Dynamic viscosity
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This document discusses fluid mechanics and viscosity. It begins by defining a fluid and explaining that fluids deform continuously under shear forces rather than resist deformation like solids. It then discusses viscosity, defining it as a fluid's resistance to flow. Viscosity exists due to molecular collisions and momentum transfer between layers of a fluid. Methods for measuring viscosity include viscometers that apply shear stresses between fluid layers. Viscosity affects fluid dynamics, causes drag, and is accounted for in the Navier-Stokes equations.
Dynamic viscosity
- 1. Department of Mechanical Engineering Don Bosco College of Engineering and Technology, ADBU By Dipjyoti Deka 1/18/2019 1
- 2. INTRODUCTION The two aspects of fluid mechanics:- 1. The nature of a fluid is much different to that of solid. 2. In fluids, we usually deal with continuous streams of fluid without a beginning or end. We normally recognize three states of matter: solid, liquid and gas. However, liquid and gas are both fluids; in contrast to solids they lack the ability to deformation. Because a fluid cannot resist the deformation force, it moves up, it flows under the action of the force. Its shape will change continuously as ling as force is applied. 1/18/2019 2
- 3. The deformation is caused by shearing forces which act tangentially to a surface. As we can see the force F acting tangentially on a rectangular element ABCD. This is a shearing force and produces the rhombus element A’B' A D B B’ C A’ Shearing force F, acting on the fluid element. Hence, we can say that A fluid is a substance which deforms continuously when subjected to shearing forces. 1/18/2019 3
- 4. VISCOSITY A property of fluid to resist the rate of deformation- a quantitive measure of a fluid’s resistance to flow (water v/s syrup). It takes place when a fluid is acted upon by a shear stress. It is an important fluid property when analyzing liquid behavior and fluid motion near solid boundaries. The shear resistance in a fluid is caused by intermolecular friction exerted when layers of fluid attempt to slide by one another. There are two related measures of fluid viscosity: • Dynamic or Absolute • Kinematic 1/18/2019 4
- 5. Why does viscosity exist in fluid flow 1/18/2019 5 Molecular collisions – the molecules of the fluid bump into each other, slowing down their motion Momentum transfer from higher momentum to lower - momentum is mass times velocity, mu. During a collision, momentum will be transferred. Measured by shear stress τ,, which is the tangential force divided by the area
- 6. Fluid with low viscosity Fluid with high viscosity 1/18/2019 6
- 7. Newton’s law of Viscosity Viscosity is the physical property that characterizes the flow resistance of simple fluids. Newton’s law of viscosity defines the relationship between the shear stress and shear rate of a fluid subjected to a mechanical stress. The ratio of shear stress to shear rate is constant, for a given temperature and pressure, and is defined as the viscosity or coefficient of viscosity. Newtonian’s fluids obey Newton’s law of viscosity. Thus, Viscosity is independent of the shear rate. Similarly, Non-Newtonian fluids do not follow Newton’s law and thus, their viscosity (ratio of shear stress to shear rate) is not constant and is dependent on the shear rate. 1/18/2019 7
- 8. Dynamic viscosity:- It is the tangential force per unit area required to move one horizontal plane with respect to an other plane- at an unit velocity- when maintaining an unit distance apart in the fluid. The shearing stress between the layers of a non-turbulent fluid moving in straight parallel lines can be defined for a Newtonian Fluid as: 1/18/2019 8
- 9. Fig shows two fluid layers at distance y and y+dy from the surface. They move with different velocities u and u+du as shown in fig. The top layer causes a shear stress on lower while lower layer causes shear stress on the top layer. The shear stress τ is proportional to the rate of change of velocity with respect y. Mathematically, 𝜏α 𝑑𝑢 𝑑𝑦 𝜏 = μ 𝑑𝑢 𝑑𝑦 Here constant of proportionality μ is known as the coefficient of dynamic viscosity 𝑑𝑢 𝑑𝑦 known as the velocity gradient. From the above equation μ= 𝜏 𝑑𝑢 𝑑𝑦 1/18/2019 9
- 10. Causes of Viscosity in Fluids 1/18/2019 10 Viscosity in Gasses The molecules of gasses are only weakly kept in position by molecular cohesion (as they are so far apart). As adjacent layers move by each other there is a continuous exchange of molecules. Molecules of a slower layer move to faster layers causing a drag, while molecules moving the other way exert an acceleration force. Mathematical considerations of this momentum exchange can lead to Newton law of viscosity. If temperature of a gas increases the momentum exchange between layers will increase thus increasing viscosity. Viscosity will also change with pressure - but under normal conditions this change is negligible in gasses.
