Convective cells by Pomeau

By Pomeau

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2. Surface tension for various pairs of fluids at 20◦ in N/m × 103 [8]. 8 487 22 29 375 <0 35 Water σdl σdl θ h 2R Fig. 7. Liquid ascending through a capillary. where U and L are a characteristic velocity and length scale of the problem, respectively. 1 (Capillary forces). Calculate the maximum height that a liquid can ascend through a capillary. Solution. Due to surface tension, a liquid inside a capillary is subject to an ascending force of 2πRσ cos θ, where θ is the contact angle between the water and the solid surface of the capillary.

Now we can proceed to defining the volumetric and mass flux. 7 (Volumetric flow rate). The volumetric flow rate Q is the volume of fluid that crosses the surface per unit time, v · n dS Q= S Its dimensions are [Q] = L3 T−1 and its units in the SI, m3 /s. 5 The Concept of Flux 27 n Fig. 11. Exterior normal to the surface of a volume. 8 (Mass flow rate). 24) S Its dimensions are [m] ˙ = MT−1 and its SI units, kg/s. n θ dA n v v S Fig. 12. Flux across a surface. 23), let us take the differential of area dA over the surface S of Fig.

11) It can be positive or negative, its minimum value being −patm (see Fig. 6). 4 Surface Tension At interfaces between two substances, the inter-molecular forces at both sides differ, appearing to be an additional force. 12) The surface tension depends on the pair of substances that form the interface and on the temperature. When the surface tension is positive, the molecules of each phase tend to be repelled back to their own phase. This is the case, for instance, of two inmiscible liquids. When the surface tension is negative, the molecules of both phases tend to mix, like two miscible liquids.

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