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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.
Capillary action of water (polar) compared to mercury (non-polar), in each case with respect to a polar surface such as glass (≡Si–OH). Capillary action (sometimes called capillarity, capillary motion, capillary rise, capillary effect, or wicking) is the process of a liquid flowing in a narrow space without the assistance of external forces like gravity.
An interesting phenomena, capillary rise of water (as pictured to the right) provides a good example of how these properties come together to drive flow through a capillary tube and how these properties are measured in a system. There are two general equations that describe the force up and force down relationship of two fluids in equilibrium.
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 hydrophobicity of an endothelial cell surface determines whether water or lipophilic molecules will diffuse through the capillary lining. The blood brain barrier restricts diffusion to small hydrophobic molecules, making drug diffusion difficult to achieve. Blood flow is directly influenced by the thermodynamics of the body.
The classic Starling principle and the equation that describes it have in recent years been revised and extended. Every day around 8 litres of water (solvent) containing a variety of small molecules (solutes) leaves the blood stream of an adult human and perfuses the cells of the various body tissues.
Diffusion through the capillary walls depends on the permeability of the endothelial cells forming the capillary walls, which may be continuous, discontinuous, and fenestrated. [4] The Starling equation describes the roles of hydrostatic and osmotic pressures (the so-called Starling forces ) in the movement of fluid across capillary endothelium .
[4] [5] One could arrive to the above formula also by considering the first particular case of the equation for a conservative body force field: in fact the body force field of uniform intensity and direction: (,,) = is conservative, so one can write the body force density as: