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The capillary length will vary for different liquids and different conditions. Here is a picture of a water droplet on a lotus leaf. If the temperature is 20 o then = 2.71mm . The capillary length or capillary constant is a length scaling factor that relates gravity and surface tension.
Being a dimensionless quantity, the capillary number's value does not depend on the system of units. In the petroleum industry, capillary number is denoted instead of . [4] For low capillary numbers (a rule of thumb says less than 10 −5), flow in porous media is dominated by capillary forces, [5] whereas for high capillary numbers the ...
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
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.
Schematic drawing of a molecule in a cylindrical pore in the case of Knudsen diffusion; are indicated the pore diameter (d) and the free path of the particle (l).Knudsen diffusion, named after Martin Knudsen, is a means of diffusion that occurs when the scale length of a system is comparable to or smaller than the mean free path of the particles involved.
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. [ 8 ]
ρ is the mass density (mass per unit volume); r 0 is the tube radius; g is the gravitational acceleration. It is only valid if the tube is cylindrical and has a radius (r 0) smaller than the capillary length (= / ()). In terms of the capillary length, the law can be written as
The Knudsen number is a dimensionless number defined as =, where = mean free path [L 1], = representative physical length scale [L 1].. The representative length scale considered, , may correspond to various physical traits of a system, but most commonly relates to a gap length over which thermal transport or mass transport occurs through a gas phase.