What does Laplace pressure depend on?

Background. According to the Young-Laplace equation, this pressure p depends on the surface tension σ and the radius of curvature r (for a sphere) or the main radii of curvature r1 and r2 (for a surface with any curvature):

How do you calculate Laplace pressure?

The Laplace pressure: P L = 2 γ L V R (Eq. 1.9) where γ L V and R are the surface tension of the liquid–vapor interface and the tip radius, respectively.

What is surface tension describe the Laplace equation?

In physics, the Young–Laplace equation (/ləˈplɑːs/) is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although use of the latter is only …

What is the Laplace law?

Laplace’s law states that the pressure inside an inflated elastic container with a curved surface, e.g., a bubble or a blood vessel, is inversely proportional to the radius as long as the surface tension is presumed to change little.

Why does surface tension happen?

Surface tension in water owes to the fact that water molecules attract one another, as each molecule forms a bond with the ones in its vicinity. This inward net force causes the molecules on the surface to contract and to resist being stretched or broken.

How do you derive Laplace equation?

The Laplace equation may be derived either by minimization of energy or by sum- ming all forces to zero. We will do both here although the concept of force in connec- tion with surface tension may be somewhat obscure.

Why is Laplace needed?

The purpose of the Laplace Transform is to transform ordinary differential equations (ODEs) into algebraic equations, which makes it easier to solve ODEs. The Laplace Transform is a generalized Fourier Transform, since it allows one to obtain transforms of functions that have no Fourier Transforms.

What is Newton Laplace equation?

For mechanic waves, the Newton-Laplace (NL) formula, us=(Bs∕ρ)1∕2 relates the sound velocity with other physical quantities of a material, including the temperature T, density ρ (or equivalently volume V), and pressure P, and can be applied to gases and liquids.

What is the equation for the Laplace pressure?

The Laplace pressure is represented by the equation: Δ P = P inside − P outside = 2 σ r where “ σ ” is surface tension at the droplet interface, “ r ” is the radius of the droplet, and “ P ” is the pressure.

What causes the difference in Laplace pressure between gas and liquid?

The pressure difference is caused by the surface tension of the interface between liquid and gas. The Laplace pressure is determined from the Young–Laplace equation given as ) is the surface tension. Although signs for these values vary, sign convention usually dictates positive curvature when convex and negative when concave.

How is surface tension related to Laplace’s law?

Granted, it’s not surface tension, but the analogy to Laplace’s relation between tension and radius is clear—for a fixed pressure, a larger radius cylindrical membrane will have a larger tension in the membrane wall and will consequently need to be “stronger” if it is not to burst.

What happens to a film under Laplace pressure?

For macroscopic films (i.e., films thicker than a few microns), the free energy is given by the sum of capillary and gravitational energies; 173 the film is stable and surface undulations (and structures) will decay with time under the Laplace pressure given by the surface tension and radius of curvature.