Advancement Time of Capillary Pump

We assume that the gravity head of the liquid column to be negligible as the height of the microchannel is very small. Therefore, the pressure at the entrance of the microchannel has a constant value. 

At the entrance of the microchannel, that is, at the input reservoir, the pressure drop due to Young-Laplace is zero due to the high width of the input reservoir  

The curved meniscus at position L t) leads to an Young-Laplace underpressure that 

Channel cross-section is rectangular, h (height) x w (width) and h w. Using the Hagen-Poiseuille result for flow rate, 

The pressure drop AP between the entrance (x = 0) and the advancing meniscus (x = L(t)) can be obtained from the Young s-Laplace relationship as 

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