A perfectly circular microfluidic channel with a radius of 100 mu m in a glass w

Question

A perfectly circular microfluidic channel with a radius of 100 mu m in a glass wafer is filled with water. The cross-section view along the middle of the channel is illustrated below. Calculate the surface tension pressure (P_gamma) on the liquid-air interface (the meniscus), or in other words, the pressure impinging on the convex side of the interface due to the surface tension of water. Useful Data: Surface tension of water = 72 Times 10^-3 N/m at 25 degree C. Calculate the surface tension force impinging on the liquid-air interface (F_gamma) and indicate the direction of the force vector F_r.

Explanation / Answer

(a) Pressure = surface tension / arc length

                     = 72 * 10^-3 / (2pi*R/3)

                     = 72 * 10^-3 / (2pi*r/(3*cos30))       r = 100 *10^-6 m

                     = 297.717 N/m^2

(c) Force = pressure * area

               = 297.717 * 2 * pi * (r/cos(30))^2 * (1 - cos(60)) = 1.247E-5 N

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