If two fluids are immiscible, like water and oil, drops coalesce because it is energetically favourable to diminish the contact area between the two phases. As long as these drops are sufficiently small, Brownian motion ensures that the suspension stays homogeneous, but it will also cause more droplets to coalesce. According to the Stokes--Einstein relation the mobility of the drops diminishes with increasing size. Therefore, when the drops grow sufficiently large, the motion due to gravitational pull becomes dominant instead of Brownian motion.

If two fluids are immiscible, like water and oil, drops coalesce because it is energetically favourable to diminish the contact area between the two phases. As long as these drops are sufficiently small, Brownian motion ensures that the suspension stays homogeneous, but it will also cause more droplets to coalesce. According to the Stokes--Einstein relation the mobility of the drops diminishes with increasing size. Therefore, when the drops grow sufficiently large, the motion due to gravitational pull becomes dominant instead of Brownian motion.

Archimede's principle: the pressure on the top of the drops is lower than at the bottom.  If the liquid of the drop is less dense than the surrounding liquid, the Archimede's thrust is greater than the weight.

dear Stefan B Lindström

thanks for your answer.But i don"t totally understand.you said the gravitational pull becomes dominant,however,when a liquid wih low density is put up on a liquid wih high density ,there is still gravitation,why the upper liquid don"t sink.Could you mind giving me a more specific answer.

thank you very much.

Yes, gravity pulls on both fluids, so when gravity becomes dominant, the net force on a lower-density drop is directed upwards, as Claude explains above.

Kind reagrds.

The Archimede's principle states that the thrust is equal and opposit to the weight of the displaced volume, that is, the weight of the more dense liquid in the volume of the drop of the less dense one. The two volumes being equal, the net force is upward.  The quantitative relation can be derived by taking a cube, and calculating the difference of the forces acted upon the top and the bottom faces, the forces upon the other faces exactly cancel two by two by symmetry.  The difference of the pressure is calculated from the height of the cube and the density of the liquid, and it must be multiplied by the surface of the faces to get the force.  That gives the volume multiplied by the density of the liquid.

Calculating forces is complicated, and there exists metastable configurations. Calculating energies is simpler.

The configuration with the heavy liquid at bottom and light liquid on top has lowest energy. Hence this is the equilibrium configuration. Other configurations may arise temporarily (out-of-equilibrium situations), as when you heat a system (adding energy to it).

It is simple buoyancy force. For lighter liquid droplet,  the buoyancy force is higher than gravitational force acting on it. So, it goes up.

assuming that a liquid droplet is surrounded by the other liquid,

buoyancy force (acting upwards) = dh*v*g   [for lighter liquid]

gravitational force (acting downward) = m*g = dl*v*g   [for lighter liquid]

dh = density of heavier liquid, dl = density of lighter liquid, v=volume of lighter droplet

d(h)>d(l). So...

Dear Saptarshi Maji,Kåre Olaussen,Claude Pierre Massé and Stefan B Lindström 

Thank you and i am sorry for being late to answer.

I Think the method of Kare is a nice idea,we can explain this things from the angle of energy.However I want to get a explaination from Microscopic point of view.Most of you tried to use Archimede's principle to explain this question,but this principle is macroscopic,and i want to ask how do we use a microscopic view to explian the assumption that pressure towrads arbitrary directions in a fluid is equal.If we can't explain it,the Archimede's principle will not be right.

thank you!