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There's gravity, there's adhesive and cohesive attractive forces. Fair enough, most materials seem to compare water to mercury in capillary tubes when explaining capillary action and above properties of fluids.

However why is water foaming a convex in an open capillary tube and concave on the open surface of glass? A calculation (basic), formula based reasoning would be great.

enter image description here

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    $\begingroup$ look up meniscus and surface tension on say Wikipedia $\endgroup$
    – user108787
    Oct 2 '16 at 4:48
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because the car example on the right has the water droplet in contact not with glass (as in the case on the left) but with car paint, or possibly car wax (the classic textbook example). water wets a clean painted surface more poorly than it does glass and even more poorly than that if the car paint has hydrophobic wax applied.

Note also that on timescales of order ~ 10 seconds, there is significant wettability hysteresis- a water droplet that wets a surface poorly upon initial contact will often "get friendly" with it after a short time. this will show up as a difference in the advancing and retreating contact angles on opposite ends of a droplet sliding down an inclined surface.

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