Provide a detailed explanation of surface tension and viscosity.

(N/A) Effect of Surface tension: Liquids generally assume the shape of their container. However,some phenomena occur due to surface tension:
$-$ Mercury forms spherical beads instead of spreading on a surface.
$-$ Soil particles at the bottom of a river remain separated but stick together when taken out.
$-$ $A$ liquid rises in a thin capillary tube upon contact.
Explanation of surface tension:
$A$ molecule in the bulk of a liquid experiences equal intermolecular forces from all sides,resulting in no net force. However,a molecule on the surface experiences a net attractive force towards the interior of the liquid because there are no molecules above it. This net downward force gives surface molecules more energy than those in the bulk. Consequently,liquids tend to minimize the number of molecules at their surface.
Surface energy: The energy required to increase the surface area of a liquid by one unit is called 'surface energy' or 'surface tension energy'.
Definition of Viscosity: Viscosity is a measure of the resistance to flow,arising from internal friction between layers of fluid as they slip past one another. Strong intermolecular forces hold molecules together and resist the movement of layers.
Laminar flow: When a liquid flows over a fixed surface,the layer in contact with the surface is stationary. The velocity of upper layers increases with distance from the fixed layer. This regular gradation of velocity is called 'Laminar flow'.
Mathematical Representation of Viscosity:
If the velocity of a layer at a distance $dz$ changes by a value $du$,the velocity gradient is $\frac{du}{dz}$.
The force $F$ required to maintain flow is proportional to the area of contact $A$ and the velocity gradient $\frac{du}{dz}$:
$(i)$ $F \propto A$
$(ii)$ $F \propto \frac{du}{dz}$
$\therefore F \propto A \left( \frac{du}{dz} \right)$
$\therefore F = \eta A \left( \frac{du}{dz} \right)$
Where $\eta$ is the coefficient of viscosity.