VISCOSITY

Viscosity is a characteristic property of all fluids. The internal resistance to flow of a liquid is called viscosity. Viscosity of a liquid is defined as its property by virtue of which it tends to oppose the relative motion between its different layers. In other words, it may be regarded as an internal friction between the different layers of a liquid. Resistance to flow is largely due to the intermolecular attractive forces-Van der Waal's forces in liquids.

A liquid that flows with ease is said to be mobile, whereas a liquid that does not flow easily is said to be viscous. To some extent, we can picture a mobile liquid as one whose molecules flow smoothly over each other, with few tangles between the layers. In a viscous liquid, tangles between molecules in different layers interfere with the smooth flow. The greater the viscosity, the less mobile will be the liquid. Molten polymeric materials and glass are highly viscous because their large molecules become greatly entangled. In order to make viscosity mare understandable, consider a liquid flowing through a tube consisting of concentric Inyers. The layers in contact with the walls of the tube remain stationary, whereas the layer in the centre has the maximum velocity and intermediate layers move with a gradation of velocities. Each layer exerts a drag on the next layer due to internal friction. When a steady flow is reached, the velocity difference between any two layers will become constant.

 

The flow of liquid through a tube is said to be stream-lined (laminar, non-turbulant or Newtonian), if the path of every moving particle of the liquid coincides with the line motion of liquid as a whole Fig. The flow is termed turbulent, if the motion of liquid particles is a disordered one, and an actual mass transport from layer to another takes place.

Consider two adjacent moving layers of a liquid, which are separated by a distance dr and have a velocity difference dv. The force of friction (F) resisting the relative motion of two layers is directly proportional to the area A and the velocity difference dv and is inversely proportional to the distance, dx, between the two layers, i.e.,

 F A dv/dx  or F = nA dv/ dx

where dv/dz is the velocity gradient and n is called the coefficient of viscosity, and is defined as, the force per unit area required to maintain a unit difference of velocity between two parallel layers of a liquid, unit distance apart at a given temperature.

 Dimensions and Units of ໗. From Eq.

  ໗= force/area×distance/velocity =newton×m/ m2×ms-1=kgms-2×m/m2×ms-1=kgm-1s-1

 

, The SI unit of coefficient of viscosity ໗ is kg m-1 s-1. the CGS system, the dimensi of n are delta' are generally cm-1 s-1 and is called a poise. Since this unit is rather large, viscosities usually given in centipoise ( 10 ^ - 2 poise). The relation of poise to SI units is, eta= force area * distance velocity = newton* m m ^ 2 * m * s ^ - 1 = (kgm * s ^ - 2 * m)/(m ^ 2 * m * s ^ - 1) = kg * m ^ - 1 * pi ^ - 1

 

          1 poise 10-1 kg m -18-1

 

The reciprocal of coefficient of viscosity is called fluidity.

         Fluidity =1/໗

 

MEASUREMENT AND VISCOSITY

Most methods, used for the measurementPoiseuille's equation. The Poiseuille's Equation for the coefficient of viscosity of liquids is

       ໗=pi ptr4/8VL

where is the volume of a liquid having viscosity n flowing through a capillary tube of radius and length L in time t (seconds) under an applied pressure  

It is found empirically that Poiseuille equation governs the flow of liquids only when the diameter of the tube is small and the flow rate is slow and steady. When the flow rate becomes higher or the diameter of the tube is enlarged, the type of flow changes from stream-lined to turbulent or non-Newtonian. Eq. (16) is applicable only to stream-lined or laminar flow of liquids.

In order to decide the type of flow, we use the Reynold's number (a dimensionles quantity) empirically defined by the equation:

Reynold's number =2rvd/n

 where is the radius of the tube, v coefficient of viscosity. (17)

 average velocity of liquid, d density, and

Empirically, it has been seen, if the Reynold's number is equal or less than 2000. the flow is Newtonian, and if the value is greater than 4000, it is turbulent (Non-Newtonian), and for the intermedinte values the type of flow cannot easily be anticipated eta =

The direct experimental measurement of absolute viscosity of a liquid using Poiseuille's equation offers considerable difficulty, since measurement of P. r. and V involves considerable difficulty. Therefore, the viscosities of liquids are expressed in relative terms, that is in terms of ratio of the viscosity of the sample of a liquid to the viscosity of water taken as the reference standard. This is called relative viscosity. If we measure the time of flow of the same volume of two different liquids through the same capillary, then the expression for relative viscosity (eta_{1} / eta_{2}) can be derived from the Poiseuille equation as:

 

eta_{1}/eta_{2} = (pi*P_{1}*t_{2} * r ^ 4)/(8VL) * (8VL)/(pi*P_{2}*t_{2} * r ^ 4) = (P_{1}*t_{1})/(P_{2}*t_{2})

 

 Since the P_{1} and P_{2} are directly proportional to the densities of the two liquids d_{1} and d_{2r} we may write:

 

or (18) eta_{1}/eta_{2} = (P_{1}*t_{1})/(P_{2}*t_{2}) = (d_{1}*t_{1})/(d_{2}*t_{2}) eta_{1} = (d_{1}*t_{7})/(d_{2}*t_{2}) * eta_{2}

d_{1} d_{2} and eta_{2} are known, determination of t_{1} and t_{2} permits the calculation of the viscosity coefficient of the liquid under examinationThe quantities t_{1} and t_{2} are conveniently determined with the help of a discoverer.