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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.
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 equation is named after Edward Wight Washburn; [1] also known as Lucas–Washburn equation, considering that Richard Lucas [2] wrote a similar paper three years earlier, or the Bell-Cameron-Lucas-Washburn equation, considering J.M. Bell and F.K. Cameron's discovery of the form of the equation in 1906. [3]
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.
When using the notation for dynamic viscosity, for the liquid-solid contact angle, for surface tension, for the fluid density, t for time, and r for the cross-sectional radius of the capillary and x for the distance the fluid has advanced, the Bosanquet equation of motion is [2]
Alongside the capillary number, commonly denoted , which represents the contribution of viscous drag, is useful for studying the movement of fluid in porous or granular media, such as soil. [1] The Bond number (or Eötvös number) is also used (together with Morton number ) to characterize the shape of bubbles or drops moving in a surrounding ...
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.
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 ...