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Powder wettability measurement with the Washburn method. In its most general form the Lucas Washburn equation describes the penetration length ( L {\displaystyle L} ) of a liquid into a capillary pore or tube with time t {\displaystyle t} as L = ( D t ) 1 2 {\displaystyle L=(Dt)^{\frac {1}{2}}} , where D {\displaystyle D} is a simplified ...
A force balance equation known as Washburn's equation for the above material having cylindrical pores is given as: [1] ...
The method of separation of variables is also used to solve a wide range of linear partial differential equations with boundary and initial conditions, such as the heat equation, wave equation, Laplace equation, Helmholtz equation and biharmonic equation.
For the condition of short time this shows a meniscus front position proportional to time rather than the Lucas-Washburn square root of time, and the independence of viscosity demonstrates plug flow. As time increases after the initial time of acceleration, the equation decays to the familiar Lucas-Washburn form dependent on viscosity and the ...
Laplace's equation on is an example of a partial differential equation that admits solutions through -separation of variables; in the three-dimensional case this uses 6-sphere coordinates. (This should not be confused with the case of a separable ODE, which refers to a somewhat different class of problems that can be broken into a pair of ...
"Spices and herbs do go bad around one to two years," Bapton says. But the type matters. "Ground spices have about half the shelf life of whole spices. For optimal baking, open the containers to ...
Note that in the one-variable case, the Hessian condition simply gives the usual second derivative test. In the two variable case, (,) and (,) are the principal minors of the Hessian. The first two conditions listed above on the signs of these minors are the conditions for the positive or negative definiteness of the Hessian.
With 1,838 yards, the seven-year veteran has to average 133.5 yards in those final two games to seize the all-time mark. Barkley has topped that number in six of his 15 games this season.