See arbitrary Lagrangian-Eulerian method.

A dimensionless number given by the ratio of surface tension forces to body forces (usually gravity) for a two-phase flow. It is also known as the Eötvös number, Eo. At high Bond numbers surface tension has a minimal effect on the flow; at low Bond numbers, surface tension dominates. The Bond number, Bo, is given by:

where ρ is the density, g is the body force acceleration, L is the characteristic length, and σ is the surface tension coefficient. The density can refer to a density difference when considering buoyancy.

A dimensionless number given by the ratio of viscous forces to surface tension for a two phase flow. At low capillary numbers flow in porous media is dominated by surface tension. The capillary number, Ca, is given by

where μ is the viscosity, v is the characteristic velocity of the problem, and σ is the surface tension coefficient.

Models the Navier–Stokes equations without the contribution of the inertia term. This is often referred to as Stokes flow and is appropriate for use when viscous flow is dominant, such as in very small channels or microfluidic applications.

See electric double layer.

A dimensionless number given by the ratio of the surface conductivity contribution to the fluid bulk electric conductivity contribution in electrokinetic phenomena. The Dukhin number, Du, is given by

where Kσ is the surface conductivity and KB is the bulk conductivity. For low Dukhin numbers, surface conductivities can be neglected when modeling electrokinetic flows.

Transport of fluid or charged particles within a fluid by means of electric fields. See also electroosmosis, electrophoresis, electrothermal flow, and dielectrophoresis.

Fluid flow in a narrow channel produced by the movement of the electric double layer (EDL) along the channel boundary under the influence of an applied electric field. Also, fluid flow through a membrane under the influence of an applied electric field. See also electric double layer.

See electroosmosis.

The electrowetting effect describes the change in solid-electrolyte contact angle that occurs when a potential difference is applied between the solid and the electrolyte.

A form of electrowetting in which a thin insulating layer separates the conducting solid surface from the electrolyte.

See Bond number.

The flow of gas molecules through a geometry which is much smaller than the mean free path (Knudsen number, Kn > 10). In the free molecular flow regime the gas molecules collide with the walls of the geometry much more frequently than they collide with themselves.

See electric double layer (EDL).

See Poiseuille’s law.

A dimensionless number that provides a measure of how rarefied a gas flow is, in other words, the mean free path of the gas molecules compared to the length scale of the flow. The following equation defines the Knudsen number Kn in terms of the mean free path λ of the molecules and a length scale L characteristic of the flow:

The Laplace number, La, (also known as the Surataman number, Su) relates the inertial and surface tension forces to the viscous forces. It is used to describe the breakup of liquid jets and sheets: at high Laplace and low Reynolds numbers the Rayleigh Instability occurs, at low Laplace and high Reynolds numbers atomization occurs. The Laplace number is given by

where ρ is the fluid density, σ is the surface tension coefficient, L is the characteristic length scale of the problem, and μ is the viscosity. The Laplace number is directly related to the Ohnesorge number, Oh, through the equation La = 1/Oh2.

Ratio of the convective speed, v, to the speed of sound in the medium, a. The Mach number, Ma, is defined by the equation

Ratio of thermal surface tension forces to viscous forces. The Marangoni number, Mg, is given by:

where σ is the surface tension coefficient, T is the absolute temperature (ΔT is the characteristic temperature difference), L is the characteristic length, and α is the thermal diffusivity (α = κ/(ρcp)), where cp is the heat capacity at constant pressure, κ is the thermal conductivity, and ρ is the density of the fluid.

A dimensionless number relating the inertial and surface tension forces to the viscous forces. Used to describe the breakup of liquid jets and sheets: at low Ohnesorge and Reynolds numbers the Rayleigh instability occurs; at high Ohnesorge and Reynolds numbers, atomization occurs. The Ohnesorge number, Oh, is given by:

where ρ is the fluid density, σ is the surface tension coefficient, L is the characteristic length scale of the problem, and μ is the viscosity. The Ohnesorge number is directly related to the Laplace number, La, through the equation Oh = 1/La1/2.

A dimensionless number describing the ratio of convection to diffusion in a fluid flow. The Peclet number, Pe, can be used to describe concentration diffusion or heat diffusion. It is given by

where v is the convective velocity, L is the flow length scale, and D is the diffusion constant.

A dimensionless number classifying how laminar or turbulent a flow is. The Reynolds number Re is a measure of the relative magnitude of the flow’s viscous and inertial forces. It is defined by the following equation where ρ is the fluid density, μ is the dynamic viscosity, ν is its kinematic viscosity, v is a velocity characteristic to the flow, and L is a length scale characteristic to the flow.

Fluid flow that occurs when the Knudsen number, Kn, is in the range 0.01 < Kn < 0.1. As a result of rarefaction effects in the Knudsen layer the no slip boundary condition fails. The flow outside the Knudsen layer can be represented by the continuum Navier–Stokes equations provided that an appropriate slip boundary condition is used for the fluid flow and the correct temperature jump boundary condition is applied at the interface.

See creeping flow.

See Laplace number.

Fluid flow that occurs when the Knudsen number, Kn, is in the range 0.1 < Kn < 10. In this regime the flow is so rarefied that continuum equations break down completely. However collisions between the molecules are still important, so free molecular flow is not applicable.

where ρ is the density of the fluid, v is the characteristic velocity of the flow, L is the characteristic length scale, and σ is the surface tension coefficient.