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Viscosity Measurement

The viscosity measurement is important in many of the process that we get to see around us. Whether its food industry or medicine, the viscosity of raw materials has a direct effect on the final product quality. In case we are looking at the ceramic industries, the quality of the raw materials affects the final product quality. In-fact, viscosity control is also very important in assembly operations that involve the application of grinding and flow of materials through pipelines.

The final assembly of such products require these materials to flow through tubes at the right consistency and rate and hence the role of viscosity becomes of utmost importance. Viscosity helps in describing the manner in which the fluid flows when a force is applied to the fluid matter. The fluid rates also vary significantly at high shear rates and the viscosity also might vary at low shear rates. The best category of example is non-Newtonian characteristics which tend to take place in emulsion, pastes and various types of slurries. 

The relationship which exists between input variables and output measurement for instruments that actually measure viscosity assumes that the measured fluid has Newtonian characteristics. For any non-Newtonian fluids, the shear rate variation correction is essential and unless these corrections are not made the measurement that is obtained is known as apparent viscosity and can differ by large margin from true viscosity. This true viscosity is also known as absolute viscosity and can change according to three specific physical principles.
  • Rate of flow of the fluid through a capillary tube
  • Rate of fall of a body inside the fluid
  • Viscous frictional force which exerts on a rotating body

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Viscosity Measurement Formula

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Viscosity describes the way in which a fluid flows when it is subjected to applied force. If we consider a cubic volume of fluid and if a shear force F is applied to one of its face with an area A, and this face moves through a distance L at a velocity of V as compared to the opposite face of cube, then the shear stress (s) and shear rate shows a relationship of: s = $\frac{F}{A}$ OR r = $\frac{V}{L}$

The coefficient of viscosity (Cv) = $\frac{s}{r}$

Hence, Cv or viscosity = $\frac{(\frac{F}{A})}{\frac{V}{L}}$

OR, Cv = $\frac{F*L}{A*V}$

Kinematic viscosity Kv = $\frac{Cv}{\rho}$ (fluid density) 

Cv is measured in $\frac{Ns}{m2}$ while Kv is measured in stokes or $\frac{m2}{s}$

Viscosity Measurement Experiment

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Viscosity of gas or liquid mixtures under pressure.
  • This is not only important in order to determine the solubility of gas but also the impact of dissolved gas in fluid viscosity.
  • This is also very importance in determining the lubricating ability of the compressor fluid during gas compression.
  • Measurement of viscosity of lubricants saturated with gas at elevated pressure is done in a fixed volume apparatus. Typically a Parr reactor equipped with a stirrer, pressure transducer, thermocouples and heating and cooling device is used to conduct these experiments at desired temperatures.
  • This vessel fitted with viscosity measurement probe suitable for measurement at high pressure.
  • Viscosity probe that can operate up to 340 bars are used in such cases.
  • Viscosity and gas solubility data at a given temperature and pressure can be obtained from same experiment.
  • Viscosity of saturated lubricant at a final pressure is measured with a viscosity probe and its associated electronics.
  • Gas solubility can be calculated from initial and final pressure using gas laws and compressibility factors and can be obtained by weighing the gas charging container both before and after equilibrium.
Absorption of the lubricant into gas phase.
  • This is one of the test procedure performed to determine the amount of lubricant lost into the gas being compressed.
  • This test is conducted by weighing the test oil into a miniscule aluminium container and then finally placed into a 50 mL stainless steel high pressure reactor heated up to 100 C.
  • The test gas is exposed to 400 bar and fed through stainless steel tubing into stainless steel reactor containing the test oil.
  • The pressure is maintained by releasing the gas through a needle valve and the overall volume of the gas getting discharged with the help of a meter.
  • Finally the aluminium vessel is measured again and weight loss if any is recorded.