- 11. 1/18/2019 11 Viscosity in Gasses
- 12. Viscosity in Liquids There is some molecular interchange between adjacent layers in liquids - but as the molecules are so much closer than in gasses the cohesive forces hold the molecules in place much more rigidly. This cohesion plays an important roll in the viscosity of liquids. Increasing the temperature of a fluid reduces the cohesive forces and increases the molecular interchange. Reducing cohesive forces reduces shear stress, while increasing molecular interchange increases shear stress. Because of this complex interrelation the effect of temperature on viscosity has something of the form: where is the viscosity at temperature T°C, and is the viscosity at temperature 0°C. A and B are constants for a particular fluid. High pressure can also change the viscosity of a liquid. As pressure increases the relative movement of molecules requires more energy hence viscosity increases. 1/18/2019 12
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- 14. Viscosity Measurements • These viscometer give the value of the ‘dynamic viscosity’. • It is based on the principle that the fluid whose viscosity is being measured is sheared between two surfaces. • In these viscometers one of the surfaces is stationary and the other is rotated by an external drive and the fluid fills the space in between. • The measurements are conducted by applying either a constant torque and measuring the changes in the speed of rotation or applying a constant speed and measuring the changes in the torque. • There are two main types of these viscometers: rotating cylinder and cone-on-plate viscometers. 1/18/2019 14
- 15. Viscosity Measurements continue….. Rotating cylinder viscometer 1/18/2019 15
- 16. Cone-on-plate viscometer Viscosity Measurements continue….. 1/18/2019 16
- 17. Fluid flow between two parallel plates The bottom plate is fixed and the top plate is accelerated by applying some force that acts from left to right. The upper plate will be accelerated to some terminal velocity and the fluid between the plates will be set into motion. Terminal velocity is achieved when the applied force is balanced by a resisting force (shown as an equal but opposite force applied by the stationary bottom plate). 1/18/2019 17
- 18. As the upper plate begins to accelerate the velocity of the fluid molecules in contact with the plate is equal to the velocity of the plate (a no slip condition exists between the plate and the fluid). Fluid molecules in contact with those against the plate will be accelerated due to the viscous attraction between them... and so on through the column of fluid. The viscosity of the fluid ( , is the attraction between fluid molecules) results in layers of fluid that are increasingly further from the moving plate being set into motion. 1/18/2019 18
- 19. The velocity gradient (the rate of change in velocity between plates; du/dy) will be constant and the velocity will increase linearly from zero at the bottom plate to Uterm at the top plate. Terminal velocity is achieved when the resisting force (the force shown applied by the bottom plate) is equal but opposite to the force applied to the top plate (forces are equal so that there is no change in velocity with time). The bottom plate and water molecules attached to it are stationary (zero velocity; no slip between molecules of fluid and the plate) so that eventually the velocity will vary from zero at the bottom to Uterm at the top which is equal to the terminal velocity of the upper plate. 1/18/2019 19
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- 22. Effect of viscosity on velocity profile 1/18/2019 22 Fluid flow is highly dependent on the viscosity of fluids. At the same time for a non-Newtonian fluid, the viscosity is determined by the flow characteristics . Looking at Figure , we can observe three very different velocity profiles depending on the fluid behavior. For all these fluids, the shear rate at the walls (i.e. the slope of the velocity profile near the wall) is going to determine viscosity. Successful characterization of viscosity is key in determining if a fluid is Newtonian or non-Newtonian, and what range of shear rates needs to be considered for an specific application.
- 23. Several fundamental effects are produced by viscosity: 1/18/2019 23 Drag: Skin friction drag caused by shear stresses at the surface contribute a majority of the drag of most airplanes. The pressure distribution: is changed by the presence of a boundary layer, even when no significant separation is present. Flow separation: Viscosity is responsible for flow separation which causes major changes to the flow patterns and pressures.
- 24. 1/18/2019 24 Viscosity and Navier–Stokes equations The Navier–Stokes equations, describe the motion of viscous fluid substances. These balance equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term and a pressure term—hence describing viscous flow. Viscosity and Coutette’s flow Couette flow is the laminar flow of a viscous fluid in the space between two parallel plates, one of which is moving relative to the other. The flow is driven by virtue of viscous drag force acting on the fluid and the applied pressure gradient parallel to the plates.
- 25. Viscosity Effects In Dynamic Light Scattering Measurements 1/18/2019 25 • Dynamic light scattering (DLS) is a method for monitoring crystallization processes, solutions. • DLS measures how fast the particles diffuse through the liquid. • Smaller particles diffuse faster than larger ones. • Solvent viscosity effect the measurement. • For precise determination of particle size, it is essential to know the exact viscosity value of the solvent.
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