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Question: a narrow glass tube of radius a is inserted in...

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A narrow glass tube of radius a is inserted in a tank of a liquid with mass density ρ. The liquid height difference h within and outside the tube may be positive (capillary rise) or negative (capillary depression), depending on the relationship of the liquid-gas (γLG), the solid-gas (γSG), and the solid-liquid (γSL) surface/interface tensions. At equilibrium, the liquid makes a contact angle θ with respect to the glass tube surface.

a) Sketch the liquid meniscus within the tube, as well as the contact angles to the tube surface. Do this for both cases: a wetting and a non-wetting liquid.

b) Considering the surface energy changes associated with the liquid rising in the tube, and combining the Young’s equation: \gamma _{LG}cos(\theta) = \gamma _{SG} - \gamma _{SL} , prove the liquid height difference within and outside the tube: h= \frac{2\gamma_{LG}cos(\theta )}{\rho ga} , where g represents the local acceleration due to gravity.

c) Explain at the molecular level why the height of the liquid within the tube is generally different from the height within the tank.

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