# Weber number

The Weber number is a characteristic number used in fluid mechanics. As a dimensionless quantity, it describes the ratio between deforming inertial forces and stabilizing cohesive forces for liquids flowing through a fluid medium. For example, the Weber number characterizes the atomizing quality of a spray and the resulting droplet size when producing emulsions.

## Background

When a liquid flows through a second fluid phase (gas or liquid), then the fluid-mechanical or aerodynamic force FA causes the drops to deform and ultimately disperse.

cw = Drag coefficient, L = Characteristic length, ρ = Density, v = Flow rate

The cohesion force FK associated with the surface tension or interfacial tension σ opposes the increase in surface area which is caused by the deformation. The drop is therefore held together by the surface or interfacial tension.

The Weber number We expresses the ratio between these two forces:

If the deforming force increases due to a higher speed or longer process length, the drops of a spray disperse more easily and drops of oil in an aqueous environment are split apart more easily. A high surface or interfacial tension counteracts this process. Surfactants, which reduce the surface tension of the liquid or the interfacial tension between the phases concerned, are therefore often used in sprays and emulsions. The same applies to extraction processes in which small droplets must ensure a large exchange surface area at the phase boundary.

When calculating the Weber number, it should be taken into account that the surface or interfacial tension of surfactant solutions does not usually reach its equilibrium value due to high process speeds. The bubble pressure method is therefore often used as measuring method for surface tension, and the drop volume method for interfacial tension. These methods measure the dynamic surface tension or interfacial tension independently of surface age.