Dynamic Viscosity

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  Liquid Physics and Liquid Chemistry (Concepts and Applications)

  • (Author)
  • 2014(Publication Date)
  • Learning Press

    (Publisher)

  Viscosity coefficients Viscosity coefficients can be defined in two ways: • Dynamic Viscosity , also absolute viscosity , the more usual one (typical units Pa.s, Poise, cP); • Kinematic viscosity is the Dynamic Viscosity divided by the density (typical units m 2 /s, Stokes, cSt). Viscosity is a tensorial quantity that can be decomposed in different ways into two independent components. The most usual decomposition yields the following viscosity coefficients: • Shear viscosity , the most important one, often referred to as simply viscosity , describing the reaction to applied shear stress; simply put, it is the ratio between the pressure exerted on the surface of a fluid, in the lateral or horizontal direction, to the change in velocity of the fluid as you move down in the fluid (this is what is referred to as a velocity gradient). • Volume viscosity or bulk viscosity , describes the reaction to compression, essential for acoustics in fluids. Alternatively, • Extensional viscosity , a linear combination of shear and bulk viscosity, describes the reaction to elongation, widely used for characterizing polymers. For example, at room temperature, water has a dynamic shear viscosity of about 1.0×10 −3 Pa·s and motor oil of about 250×10 −3 Pa·s. Viscosity measurement Viscosity is measured with various types of viscometers and rheometers. A rheometer is used for those fluids which cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. Close ________________________ WORLD TECHNOLOGIES ________________________ temperature control of the fluid is essential to accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change of only 5 °C. For some fluids, viscosity it is a constant over a wide range of shear rates (Newtonian fluids). The fluids without a constant viscosity (non-Newtonian fluids)) cannot be described by a single number.

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  Oxygen-Enhanced Combustion

  • Charles E. Baukal Jr.(Author)
  • 2013(Publication Date)
  • CRC Press

    (Publisher)

  The purpose of this section is to describe viscosity. 9.2.3.1 General Description of Viscosity All fluids exhibit a resistance to flow; this property is called viscosity . In general, viscosity determines the rate at which the motion of fluid flow is slowed or damped. Some fluids exhibit a higher viscosity than other fluids. For example, a highly viscous liquid called pitch flows much slower than water under the influence of gravity; pitch is approximately 230 billion (2.3 × 10 11 ) times more viscous than water. 17 Figure 9.2 is a photograph showing pitch flowing out from a funnel; the flow started in 1927 and is still flowing today. 9.2.3.2 Dynamic Viscosity The Dynamic Viscosity is typically represented by the Greek letter μ (pronounced mu) and is sometimes referred to as the absolute viscosity or pure viscosity. The Dynamic Viscosity is dimensionally equal to mass per length per time (mass/length-time). For example, in SI units, one can write kg/m-s, which is equivalent to N-s/m 2 or Pa-s or dyne-s/cm 2 . The most common unit of viscosity is the dyne-second per square centimeter (dyne-s/cm 2 ), which is usually referred to as poise (P), named after the French physician Jean Louis Marie Poiseuille. Water at 68.4°F (20.2°C) has a Dynamic Viscosity of 1 cP. Several useful conversions are listed in the following: 1 poise p 1 dyn-s/cm 1 g/cm-s 2 ( ) = = 166 Oxygen-Enhanced Combustion 1 poise p 1 centiPoise cP ( ) ( ) = 00 1 poise p 1 Pa-s 1 N-s m 1 kg m-s 2 ( ) . . / . / = = = 0 0 0 1 poise p 2 885 lb -s ft f 2 ( ) . / = 0 00 0 9.2.3.3 Kinematic Viscosity Oftentimes, the viscosity is reported in literature as the Dynamic Viscosity divided by the density of the fluid (μ/ ρ ). This quantity is called the kinematic viscosity and is usually represented by the Greek letter υ (pro-nounced nu): υ μ ρ = (9.6) One reason the kinematic viscosity is often tabulated is because it frequently appears in flow calculations.

