The Weber number (We) is a
dimensionless number in
fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for
multiphase flows with strongly curved surfaces.[1] It is named after
Moritz Weber (1871–1951).[2] It can be thought of as a measure of the relative importance of the fluid's
inertia compared to its
surface tension. The quantity is useful in analyzing thin film flows and the formation of droplets and bubbles.
For a fluid of constant density and
dynamic viscosity, at the free surface interface there is a balance between the normal stress and the
curvature force associated with the surface tension:
Where is the unit normal vector to the surface, is the
Cauchy stress tensor, and is the
divergence operator. The Cauchy stress tensor for an incompressible fluid takes the form:
Introducing the dynamic pressure and, assuming high
Reynolds number flow, it is possible to
nondimensionalize the variables with the scalings:
The free surface boundary condition in nondimensionalized variables is then:
Where is the
Froude number, is the Reynolds number, and is the Weber number. The influence of the Weber number can then be quantified relative to gravitational and viscous forces.
Applications
One application of the Weber number is the study of heat pipes. When the momentum flux in the vapor core of the heat pipe is high, there is a possibility that the
shear stress exerted on the liquid in the wick can be large enough to entrain droplets into the vapor flow. The Weber number is the dimensionless parameter that determines the onset of this phenomenon called the entrainment limit (Weber number greater than or equal to 1). In this case the Weber number is defined as the ratio of the momentum in the vapor layer divided by the surface tension force restraining the liquid, where the characteristic length is the surface pore size.