Viscosity Measurement Methods

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The most important thing we need to remember is that measuring viscosity of any fluid essentially is temperature dependent. The idea of viscosity measuring is very important in both manufacturing and academic circle. The specific viscosity knowledge is essential for various industrial process and theories which are developed for predicting or estimating viscosity. The various instruments that are used for such measurement activities are classified into 
  • Capillary viscometers
  • Orifice viscometers
  • High temperature and high shear rate viscometer
  • Rotational viscometer
  • Vibrational viscometer
  • Ultrasonic viscometer
  • Falling ball viscometer
A number of viscometers combine features of two or three types of viscometers and calibrate all the readings into one. 

Absolute viscosity
The derived units of absolute viscosity µ in SI is Kg / m*s which is equivalent to Pa * s or Pascal seconds. In CGS system the units is dyne * s / cm2 and is better known as Poise. The Poise is used in FPS system of units.

Kinematic viscosity 
Kinematic viscosity (v) is defined as the absolute viscosity divided by the fluid density ρ (rho). The fundamental units in SI for kinematic viscosity are meter square per second and is identical to the units of thermal diffusivity used in heat transfer and mass of the matter diffusivity used in diffusion. 

This gives us the idea that kinematic viscosity referred as coefficient of momentum diffusivity is cm2 / second or better known as stokes.  

Driving pressure P can be replaced by h * g * ρ where, h is the mean head, g as the gravity and ρ as fluid density.

The Hagen Poiseuille equation is given out as: 

η = K ρ t where, K is the instrument conversion factor and is also a constant for each instrument.

Hence, $\frac{\eta}{\rho}$ = Kt or v = Kt as kinematic viscosity v = $\frac{\eta}{\rho}$

The kinematic viscosity of the fluid is obtained by multiplying the measured effux time with instrument conversion factor. If the instrument conversion K is not available then it can be obtained by measuring the effux time for a fluid of known viscosity.

Glass capillary viscometer 
These are widely used for measuring low to medium viscosity Newtonian fluids as their degree of accuracy and cost factors are low.

Application of Viscosity Measurement

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Collection of viscosity data on a particular material gives the manufacturers the advantage of predicting how a material will behave in utility point. Products like toothpaste, and creams can be made to perfection if the viscosity is known as these help the manufacturers to gauge how the product will behave at consumer level and specific weather pattern. These also help in perfecting product design and transporting these to long destinations.

Food industry:
Viscosity measurement are widely used for the product consistency as the consumer level satisfaction is utmost. Optimisation of products depend upon how the product is packaged and how these are transported and reaches the consumers in good condition.

Adhesive industry:
The type of consistence an adhesive product behaves also goes a long way to create a brand image as the faster the glue sticks and dries can help design the package and container for such brands.

Petroleum industry:
The oil mix and engine oil viscosity is utmost for the longevity of vehicle engine and this goes a long way in creating a brand niche and hence the viscosity of these products is very important as it can make or break an engine completely along with the manufacture goodwill.  

Cosmetic industry:
The cosmetic industry thrives on consumer satisfaction and hence, the same type of products with different viscosity can go for a toss as most of the products are rejected at consumer level due to the viscosity factor.

Dynamic Viscosity Measurement

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Viscosity is nothing but the resistance provided by the fluids to shear. The fluid molecules in contact with the bottom plate are considered to be at rest and the molecules in contact with top plate are moving at a velocity v. 

The velocity profile for the two plates are created and the velocity profile’s slope would be given out as: 

Slope = $\frac{\Delta V}{\Delta y}$. 
Velocity Profile Slope
These plates with a cross section area of A, would require a force F to keep this fluid in motion and hence the velocity v. 

The shear stress (Ï„) = $\frac{F}{A}$

The dynamic viscosity or also known as absolute viscosity is defined as the ratio between the shear stress and slope. 

Hence, µ =$\frac{\tau}{\frac{v}{y}}$ 

Or, µ = $\frac{F*y}{v*A}$

Here, the force F is in dyne, y is given out in cm, velocity in cm / seconds and A is given out in square cm. the units of dynamic viscosity is given out by g / (s *cm). This is given out as Poise. If we divide this value by 100 then we get Centi poise.

Kinematic viscosity is considered as ‘dynamic viscosity / fluid density’ under same temperature values. This is in other words considered as dynamic viscosity measurement. The µ is dynamic viscosity (g / s cm) and ρ is density (g / cc)
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