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  Mechanical Engineers' Handbook, Volume 1

  Materials and Engineering Mechanics

  • Myer Kutz(Author)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  Figure 1 Fluid (viscous) versus solid (elastic) behavior. (a) Fluid (viscous) behavior: A thin layer of fluid held between two parallel plates, the top plate caused to move relative to the bottom plate by application of a shear stress, will continue to deform (experience shear strain) as long as the shear stress is applied. The rate of shear strain is related to the magnitude of the shear stress. When the shear stress is removed the fluid will remain in its deformed state. (b) Solid (elastic) behavior: A solid will deform (experience shear strain) through some fixed angle when a shear stress is applied. The amount of shear strain is related to the magnitude of the shear stress. When the shear stress is released the solid will return to its original.

  Viscosity (or more precisely the shear viscosity, defined below) is the material property that defines the quantitative relation between the applied shear stress and the shear deformation rate in a fluid. Qualitatively the viscosity indicates the “thickness” or resistance to flow of a fluid. Since viscosity is the property that controls and quantifies the shear stress/shear rate behavior that is definitional to fluids, it is in many regards the most important physical property of a fluid.

  Unfortunately, as alluded to above, the term viscosity is actually used to denote several related, but different, physical properties. It is important to understand these distinctions in terms from the outset. First, the term viscosity is most commonly used in conjunction with effects arising from shear forces and shear deformations in fluids. When used in this context, the most common one, the property is more precisely called the shear viscosity or the “first coefficient of viscosity.” However, when used in this sense, it is almost always simply referred to as “viscosity.” This is contrasted with the bulk viscosity, associated with volume dilatation. Bulk viscosity is rarely an important parameter and hence is not as well known or understood as the more common shear viscosity. Bulk viscosity is discussed briefly in Section 2.5. Second, it should be noted that even the shear viscosity described above is often stated in two different forms, the absolute or dynamic viscosity, , and the kinematic viscosity or momentum diffusivity, , where and

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  Air and Water

  The Biology and Physics of Life's Media

  • Mark Denny(Author)
  • 2020(Publication Date)
  • Princeton University Press

    (Publisher)

  The more viscous the fluid, the greater the force per area required to maintain a given rate of deformation. We can express these ideas mathematically: (5.1) and this relationship is used as a definition of Dynamic Viscosity: 59 F/A u/y ' (5.2) Dynamic Viscosity has the units of N s m 2 . As we have seen, the ratio u/y is a measure of the rate at which the fluid is sheared. This expression for the gradient of velocity is sufficiently precise for the simple geometry used in this example; but for the more general case in which shear can vary from place to place, the gradient is better described as du/dy. Furthermore, the quantity F/A is the shear stress, r, so that one will often see eq. 5.1 and eq. 5.2 expressed in the form T ~ du dy' T du/dy (5.3) (5.4) Implicit in this example is the assumption that by moving one solid plate relative to another, the fluid in between is sheared. In essence, this requires the fluid to stick to each of the plates—if fluid could slip along the plates, movement of the plates would not necessarily shear the fluid. It is an empirical fact, however, that fluid directly in contact with a solid surface does not slide along that surface. The physical basis for this no-slip condition is complicated and not entirely understood (Khurana 1988), but it has immense practical importance. Because of the no-slip condition, the fluid in contact with a solid object is constrained to move at the same speed as the object itself, and if the object is moving relative to the bulk of the fluid, the fluid must be sheared. From eq. 5.1 or eq. 5.3 we see that this shear is accompanied by a force proportional to surface area and to the viscosity of the fluid. Thus, for an object of a given size, the force it feels in moving through a fluid is (at least in part) proportional to viscosity. Therein lies an important set of differences between water and air. The dynamic viscosities of air, fresh water, and seawater are given in table 5.1.

