Excess Pressure

Excess pressure is a term used in physics to describe the additional pressure exerted by a fluid at a curved interface or inside a droplet.

Surface Tension

Surface tension is the cohesive force between molecules at the surface of a liquid that causes it to behave like a stretched elastic sheet. This force is responsible for phenomena such as capillary action and meniscus formation.

Viscosity and Poiseuille flow

Viscosity is a measure of a fluid's resistance to flow. It describes the friction between adjacent layers of a fluid as they move past each other. Poiseuille flow refers to the flow of a viscous fluid through a cylindrical pipe or tube.

Excess Pressure and Surface Tension

When a liquid interface or a droplet is curved, the molecules at the surface experience a net inward force due to surface tension. This force is perpendicular to the surface and tends to minimize the surface area. As a result, there is an excess pressure inside the curved interface or droplet compared to the pressure outside.

The excess pressure can be calculated using the Laplace's law, which states that the excess pressure (∆P) is directly proportional to the surface tension (σ) and the curvature (1/r) of the interface or droplet. Mathematically, it can be expressed as ∆P = 2σ/r, where r is the radius of curvature.

Excess Pressure and Capillary Rise

Excess pressure also plays a crucial role in capillary action, which is the rise or fall of liquids in narrow tubes or capillaries. When a liquid wets a capillary, the surface tension causes the liquid to rise in the tube against the force of gravity. The excess pressure inside the capillary is balanced by the weight of the liquid column above it. The height of the liquid rise can be determined using the equation h = (2σ cosθ)/(ρgr), where h is the height, σ is the surface tension, θ is the contact angle, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the capillary.

Excess Pressure and Liquid Drops

Excess pressure inside a liquid droplet also affects its stability. For small droplets, the excess pressure is high, leading to a spherical shape due to the surface tension forces. However, for larger droplets, the excess pressure decreases, and gravity becomes dominant. This results in a flattened shape as the droplet spreads out.

In conclusion, excess pressure is the additional pressure exerted by a fluid at a curved interface or inside a droplet due to surface tension. It plays a crucial role in various phenomena such as capillary rise and droplet stability. Understanding excess pressure is essential for analyzing the mechanical properties of fluids.