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The capillary length or capillary constant is a length scaling factor that relates gravity and surface tension. It is a fundamental physical property that governs the behavior of menisci, and is found when body forces (gravity) and surface forces ( Laplace pressure ) are in equilibrium.
The Bond number can also be written as = (), where = / is the capillary length. A high value of the Eötvös or Bond number indicates that the system is relatively unaffected by surface tension effects; a low value (typically less than one) indicates that surface tension dominates. [ 7 ]
The capillary length is a length scaling factor that relates gravity, density, and surface tension, and is directly responsible for the shape a droplet for a specific fluid will take. The capillary length stems from the Laplace pressure, using the radius of the droplet. Using the capillary length we can define microdrops and macrodrops.
Phase-field equations in principle reproduce the interfacial dynamics when the interface width is small compared with the smallest length scale in the problem. In solidification this scale is the capillary length , which is a microscopic scale. From a computational point of view integration of partial differential equations resolving such a ...
In fluid dynamics, the capillary number (Ca) is a dimensionless quantity representing the relative effect of viscous drag forces versus surface tension forces acting across an interface between a liquid and a gas, or between two immiscible liquids.
The equation is derived for capillary flow in a cylindrical tube in the absence of a gravitational field, but is sufficiently accurate in many cases when the capillary force is still significantly greater than the gravitational force. In his paper from 1921 Washburn applies Poiseuille's Law for fluid motion in a circular tube.
The Weber number appears in the incompressible Navier-Stokes equations through a free surface boundary condition. [3]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:
Capillary rise or fall in a tube. Jurin's law , or capillary rise , is the simplest analysis of capillary action —the induced motion of liquids in small channels [ 1 ] —and states that the maximum height of a liquid in a capillary tube is inversely proportional to the tube's diameter .