You can calculate survace tension across any curve drawn on droplet; the difference would be is what most of curves would require to take integrals including as inputs curvature of surface, slope and gravity - much more complicated than simple multiplication at the perimeter of droplet.Vivek98phyboy said:When calculating force due to surface tension across a hemispherical drop, we look at only the circumference and multiply it by the value of surface tension. When we know that it is the surface tension which is responsible for the curved surface of the liquid drop, why don't we calculate the force due to surface tension along the curved surface as well?
But as far as I've checked all the books and internet, there is no such example of using integral over the hemispherical surface. All they did was calculating T×2πr by only considering forces due to the other hemispherical part along the periphery.trurle said:You can calculate survace tension across any curve drawn on droplet; the difference would be is what most of curves would require to take integrals including as inputs curvature of surface, slope and gravity - much more complicated than simple multiplication at the perimeter of droplet.
If you did not found such integral in literature, write it yourself. There is no rule against.Vivek98phyboy said:But as far as I've checked all the books and internet, there is no such example of using integral over the hemispherical surface. All they did was calculating T×2πr by only considering forces due to the other hemispherical part along the periphery.
If i were to integrate it across the curved surface then i would get T×2πr² but it won't give you the answertrurle said:If you did not found such integral in literature, write it yourself. There is no rule against.
They directly stated that pressure on the patch= surface tension along perimeterLord Jestocost said:You can get the sample chapter "Fluid Interfaces and Capillarity" of John C. Berg's book "An Introduction to Interfaces and Colloids - The Bridge to Nanoscience" on https://www.worldscientific.com/worldscibooks/10.1142/7579.
To my mind, the relationships become clearer when one considers the force balance on a tiny patch of a curved surface (see Fig. 2-25 in that chapter).
Vivek98phyboy said:why don't we calculate the force due to surface tension along the curved surface as well?
Surface tension is a physical property of liquids that describes the force exerted on the surface of the liquid due to the cohesive forces between the molecules. It is the reason why some insects can walk on water and why water forms droplets on a surface instead of spreading out.
Calculating surface tension is important for understanding the behavior of liquids and how they interact with other substances. It is also crucial in various industries such as pharmaceuticals, cosmetics, and food production, where surface tension affects the stability and performance of products.
Surface tension is typically measured in units of force per unit length, such as newtons per meter. One common method of measuring surface tension is the drop weight method, where the weight of a droplet is measured as it forms and falls from a capillary tube. Other methods include the Wilhelmy plate method and the Du Nouy ring method.
Surface tension is affected by several factors, including temperature, pressure, and the presence of impurities. Generally, surface tension decreases as temperature increases and as pressure decreases. Impurities, such as oils or surfactants, can also lower the surface tension of a liquid.
Surface tension is a result of the intermolecular forces between molecules in a liquid. These forces, such as hydrogen bonding or van der Waals forces, cause the molecules at the surface of the liquid to be pulled inward, creating a cohesive force. The strength of these intermolecular forces determines the magnitude of the surface tension.