Viscosity
The internal friction of liquids and the mechanics of Laminar Flow.
Why does water flow quickly out of a glass, while honey or thick motor oil pours very slowly? This resistance to flow is known as Viscosity. It is essentially the internal friction present between the different layers of a moving liquid.
1. Laminar Flow & The Velocity Gradient
When a liquid flows steadily over a fixed surface (like the bottom of a pipe or a glass plate), it doesn't move as one solid block. It flows in layers. This is called Laminar Flow.
- The layer in direct contact with the stationary surface is held back by strong adhesive forces and has zero velocity.
- As you move upward, each subsequent layer slides over the one below it. The upper layer tries to accelerate the lower layer, while the lower layer tries to drag the upper layer backward (internal friction).
- The change in velocity ($dv$) over a vertical distance ($dz$) is called the Velocity Gradient ($\frac{dv}{dz}$).
2. Coefficient of Viscosity ($\eta$)
Sir Isaac Newton observed that the internal frictional force ($F$) acting between two layers of a liquid is directly proportional to:
1. The area of contact between the layers ($A$).
2. The velocity gradient ($\frac{dv}{dz}$).
To remove the proportionality sign, we introduce a constant ($\eta$, pronounced "eta"):
Definition: The Coefficient of Viscosity ($\eta$) is defined as the force of friction required to maintain a unit velocity difference between two parallel layers of a liquid, each of unit area, separated by a unit distance.
3. Units and Dimensional Formula
Because viscosity is heavily tested in physics and chemistry, mastering its units is non-negotiable.
A. SI Units
Rearranging the formula gives $\eta = \frac{F}{A \cdot (dv/dz)}$.
Plugging in SI units: $\frac{\text{Newton}}{\text{m}^2 \cdot (\text{m/s}) / \text{m}} = \text{Newton} \cdot \text{second} \cdot \text{meter}^{-2} \mathbf{(N \cdot s \cdot m^{-2})}$.
Since $1 \text{ N/m}^2 = 1 \text{ Pascal (Pa)}$, the standard SI unit is $\text{Pascal-second (Pa} \cdot \text{s)}$.
B. CGS Units (The Poise)
In the older CGS system, the unit is $g \cdot cm^{-1} \cdot s^{-1}$. In honor of Jean Poiseuille, this unit is called the Poise (P).
The Critical Conversion:
$$1 \text{ Pa} \cdot \text{s} = 10 \text{ Poise}$$
$$1 \text{ Poise} = 0.1 \text{ Pa} \cdot \text{s}$$
4. Factors Affecting Viscosity
1. Intermolecular Forces
Viscosity is a direct reflection of how strongly molecules hold onto each other. Liquids with strong intermolecular forces (like hydrogen bonding) are highly viscous.
Example: Glycerol has three $-OH$ groups, allowing extensive hydrogen bonding. It is much more viscous than water (one $-OH$ equivalent) and ether (no hydrogen bonding).
2. Molecular Size and Shape
Large, complex, or long-chain molecules (like those in heavy motor oils or polymers) tend to entangle with each other as they flow, creating massive internal friction and very high viscosity. Compact, spherical molecules flow much easier.
3. Temperature (Crucial Concept)
For liquids, viscosity decreases sharply as temperature increases. Heating a liquid increases the kinetic energy of its molecules, allowing them to overcome the attractive forces that bind the layers together.
The relationship roughly follows an Arrhenius-type equation: $\eta = A e^{E_a / RT}$, meaning viscosity drops exponentially with temperature.
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