BOSANQUET EQUATION PDF

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In physics , Washburn's equation describes capillary flow in a bundle of parallel cylindrical tubes; it is extended with some issues also to imbibition into porous materials. 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.

Bell and F. Cameron's discovery of the form of the equation in Washburn's equation is also used commonly to determine the contact angle of a liquid to a powder using a force tensiometer.

In his paper from Washburn applies Poiseuille's Law for fluid motion in a circular tube. The pressures in turn can be written as. In the derivation of Washburn's equation, the inertia of the liquid is ignored as negligible. An improved version of Washburn's equation, called Bosanquet equation , takes the inertia of the liquid into account.

The penetration of a liquid into the substrate flowing under its own capillary pressure can be calculated using a simplified version of Washburn's equation: [11] [12].

In reality, the evaporation of solvents limits the extent of liquid penetration in a porous layer and thus, for the meaningful modelling of inkjet printing physics it is appropriate to utilise models which account for evaporation effects in limited capillary penetration. According to physicist and Ig Nobel prize winner Len Fisher, the Washburn equation can be extremely accurate for more complex materials including biscuits. The flow behaviour in traditional capillary follows the Washburn's equation.

Recently, novel capillary pumps with a constant pumping flow rate independent of the liquid viscosity [16] [17] [18] [19] were developed, which have a significant advantage over the traditional capillary pump of which the flow behaviour is Washburn behaviour, namely the flow rate is not constant. These new concepts of capillary pump are of great potential to improve the performance of lateral flow test. From Wikipedia, the free encyclopedia. Washburn Physical Review.

Bibcode : PhRv Kolloid Z. Powder Technology. New York: Academic Press. Can we obtain the contact angle from the Washburn equation? In Mittal, K. Contact Angle, Wettability and Adhesion. Journal of the ACM. Peter Colloids and Surfaces in Reprographic Technology. ACS Symposium Series. Progress in Organic Coatings. Improbable Research. Retrieved Len Fisher, discoverer of the optimal way to dunk a biscuit. BBC News. Bibcode : Natur. Washburn will be turning in his grave to learn that the media have renamed his work the "Fisher equation".

Capillary pumping with a constant flow rate independent of the liquid sample viscosity and surface energy. Bibcode : MicNa Categories : Equations of fluid dynamics Porous media.

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Washburn's equation

In the theory of capillarity, Bosanquet equation is an improved modification of the simpler Lucas—Washburn theory for the motion of a liquid in a thin capillary tube or a porous material that can be approximated as a large collection of capillaries. In the Lucas—Washburn model, the inertia of the fluid is ignored, leading to the assumption that flow is continuous under constant viscous laminar Poiseuille flow conditions without considering effects of mass transport undergoing acceleration occurring at the start of flow and at points of changing internal capillary geometry. The Bosanquet equation is a differential equation that is second-order in the time derivative, similar to Newton's Second Law , and therefore takes into account the fluid inertia. Equations of motion, like the Washburn's equation, that attempt to explain a velocity instead of acceleration as proportional to a driving force are often described with the term Aristotelian mechanics.

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Bosanquet equation

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