.6 Concluding Remarks and Future Directions 1322 21. Dispersed Flow in Non-Newtonian Fluids have been made in some simple geometries like flow in ducts of circular and noncircular cross sections (Lawal and Mujumdar, 1987, Chhabra, 1999), porous media flows (Chhabra, 1993, 2006, Chhabra et al., 2001), batch mixing vessels (Chhabra, 2003, Paul et al., 2004, Chhabra and Richardson, 2008), etc.

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  Solved Practical Problems in Fluid Mechanics

  • Carl J. Schaschke(Author)
  • 2015(Publication Date)
  • CRC Press

    (Publisher)

  221 9 Rheology and Non-Newtonian Fluids Introduction The majority of known fluids do not exhibit simple Newtonian behaviour in which the viscosity is independent of shear stress and time, but instead exhibit wide and varied rheological properties. Some flow under the influence of gravity, change shape and form while others remain solid at a particular tem-perature but are liquid and capable of flow at another, such as waxes. Paints, polymers, and many foods retain their form until a sufficient external force is applied causing them to flow. De-icing fluids sprayed onto the wings of com-mercial aircraft are formulated to remain in place and prevent ice buildup until the aircraft is at the point of takeoff, where the shear force effects of the air passing over the surface are sufficient to remove them. Toothpaste is designed to remain in place on the toothbrush once squeezed from the tube until sufficient shear is applied by the action of cleaning the teeth. Fluids that do not exhibit Newtonian behaviour are broadly classified as non-Newtonian fluids. That is, the rate of shear is not directly proportional to the shear stress over all values of shear stress. Instead, the apparent viscos-ity depends on the shear stress and/or time. Non-Newtonian fluids are fur-ther classified as being time dependent, time independent, and viscoelastic (Figure 9.1). While Newtonian fluids are time-independent fluids, non- Newtonian fluids exhibit characteristics where the apparent viscosity either increases or decreases with an increasing shear rate. Examples in which the viscosity decreases with shear stress include polymer melts, paper pulp, wallpaper paste, printing inks, tomato purée, mustard, rubber solutions, and protein concentrations, and are known as pseudoplastic or shear-thinning liquids. Dilatants are fluids in which the apparent viscosity increases with the increasing shear rate.

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  Meeting the Pump Users Needs

  The Proceedings of the 12th International Pump Technical Conference

  • Sam Stuart(Author)
  • 2013(Publication Date)
  • Elsevier

    (Publisher)

  Far more fluids are non-Newtonian and their viscosity will change as a function of shear rate and some are also affected by the length of time they are subjected to shearing. To make the problem more interesting the viscosity of some fluids is directly proportional to the shear rate while the viscosity of other fluids is inversely proportional to the shear rate. Since 1957 several thousand fluids have been evaluated in the fluids laboratory at Robbins & Myers. Most of the fluids evaluated have been non-Newtonian. Non-Newtonian fluids are classified as fluids which increase or decrease in viscosity with an increase in shear rate. Since the viscosity will change as a function of shear rate, system pressures, pump efficiencies, power requirements, and indeed even the ability of the pump to handle the fluid are affected by the viscosity. Therefore it is important to accurately determine and understand the rheological properties of fluids to be pumped. 436 Non-Newtonian fluids will exhibit either an increase or decrease in viscosity when subjected to shearing. For this reason non-Newtonian fluids are often referred to as either shear thinning or shear thickening. Non-Newtonian fluids are also classified as time dependent or time independent depending on whether or not the viscosity is affected by the length of time the fluid is sheared as well as the shear rate. Figure 1 shows the different types of fluids and the relationship of viscosity to shear rate. Pseudoplastic and thixotropic fluids are shear thinning, pseudoplastic fluids being time independent and thixotropic fluids being time dependent. The viscosity of thixotropic fluids will continue to decrease with time whereas pseudoplastic fluids are not affected by the length of time they are subjected to shearing. Paints and emulsions are examples of pseudoplastic fluids. Heavy greases, slurries, and some polymers are good examples of thixotropic fluids.

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  eBook - ePub

  Non-Newtonian Flow and Applied Rheology

  Engineering Applications

  • R. P. Chhabra, J.F. Richardson(Authors)
  • 2011(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Table 1.2 reveals the widespread occurrence of non-Newtonian flow behaviour in materials encountered in everyday life as well as in diverse industrial settings.

