Surface tension_another problem

[i_island0]

Suppose that there is a small spherical ball of mass 'm' floating on surface of a liquid due to surface tension. The contact angle between ball and liquid is theta. Is there any way to calculate exactly as what fraction of ball will be inside the fluid. Buoyancy should not be neglect.

 

[i_island0]

i shall rephrase my question.
A small spherical ball is floating in liquid layer due to surface tension. Thus it depresses the liquid layer as if it is an elastic membrane. So shall we say that buoyant force doesn't act on it?

 

[astrokreng]

Thank you for bringing up this interesting problem. Surface tension is the force that exists at the interface between a liquid and another medium, such as air. It is caused by the cohesive forces between the molecules of the liquid, which allow it to resist external forces and maintain its shape.

In the scenario you have described, the spherical ball is floating on the surface of the liquid due to the surface tension. The contact angle between the ball and the liquid, theta, is an important factor in determining the amount of the ball that will be submerged in the liquid. This is because the surface tension will act tangentially to the surface of the liquid and will cause the ball to deform slightly, resulting in a contact angle between the two.

To calculate the fraction of the ball that will be submerged in the liquid, we need to consider both the surface tension and buoyancy forces acting on the ball. The surface tension force will act to minimize the surface area of the liquid in contact with the ball, while the buoyancy force will act to push the ball upwards.

The exact calculation of the fraction of the ball that will be submerged is a complex problem that requires knowledge of the geometry and material properties of the ball. It also depends on the contact angle, which can vary depending on the surface properties of the ball and the liquid.

One possible approach to solving this problem would be to use the concept of wetting, which is a measure of the ability of a liquid to maintain contact with a solid surface. The contact angle is related to the wetting properties of the liquid and can be used to determine the fraction of the ball that will be submerged.

In conclusion, while there is no simple formula to calculate the exact fraction of the ball that will be submerged in the liquid, the contact angle between the ball and the liquid is an important factor that can be used to estimate it. It is also important to consider the effects of both surface tension and buoyancy forces in this calculation. I hope this helps in understanding the problem better.