# Dynamics of Capillary filling

Rishav Roy
When we write the equation for expressing the dynamics of capillary filling, why don't we include the effects of pressure difference?

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What equation?

Rishav Roy
m(d^2x/dt^2)=-mg+(wetted perimeter)*surface tension-viscous forces.
This is the Lucas -Washburn equation.
Even during finding the equilibrium height (Jurin's height) at which the movement of fluid stops, we equate the gravitational forces to the surface tension forces, without considering the pressure difference. Why is that?

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What pressure difference?

Rishav Roy
Coming to the question, we can compute a pressure difference between the two sides of a meniscus (Laplace pressure) due to the presence of a curvature. but this computation is done when the system is static. But when we write equations describing the dynamics (Lucas-Washburn equations mentioned in my previous reply), why don't we include the force due to this pressure-difference?

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What direction does this force act?

Rishav Roy
Consider a simple case of water rising up due to capillary action. Then this force due to pressure difference acts in the downward direction.