Rotation Viscometer
- 2. o VISCOSITY A fluid flow property. Internal property of a fluid that offers resistance to flow. It is a measure of how easily a fluid can flow. It can also be viewed as viscosity is a resistance to shear force (𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦) 𝛼 Resistance • Formula : Viscosity = Shear str𝑒𝑠𝑠 Shear 𝑅𝑎𝑡𝑒 Introduction
- 3. • There are two types of Viscosity: • 1. Dynamic/Absolute Viscosity(𝝁) Units: 1 Pa.s = 1 kg/(m.s) = 1 N.s/𝑚2 1 Poise = 100 cP = 0.1 Pa.s • 2. Kinetic Viscosity(𝝑): Units: 1 stoke = 1 𝑐𝑚2 /s = 0.0001 𝑚2 /s • Relation between Dynamic and Kinetic viscosity : 𝜗(𝐾𝑖𝑛𝑒𝑡𝑖𝑐) = 𝜇 (𝐷𝑦𝑛𝑎𝑚𝑖𝑐) 𝜌
- 4. • Newtons law of Viscosity : Newton’s law of Viscosity states that, the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers. 𝜏 ∝ ⅆ𝑢 ⅆ𝑦 𝝉 = 𝝁 ⅆ𝒖 ⅆ𝒚 Where, 𝝉 = Shear stress = 𝐹 𝐴 𝝁= Dynamic Viscosity ⅆ𝒖 ⅆ𝒚 = Rate of Shear strain Shear strain
- 5. Methods of Viscosity Measurement • Viscometers • A Viscometer is an instrument used to measure the viscosity of a fluid. • It is also known as Viscosimeter. • Viscometers only measures under one flow condition. Based on working principle, viscometers are divided into three categories: 1. Drag experienced by a falling ball through a fluid (Falling ball viscometer) 2. Drag experienced by one of the concentric cylinders carrying fluid between them when the other cylinder is rotating (Rotating concentric cylinder viscometer) 3. Flow through a capillary tube (Capillary tube viscometer, Ostwald viscometer)
- 6. Rotating Viscometers • These viscometers are suitable for both Newtonian and non-Newtonian systems. • Amongst the most widely used viscometer • Very simple construction
- 7. Eg. MacMicheal viscometer Searle type viscometer (Upper cylinder rotates) Couette type viscometer (Lower cylinder rotates) Eg. Brookfield viscometer Rotation Viscometer Eg. Stormer viscometer Types :
- 8. Construction • Lower cylinder (cup) revolving • Upper cylinder (bob) • Liquid under test • Pulley • Torsion wire • Scale and pointer Lower cylinder revolving at constant angular velocity. To get constant angular velocity, motor is connected to pulley
- 9. Working Principle: • Newton’s law is the basis of the Rotating viscometer. • Based on the principle that the fluid whose viscosity is being measured is sheared between two surfaces. • In these viscometer one of the surface is stationary and other is rotated by an external drive and fluid fills the space in between. • The measurements are conducted by Appling 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.
- 10. 1. Initially, Lower cylinder rotates at 𝜔0 and upper cylinder rotates at 𝜔. 2. After some time, torsion wire get rotated by 𝜃 and angular velocity of upper cylinder becomes zero. 3. At equilibrium condition, torque due to sheared liquid and due to torsion wire will be equal. 4. No slip condition will be obtained at the equilibrium. 5. Equating both torque, we get coefficient of viscocity.
- 11. Derivation Velocity gradient = ⅆ𝑢 ⅆ𝑥 = ⅆ(𝑤𝑥) ⅆ𝑥 = w + x ⅆ𝑤 ⅆ𝑥 Here angular velocity gradient = x ⅆ𝑤 ⅆ𝑥 Considering any layer at distance x from centre line, Force on second layer due first layer is given by, 𝐹 = −𝜂𝐴ⅆ𝑥 ⅆ𝑢 Where , 𝜂 – coefficient of viscosity A – area of cylindrical layer F = −𝜂(2𝛱𝑙)𝑥2 ⅆ𝑤 ⅆ𝑥 (negative due to sig Now , torque is given by 𝜏 = 𝐹𝑥 = −𝜂(2𝛱𝑙)𝑥3 ⅆ𝑤 ⅆ𝑥 Therefore , ⅆ𝜔 = 𝜏 𝜂(2𝛱𝑙)𝑥2 ⅆ𝑥 Integratinng from x=R2 (bob), 𝜔=0 to x=R1 (cup) , 𝜔= 𝜔O
- 12. Finally, we get 𝜏 = 4𝛱𝜂𝑙𝑤𝑜 𝑅1 𝑅2 𝑅1 2−𝑅2 2 For torsion string, 𝜏 = c 𝜃 = (torsional rigidity) 𝑥 (angle rotated) Equating both torque , we get value of coefficient of viscosity. Final equation can be reduced to the form η=K/w Where , K - instrument constant
- 13. Advantages : Can measure viscosities of opaque, settling, or non-Newtonian fluids. Useful for characterizing shear- thinning and time dependent behavior. Speed of the rotating part easily adjusted. Often linked to computers for semiautomated measurement. Disadvantages : Can be relatively expensive. Often large and not portable.