  Table 1.2. Examples of substances exhibiting non-Newtonian fluid behaviour

  Adhesives (wall paper paste, carpet adhesive, for instance) Ales (beer, liqueurs, etc.) Animal waste slurries from cattle farms Biological fluids (blood, synovial fluid, saliva, etc.) Bitumen Cement paste and slurries Chalk slurries Chocolates Coal slurries Cosmetics and personal care products (nail polish, lotions and creams, lipsticks, shampoos, shaving foams and creams, toothpaste, etc.) Dairy products and dairy waste streams (cheese, butter, yogurts, fresh cream, whey, for instance) Drilling muds Fire fighting foams

  Foodstuffs (fruit/vegetable purees and concentrates, sauces, salad dressings, mayonnaise, jams and marmalades, ice-cream, soups, cake mixes and cake toppings, egg white, bread mixes, snacks) Greases and lubricating oils Mine tailings and mineral suspensions Molten lava and magmas Paints, polishes and varnishes Paper pulp suspensions Peat and lignite slurries Polymer melts and solutions, reinforced plastics, rubber Printing colours and inks Pharmaceutical products (creams, foams, suspensions, for instance) Sewage sludge Wet beach sand Waxy crude oils

  1.2.2. Non-Newtonian Fluid Behaviour

  A non-Newtonian fluid is one whose flow curve (shear stress versus shear rate) is non-linear or does not pass through the origin, i.e. where the apparent viscosity, shear stress divided by shear rate, is not constant at a given temperature and pressure but is dependent on flow conditions such as flow geometry, shear rate, etc. and sometimes even on the kinematic history of the fluid element under consideration. Such materials may be conveniently grouped into three general classes:

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  eBook - ePub

  Non-Newtonian Flow

  Fundamentals and Engineering Applications

  • R. P. Chhabra, J.F. Richardson(Authors)
  • 1999(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Chapter 1

  Non-Newtonian fluid behaviour

  1.1 Introduction

  One may classify fluids in two different ways; either according to their response to the externally applied pressure or according to the effects produced under the action of a shear stress. The first scheme of classification leads to the so called ‘compressible’ and ‘incompressible’ fluids, depending upon whether or not the volume of an element of fluid is dependent on its pressure. While compressibility influences the flow characteristics of gases, liquids can normally be regarded as incompressible and it is their response to shearing which is of greater importance. In this chapter, the flow characteristics of single phase liquids, solutions and pseudo-homogeneous mixtures (such as slurries, emulsions, gas–liquid dispersions) which may be treated as a continuum if they are stable in the absence of turbulent eddies are considered depending upon their response to externally imposed shearing action.

  1.2 Classification of fluid behaviour

  1.2.1 Definition of a Newtonian fluid

  Consider a thin layer of a fluid contained between two parallel planes a distance dy apart, as shown in Figure 1.1 . Now, if under steady state conditions, the fluid is subjected to a shear by the application of a force F as shown, this will be balanced by an equal and opposite internal frictional force in the fluid. For an incompressible Newtonian fluid in laminar flow, the resulting shear stress is equal to the product of the shear rate and the viscosity of the fluid medium. In this simple case, the shear rate may be expressed as the velocity gradient in the direction perpendicular to that of the shear force, i.e.

  Figure 1.1 Schematic representation of unidirectional shearing flow.

  (1.1)

  Note that the first subscript on both τ and indicates the direction normal to that of shearing force, while the second subscript refers to the direction of the force and the flow. By considering the equilibrium of a fluid layer, it can readily be seen that at any shear plane there are two equal and opposite shear stresses–a positive one on the slower moving fluid and a negative one on the faster moving fluid layer. The negative sign on the right hand side of equation (1.1) indicates that τyx is a measure of the resistance to motion. One can also view the situation from a different standpoint as: for an incompressible fluid of density ρ, equation (1.1)

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  Rheology V1

  Theory and Applications

  • Frederick Eirich(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  CHAPTER 16 NON-NEWTONIAN FLOW OF LIQUIDS AND SOLIDS J. G. Oldroyd I. General 653 II. Materials of Variable Viscosity 654 1. Liquids 654 2. Flow of Plastic Solids 658 3. Anomalous Flow near a Wall 659 III. Special Types of Flow 660 1. Rectilinear Flow Produced by Moving Boundaries 660 2. Flow through Pipes 662 3. Flow between Rotating Coaxial Cylinders 666 4. Flow between Rotating Cones 670 IV. More General Liquids 671 1. Classification 671 2. Inelastic Liquids 672 3. Liquids possessing Elasticity of Shape 674 4. Oscillatory Motion 678 Nomenclature 682 I. General The theory of flow of liquids whose behavior in shear is describable in terms of a single constant viscosity coefficient, usually referred to as New-tonian flow, is widely treated in textbooks. But the behavior of liquids which appear to have different viscosities when observed in different types of apparatus, or at different rates of flow in the same apparatus, under uniform temperature conditions, is not so readily amenable to theoretical analysis. It is our purpose in the present chapter to consider the theoretical methods available for treating such non-Newtonian flow. When the isothermal flow of a material is observed to be non-Newtonian, it may still be possible to explain its properties completely in terms of a single viscosity coefficient, if this is considered to be a function of the local rate of strain in the material. The theory of flow characterized by a variable viscosity coefficient is discussed in Sections II and III. Non-Newtonian flow of this kind can be thought of as arising from a change in structure of a * Now Professor of Applied Mathematics at the University College of Swansea, University of Wales. This chapter was written while the author was a member of the Maidenhead Research Laboratories of Courtaulds, Ltd., England. 653 654 J. G. OLDROYD material with the rate at which it is being strained, or with the applied stress.

