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# Viscosity of Liquids

The viscosity of a liquid is a measure of its resistance to deformation and is mainly because of the internal frictional force which develops in between the various layers of liquids. These layers are forced to move in relative to each other. The viscosity of a liquid is considered to be directly related to the overall pumping power necessary to transfer a liquid in a pipe or to move a body through a liquid.

Viscosity is mainly caused by the omnipresent cohesive forces in between the liquid molecules and also by the collisions rate of the gaseous molecules. These keeps varying in great limits with temperature.

Viscosity of liquids decrease with temperature and compared to this viscosity of gases increase with temperature. This peculiarity is mainly because liquids molecules possess more energy at higher temperature and can oppose the large cohesive inter molecular forces and move freely. In liquid mechanics and heat transfer, the ratio is given the name kinematic viscosity and pioneering work on this was done by Eugene Bingham in early 20th century.

## Viscosity of Liquids Definition

When two solids are in contact they move relative to each other and develop a frictional force at the surface of contact in the opposite direction of motion. The magnitude of the force needed to move along depends on the friction coefficients between the two bodies. A similar situation is observed when a liquid moves relative to a solid or when two liquids move relative to each other.

Moving in air is easy but not in liquid and is more difficult in more viscous liquid like oil. It appears that there is property that represent the internal resistance of a liquid to motion or the liquidity. This property is better known as viscosity.

The force, a flowing liquid exerts on a body in the flow direction is called drag force and the magnitude of this force depends partly on viscosity.
Viscosity values corresponds to a nominal pressure of 1 atm. If a value is given at a temperature above the normal boiling point, the applicable pressure is understood to be the vapour pressure of liquid at that temperature.

A few values are observed at a temperature slightly below the normal freezing point and hence refer to the super cooled liquid.

In order to find a working relationship for viscosity we usually take a liquid layer in between a couple of very large parallel flow edges. These flow edges are separated by a specific distance of ‘I’ along with a constant parallel force ‘F’.

This force is worked out for the given upper flow edge and at the same time the lower flow edge remains fixed.

Once the initial transient is over we get to see the upper flow edge moving continuously due to the effect of this force at a constant speed V.
The liquid which is flowing and is in contact with the top flow edge now sticks to the plate surface and begins moving along with it.

The speed remains same and the shear stress $\tau$ acting on this liquid layer is given out in a specific relationship as:

Hence, $\tau$ = $\frac{F}{A}$

Where, A is considered as the overall area between the edge of the container surface and that of the liquid.

The liquid region which is in contact with the lower flow edge now carries the flow velocity of zero.

In this steady laminar flow, the velocity of the liquid between these two surface edges now differs in a straight line between 0 and velocity attained V.

So we get to see a velocity profile along with velocity gradient given out as follows:
• u (y) = (y / L) V
• and, $\frac{du}{dx}$ = $\frac{V}{L}$
Here, ‘x’ is considered to be the perpendicular distance between the two flow edges.

The absolute viscosity of some common liquids within the temperature between -25 C and 100 C is given according to the experimental data to suit expressions for the temperature dependence.

The rate at which the deformation for liquids takes place is found to be linearly proportional to the affected shear stress.

The velocity of each of these successive layers keep increasing as we move from the edge of the flow towards the centre of the flow. Each of these layers move with higher velocity over the other with lower velocity and hence these layers of flow experience a retarding effect due to frictional force existing in between.

The resistance which these subsequent layers come to experience in between the differently moving liquid flow give rise to the viscous characteristics.

If we consider the area of such layers, then A is designated as the area of the layer, dx as the distance between the layers, and du as the difference which exist between the velocity flows.

The tangential force which will be now required to maintain a constant velocity in between the layers for a flow to work efficiently, will be directly proportional to ‘A’ and ‘du’.

This tangential force is indirectly proportional to ‘dx’.

Therefore, F $\propto$ A  $\frac{du}{dx}$

Or, F = $\eta$ A $\frac{du}{dx}$

Here, the η is considered as the proportionality constant for viscosity or simply coefficient of viscosity. The reciprocal of this is termed as fluidity.
The coefficient of viscosity η = (dynes) (cm) / (cm2) (cm/s) or, dynes / cm2 s

The shear force acting on a Newtonian liquid layer is,
Shear force: F = τ A = $\eta$ A $\frac{du}{dx}$

Where, A is the contact area between the edge of flow and liquid.

Then the force, F necessary in order to move the upper edge of the liquid flow and the lower edge of the liquid flow remaining stationary at a constant speed V is given by:

F = $\eta$ A  $\frac{V}{I}$

In a gas intermolecular forces are of very negligible value and the gaseous molecules move fast and in a random manner at high temperatures.
These random movements give rise to more collisions amongst the participating molecules per unit volume and unit time. This results in greater resistance to flow.