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  On-Line Analysis Instrument

  Instrument Technology

  • E. B. Jones(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  T h e oil industry has for m a n y years been concerned with the kinematic viscosity of liquids. For these reasons the British Standards Institution now specifies kinematic viscosities. Occasionally, particularly in the study of colloids, the term 'fluidity' is used. This is the reciprocal of the viscosity in poises. Laboratory methods of determining viscosity are largely based u p o n equation 7.1 or u p o n Poiseuille's law for the volume Q discharged in a unit time from a tube of length / a n d radius a, i.e. β = τ τ / ν / 8 η / (7.2) where Ρ is the pressure difference between the ends of the tube and η the d y n a m i c viscosity. T h i s equation also forms the basis of a continuous on-line viscometer in which Q is constant a n d Ρ is measured. T h i s relationship holds 263 MEASUREMENT OF VISCOSITY 264 M E A S U R E M E N T OF V I S C O S I T Y only if the flow is streamlined or laminar, i.e. if the Reynolds n u m b e r * is less than the limiting value. Viscosity m e a s u r e m e n t may also be based u p o n the m e a s u r e m e n t of the drag upon a stationary cylinder when placed in a concentric rotating cylinder containing the liquid to be tested, or upon the d r a g on a rotating cylinder w h e n placed in a stationary concentric cylinder. In m o d e r n industrial instruments used for continuous m e a s u r e m e n t s on the processes, other methods of measuring the force required to produce relative motion in a liquid are also used. Ν on-Newtonian liquids Newton's equation (7.1) is based upon the assumption that the force required to maintain a difference of velocity between two planes in a liquid is proportional to the velocity gradient in the liquid between the planes.

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  Essentials and Applications of Food Engineering

  • C. Anandharamakrishnan, S. Padma Ishwarya(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  Table 4.1 .

  4.2.2 Specific Gravity

  Specific gravity is the ratio of the density of a given liquid to the density of water at a given temperature. If the specific gravity is known, the density of the liquid can be determined. An instrument namely hydrometer (Figure 4.1 ) is used to determine the specific gravity of liquids.

  4.3 The Concept of Viscosity

  Viscosity is defined as the internal resistance offered by a fluid to the externally acting forces of deformation. In accordance with Newton’s first law, a fluid continues to flow or remain at rest, until an external force acts on it. The extent of the force required to induce flow of a fluid at a particular velocity depends on its viscosity. The viscosity of a fluid can be expressed in different ways, as explained in the forthcoming sections.

  TABLE 4.1 Density of Selected Liquid Foods at Atmospheric Pressure

  FIGURE 4.1    Schematic diagram of a hydrometer. (Reproduced with permission from Maheshwari, R., Todke, P., Kuche, K., Raval, N. and Tekade, R. K. 2018. Micromeritics in pharmaceutical product development. In Advances in Pharmaceutical Product Development and Research, Dosage Form Design Considerations , ed. R. K. Tekade, 599–635. London: Academic Press.)

  4.3.1 Dynamic Viscosity

  According to Newton, direct proportionality exists between the shear stress and the shear rate. Therefore,

  σ ∝ γ

  ( 4.5 )

  where σ is the shear stress (Pa) and γ is the shear rate (s−1 ).

  A constant of proportionality is introduced to remove the proportionality sign. Thus, Eq. (4.5 ) changes to

  σ = μ γ

  ( 4.6 )

  where μ is the Dynamic Viscosity often called absolute viscosity or viscosity . Thus, viscosity can be defined as the ratio between shear stress and shear strain Eq. (4.7

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  Principles of Polymer Systems

