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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.
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 ]
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.
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.
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.
Flow through the pores in an oil reservoir has capillary number values in the order of 10 −6, whereas flow of oil through an oil well drill pipe has a capillary number in the order of unity. [ 4 ] The capillary number plays a role in the dynamics of capillary flow ; in particular, it governs the dynamic contact angle of a flowing droplet at ...
Oregon quarterback Dillon Gabriel speaks to reporters during a press conference in Los Angeles, Monday, Dec. 30, 2024. (AP Photo/Kyusung Gong)
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 ...