The gaseous kinetic theory gives an idea that the viscosity of gases is proportional to the square root of temperature.
For gases:

$\mu$ = [(a T1/2) / (1 + b/T)]

Where, T is absolute temperature and ‘a’ and ‘b’ are both determined constants calculated experimentally.
The measuring viscosity at two different temperatures is sufficient to determine these constants.
For liquids the viscosity is:

$\mu$ = a 10b / (T – c)

Where, T is the absolute temperature, while a, b, and c are the determined constants calculated from experiments.

The viscosities of some liquids at room temperature differ by several orders of magnitude. Also note that it is comparatively difficult to push an object in a liquid with higher viscosity like organic oils than in a liquid with lower viscosity like water.

Liquids are much more viscous than gases.

For non- Newtonian liquids, the relationship which exist between shear stress and rate at which the deformation takes place is not linear.
The curve slope given out by τ versus $\frac{du}{dx}$ is notably considered as the apparent viscosity of the liquid.

## Viscosity of Liquids Formula

$\mu$ = a 10b / (T – c)

Where, T is absolute temperature and a, b, and c are experimentally determined constants.

## Viscosity of Liquids Experiment

The viscosity of liquid results from the overall internal friction which exist in the liquid and is distinctly considered to be the resistance of the liquid to flow.

Newtonian liquids have a constant viscosity regardless of strain rate. Low molecular weight pure liquids are examples of Newtonians liquids.
Non-Newtonian liquids do not have a constant viscosity and will either thicken or thin when strain is applied. The examples are polymers, colloidal suspensions and emulsions.

Experimentally the calculated viscosity values are usually observed as either the absolute viscosity (η) or as the kinematic values (v).
Kinematic viscosity is nothing but the absolute viscosity standardised by the liquid density. The relationship which exist between absolute viscosity ${\eta}$, density ${\rho}$ and kinematic viscosity (v) is as follows:

v =  $\frac{\eta}{\rho}$

The viscosities of ionic liquids are normally measured using one of three methods:
• rolling ball
• capillary
• rotational
Falling ball viscometer can be made easily by using a graduated cylinder with perfectly characterised ball bearings.
• The ball bearing material and diameter can be varied.
• The experiment is conducted by filling the graduated cylinder with the liquid to be investigated and carefully dropping the ball through the liquid.
After allowing the ball to reach steady state the velocity is measured. The absolute viscosity is calculated using stokes law.

η = (2/9) [(ρs – ρ) g R2 / v]

Where, η is absolute viscosity, ρs is density of ball, ρ is the density of liquid, g is the gravity constant and R is the radius of the ball, finally the ‘v’ is steady state velocity of the ball.

Any common falling or rolling ball viscometer is calibrated with a standard liquid that is similar in viscosity of the liquid of interest and an instrument constant is then determined (k).

## Viscosity of Liquids Table

The viscosity of liquids at various temperature are as follows:

 Liquid 0 C 20 C 40 C 70 C Water 1.787 1.002 0.653 0.407 Ether 0.286 0.234 0.197 NA Chloroform 0.7 0.564 0.465 NA Benzene 0.902 0.649 0.492 0.351

## Factors Affecting Viscosity of Liquids

There is usually a direct non-linear relationship between the concentration of a solute and viscosity at constant temperature. It is typical of the concentration effect on viscosity. The concentration may also determine the type of flow behavior.
• Amongst similar substances an increase in molecular weight results in an increase in viscosity
• Branched chain compounds have higher viscosity than those involving straight chains
• The polar compounds are more viscous than the non-polar ones. Presence of directed bonds such as hydrogen bond causes the viscosity to increase
• The viscosity of liquids increase by the presence of solutes lyophilic colloids and suspended impurities
• Temperature has a marked influence on the viscosity of a liquid. Increase in temperature results in rapid decrease in viscosity
The influence of temperature on viscosity is best given out as:

η = AeB/RT

Where, A and B are constants for the given liquid.

Molecular viscosity is the result of molecular surface product, or molecular viscosity = (M /d)2/3 η

Where, M and ‘d’ are the molecular weight and density of the liquid.

Unlike the viscosity, the molecular form is independent of temperature and is both additive as well as constitutive property. Rheochor is the product of molar volume and eight root of coefficient of viscosity is also a constant, and independent of temperature. Newton called this as Rheochor which is both additive and constitutive property.

Rheochor = M η1/8 / d

Factors which affect the viscosity of a liquid are as follows:
• Temperature: viscosity of a liquid decrease rapidly with increasing temperature
• Size and weight of molecules: viscosity increases with increasing molecular weight but for compounds belonging to same chemical class
• Shape of molecules: viscosity increase as branching in chain increases as well Intermolecular forces: polar compounds are more viscous than non-polar ones because of hydrogen bonding between the molecules. Example, chloroform is heavier than water but viscosity is less than water.
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