Two clean glass capillary tubes

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Fluid statics and the continuum picture · Fluid statics and the continuum picture

Fluids and Continuum Physics, Ch Surface tension, capillarity and wetting

Problem

Two clean glass capillary tubes, of internal radii a1=0.30a_1 = 0.30 mm and a2=0.60a_2 = 0.60 mm, stand vertically in a dish of water. Water wets clean glass completely, so take the contact angle as θc=0\theta_c = 0. Take γ=0.072\gamma = 0.072 N m−1^{-1}, ρ=1000\rho = 1000 kg m−3^{-3} and g=9.8g = 9.8 m s−2^{-2}. The Bond number of the meniscus is Bo=ρga2/γBo = \rho g a^{2}/\gamma. ((a)) Find the capillary rise in each tube. ((b)) Find the Bond number for each tube. ((c)) State how the rise depends on the tube radius, and say from the Bond numbers whether gravity or surface tension fixes the shape of the meniscus in these tubes. ((d)) The narrower tube is dipped instead into mercury, which meets clean glass at θc=140∘\theta_c = 140^\circ, with γ=0.48\gamma = 0.48 N m−1^{-1} and ρ=13600\rho = 13600 kg m−3^{-3}. Find the change of level inside the tube, and say whether it is a rise or a fall.

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