  • Ferdinand Rodriguez, Claude Cohen, Christopher K. Ober, Lynden Archer(Authors)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  Chapter 8 extends this coverage to elastic properties of polymers, which can be as important as viscous flow properties in fabrication processes. Chapters 9 and 10 describe mechan-ical properties and failure characteristics of polymers. 7.2 VISCOSITY 7.2.1 D EFINITIONS AND M ICROSCOPIC O RIGINS We have used the term viscosity up to now without a strict definition. The magnitude of a fluid’s viscosity provides a measure of its resistance to flow. Viscosity is also related to the energy dissipated by a fluid in motion under the action of an applied force. In polymers, energy dissipation arises fundamentally from friction between molecules as they slide by each other in flow. Both the geometry of the polymer repeat unit and the strength of intermolecular forces between these units therefore determine the magnitude of the viscosity. Polymer solutions are generally less vis-cous than their melts because solvent present in the former mediate and in many cases lubricate sliding contacts between molecules. Polymer liquids made up of higher molecular-weight molecules are also usually more viscous because of the larger number of repeat units per polymer chain, which increases the overall fric-tion. Thermodynamic state variables such as pressure and temperature can also affect viscosity. Typically the viscosity of polymer melts decreases with increasing tem-perature and increases with pressure. The flow resistance of a polymer during a fab-rication process is therefore a function of the unique chemical characteristics of the material and the processing conditions such as temperature and applied force. The device depicted in Figure 7.1. is termed a planar Couette shear cell. It pro-vides a simple means for measuring the viscosity of a polymer and also allows for an operational definition of viscosity. In this device, a liquid is sandwiched between two parallel planes separated by a distance d in the y direction.

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  Plastics Engineered Product Design

  • D.V. Rosato, D.V. Rosato(Authors)
  • 2003(Publication Date)
  • Elsevier Science

    (Publisher)

  The general design criteria applicable to plastics are the same as those for metals at elevated temperature; that is, design is based on (1) a deformation limit, and (2) a stress limit (for stress-rupture failure). There are cases where weight is a limiting factor and other cases where short-term properties are important. In computing ordinary short-term characteristics of plastics, the standard stress analysis formulas may be used. For predicting creep and stress-rupture behavior, the method will vary according to circumstances. In viscoelastic materials, relaxation data can be used to predict creep deformations. In other cases the rate theory may be used.

  Viscosity

  In addition to its behavior in viscoelastic behavior in plastic products, viscosity of plastics during processing provides another important relationship to product performances (Chapter 1 ). Different terms are used to identify viscosity characteristics that include methods to determine viscosity such as absolute viscosity, inherent viscosity, relative viscosity, apparent viscosity, intrinsic viscosity, specific viscosity, stoke viscosity, and coefficient viscosity. Other terms are reduced viscosity, specific viscosity, melt index, rheometer, Bingham body, capillary viscometer, capillary rheometer, dilatancy, extrusion rheometer, flow properties, kinematic viscosity, laminar flow, thixotropic, viscometer, viscosity coefficient, viscosity number, viscosity ratio, viscous flow, and yield value.

  The absolute viscosity is the ratio of shear stress to shear rate. It is the property of internal resistance of a fluid that opposes the relative motion of adjacent layers. Basically it is the tangential force on a unit area of either of two parallel planes at a unit distance apart, when the space between the planes is filled and one of the planes moves with unit velocity in its own plane relative to the other. The Bingham body is a substance that behaves somewhat like a Newtonian fluid in that there is a linear relation between rate of shear and shearing forces, but also has a yield value.

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  Rheology for Chemists

  An Introduction

  • J W Goodwin, R W Hughes(Authors)
  • 2019(Publication Date)
  • Royal Society of Chemistry

    (Publisher)

  CHAPTER 3 Viscosity: Low Deborah Number Measurements

  3.1 INITIAL CONSIDERATIONS

  The flow of materials occurs when the deformation that we have produced by applying a stress to the material is not recovered fully after the stress has been removed. This is a familiar concept when we think of the behaviour of common materials such as light oils or water. Indeed, it would be surprising if any of the deformation was recovered, although we shall see that with some solutions and dispersions this is not the case.

  We have seen that with high Deborah number experiments the work done when a stress was applied was stored throughout the microstructure as the components were moved into a higher energy configuration. At Deborah numbers ≪1, the thermal or diffusive motion is sufficient for the microstructure to remain at, or very close to, the low-energy configuration. In other words, the work done is continually dissipated. This gives us the mechanical equivalence of heat and results in the concept of an internal friction coefficient. When the stress that we apply is kept constant, the deformation will occur at a constant rate. As an example of this, we have a sample of our material in a cup with a bob immersed in it, as illustrated in Figure 3.1 . When we apply a constant torque to the bob, it will rotate at a constant angular velocity and so the strain will be increasing at a constant rate. The tangential velocity of the bob surface is v  = dx /dt , and so the rate of strain, , is d(dx /dt )/dt or the velocity gradient. A typical rheogram for water at 25 °C is shown in Figure 3.2 . This rheogram shows a linear relationship between the shear stress and the shear rate and a fluid that exhibits this type of behaviour is known as a Newtonian fluid. The slope of the line gives the coefficient of (shear) viscosity, i.e. , which in this case is ∼9 × 10−4  Pa s. The reciprocal of the viscosity is known as the fluidity, φ

