# Laplace Number

on . Posted in Dimensionless Numbers

Laplace number, abbreviated as La, a dimensionless numbers, is used in fluid dynamics to describe the relative importance of surface tension forces to viscous forces in a fluid flow.  The Laplace number is used to determine whether surface tension effects are significant in a particular fluid flow situation.  The value of the Laplace number can provide insights into the shape and behavior of liquid drops, bubbles, or menisci (curved liquid surfaces) in various systems.

### Key points about Laplace number

• La < 1  -  In this case, surface tension forces are relatively weak compared to viscous forces.  This means that the fluid's shape and behavior are primarily determined by viscosity, and surface tension effects can be neglected.
• La ≈ 1  -  When the Laplace number is of the order of unity, both surface tension and viscous forces are significant, and their effects are comparable.  This often occurs in situations where the surface tension and viscosity are both relevant in determining the behavior of the fluid interface.
• La > 1  -  In this regime, surface tension forces dominate over viscous forces.  Surface tension becomes the dominant factor in shaping and controlling the behavior of the fluid interface.  This is often the case in small scale systems, such as microfluidic devices or capillary flows, where surface tension plays a critical role.

The Laplace number is particularly important in understanding phenomena involving capillary action, droplet formation, and bubble dynamics.  It helps engineers and scientists predict how surface tension influences the behavior of fluids in different contexts and can guide the design and analysis of systems where surface tension effects are significant.

### Laplace number formula

$$La \;=\; \sigma \; \rho \; l \;/\; \eta^2$$     (Laplace Number)

$$\sigma \;=\; La \; \eta^2 \;/\; \rho \; l$$

$$\rho \;=\; La \; \eta^2 \;/\; \sigma \; l$$

$$l \;=\; La \; \eta^2 \;/\; \sigma \; \rho$$

$$\eta \;=\; \sqrt{ \sigma \; \rho \; l \;/\; La }$$

Symbol English Metric
$$La$$ = Laplace number $$dimensionless$$ $$dimensionless$$
$$\sigma$$  (Greek symbol sigma) = surface tension $$lbf\;/\;ft$$ $$N\;/\;m$$
$$\rho$$  (Greek symbol rho) = density $$lbm\;/\;ft^3$$ $$kg\;/\;m^3$$
$$l$$ = length $$ft$$ $$m$$
$$\eta$$  (Greek symbol eta) = viscosity of liquid $$lbf-sec\;/\;ft^2$$ $$Pa-s$$

Tags: Flow Viscosity