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  Numerical Simulations

  Examples and Applications in Computational Fluid Dynamics

  • Lutz Angermann(Author)
  • 2010(Publication Date)
  • IntechOpen

    (Publisher)

  0 Numerical Simulation in Steady flow of Non-Newtonian Fluids in Pipes with Circular Cross-Section F.J. Galindo-Rosales 1 and F.J. Rubio-Hern´ andez 2 1 Transport Phenomena Research Center University of Porto, 4200-465 Porto 2 Department of Applied Physics II University of M´ alaga, 29071 M´ alaga 1 Portugal 2 Spain 1. Introduction In the chemical and process industries, it is often required to pump fluids over long distances from storage to various processing units and/or from one plant site to another. There may be a substantial frictional pressure loss in both the pipe line and in the individual units themselves. It is thus often necessary to consider the problems of calculating the power requirements for pumping through a given pipe network, the selection of optimum pipe diameter, measurement and control of flow rate, etc. A knowledge of these factors also facilitates the optimal design and layout of flow networks which may represent a significant part of the total plant cost (Chhabra & Richardson, 2008). The treatment in this chapter is restricted to the laminar, steady, incompressible fully developed flow of a non-Newtonian fluid in a circular tube of constant radius. This kind of flow is dominated by shear viscosity. Then, despite the fact that the fluid may have time-dependent behavior, experience has shown that the shear rate dependence of the viscosity is the most significant factor, and the fluid can be treated as a purely viscous or time-independent fluid for which the viscosity model describing the flow curve is given by the Generalized Newtonian model. Time-dependent effects only begin to manifest themselves for flow in non-circular conduits in the form of secondary flows and/or in pipe fittings due to sudden changes in the cross-sectional area available for flow thereby leading to acceleration/deceleration of a fluid element.

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  Numerical Simulation of Non-Newtonian Flow

  • M.J. Crochet, A.R. Davies, K. Walters(Authors)
  • 2012(Publication Date)
  • Elsevier Science

    (Publisher)

  In non- Newtonian f l u i d m e c h a n i c s , t h e c h o i c e o f r h e o l o g i c a l model depends c r i t i c a l l y on t h e t y p e o f f l o w being c o n s i d e r e d ( c f . Chapters 2 and 3) and i t i s t h i s b a s i c c o n s i d e r a t i o n which makes non-Newtonian f l u i d mechanics b a s i c a l l y d i f f e r e n t from c l a s s i c a l f l u i d m e c h a n i c s , where t h e N a v i e r - S t o k e s e q u a t i o n s can be i m m e d i a t e l y accepted as being v a l i d f o r a l l f l o w s i t u a t i o n s ( c f . A s t a r i t a 1 9 7 6 ) . Having chosen t h e most a p p r o p r i a t e r h e o l o g i c a l m o d e l , i t i s t h e n n e c e s s a r y t o s o l v e t h e a s s o c i a t e d e q u a t i o n s i n c o n j u n c t i o n w i t h t h e f a m i l i a r s t r e s s e q u a t i o n s o f m o t i o n and t h e e q u a t i o n o f c o n t i n u i t y , s u b j e c t t o a p p r o p r i a t e boundary c o n - d i t i o n s . Non-Newtonian f l u i d mechanics o f t e n r e q u i r e s t h e s t r e s s components t o be t r e a t e d as dependent v a r i a b l e s a l o n g w i t h t h e v e l o c i t y components and t h e p r e s s u r e - a f u r t h e r c o m p l i c a t i o n from t h e c l a s s i c a l s i t u a t i o n . F u r t h e r m o r e , i t i s n o t i n general s u f f i c i e n t t o s i m p l y t a k e over t h e boundary c o n d i t i o n s o f Newtonian f l u i d mechanics and t h e s e have t o be adapted and extended t o meet t h e new c h a l l e n g e s o f f l u i d s w i t h memory. A l l t h e s e p o i n t s w i l l be e x p l o r e d i n d e p t h i n subsequent c h a p t e r s . The f i n a l e x e r c i s e i n t h e n u m e r i c a l s i m u l a t i o n o f non-Newtonian f l o w r e q u i r e s t h e usual comparison between p r e d i c t i o n s and e x p e r i m e n t a l d a t a .

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