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  Physics of Continuous Matter

  Exotic and Everyday Phenomena in the Macroscopic World

  • B. Lautrup(Author)
  • 2011(Publication Date)
  • CRC Press

    (Publisher)

  15 Viscosity All fluids are viscous, except for a component of liquid helium close to absolute zero tem-perature. Air, water, and oil all put up resistance to flow; and part of the money we spend on transport by plane, ship, or car goes to overcome fluid friction. All the energy in the fuel eventually contributes a small amount to heating the atmosphere and the sea. It is primarily the interplay between the mechanical inertia of a moving fluid and its vis-cosity, that gives rise to all the interesting and beautiful phenomena, the whirling and the swirling that we are so familiar with. If a volume of fluid is set into motion, inertia would dic-tate that it continue in its original motion, were it not checked by the action of internal shear stresses. Viscosity acts as a brake on the free flow of a fluid and will eventually make it come to rest in mechanical equilibrium, unless external driving forces continually supply energy to keep it moving. In an Aristotelian sense the “natural” state of a fluid is thus at rest with pres-sure being the only stress component. Disturbing a fluid at rest slightly, setting it into motion with spatially varying velocity field, will to first order of approximation generate stresses that depend linearly on the spatial derivatives of the velocity field. Fluids with a linear relation-ship between stress and velocity gradients are said to be Newtonian , and the coefficients in this relationship are material constants that characterize the strength of viscosity. In this chapter the formalism for Newtonian viscosity will be set up, culminating in the formulation of the Navier–Stokes equation for incompressible fluids. The slightly more com-plicated generalization to compressible fluids is presented at the end of the chapter. Superfi-cially simple, the Navier–Stokes equation is a nonlinear differential equation for the velocity field that nevertheless continues to be a formidable challenge to engineers, physicists, and mathematicians.

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  Introduction to Chemical Engineering Fluid Mechanics

  • William M. Deen(Author)
  • 2016(Publication Date)
  • Cambridge University Press

    (Publisher)

  Part I Use of experimental data 1 Properties, dimensions, and scales 1.1 INTRODUCTION Fluids, including both gases and liquids, are materials that deform continuously when subjected to shearing forces. If a flowing fluid contains a dye or other tracer, the labeled region tends to change shape from instant to instant. The viscosity of a fluid is a reflection of its resistance to such deformations. This chapter begins with definitions of viscosity and three other material properties that are important in fluid mechanics, namely density, kinematic viscosity, and surface tension. Representative values of each are presented, and some of the differences between Newtonian and non-Newtonian fluids are described. Physical quantities have dimensions , such as mass (M), length (L), and time (T). The concepts of mass, length, and time are more fundamental than the units in a particular system of measurement, such as the kilogram (kg), meter (m), and second (s) that under-lie the SI system. To have general validity, a physical relationship must be independent of the observer, including the observer’s choice of units. That can be achieved by making each variable or parameter in an equation dimensionless , which means that the physical quantities are grouped in such a way that their dimensions cancel. Dimensionless param-eters are ratios, and often the numerator and denominator are each the scale of a variable. A scale is the maximum value of something, such as a velocity or force. Thus, the numer-ical value of such a group reveals how two things compare, and thereby offers insight into what is important in the process or phenomenon under consideration and what might be negligible. Several dimensionless groups that arise in fluid mechanics are discussed. Dimensional analysis, the last major topic of the chapter, provides a systematic way to identify the dimensionless groups that are involved in something of interest.

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