maajdl said:As far as I understand you notations, ... your equation must wrong, as can be seen from a simple case.
When two bubbles of same radius coalesce, the common surface that separate them is flat.
This is so because the pressure on both side will be the same.
Your equation does not predict that, as far as I understand you notations ...
What are the meaning of r1 and r2?
Are these numbers supposed to be always positive, or do they have an orientation (sign)?
The curvature of the common surface is related to the pressure difference across that surface.
dauto said:No that's still wrong because the radii of the bubbles change when they coalesce. The total amount of air inside each bubble is preserved and if one side of it becomes flat due to the contact with another bubble than the radius of the remainder must expand in order to preserve the air content of the bubble.
The original equation is fine - you just have to remember that from the perspective of the common boundary one of r1 and r2 is negative. In fact, the sign of the result tells you which way the common boundary will bulge.utkarshakash said:[itex]4T \left( | \frac{1}{r_1} - \frac{!}{r_2} | \right) = \frac{4T}{R'} [/itex]
Technically, yes, but I think you're expected to ignore that here.dauto said:No that's still wrong because the radii of the bubbles change when they coalesce. The total amount of air inside each bubble is preserved and if one side of it becomes flat due to the contact with another bubble than the radius of the remainder must expand in order to preserve the air content of the bubble.
Soap bubbles stick together due to the surface tension of the soapy water. This surface tension is created by the soap molecules that are attracted to each other, causing them to form a thin film around the air trapped inside the bubble. When two bubbles come in contact, their surface tension combines and causes them to stick together.
The ability of soap bubbles to stick together depends on the quality and amount of soap in the water. If the soap concentration is too low, the bubbles may not have enough surface tension to stick together. Additionally, external factors such as wind or uneven surfaces can also prevent bubbles from sticking together.
Yes, the type of soap used can affect the stickiness of bubbles. Some soaps have a higher concentration of soap molecules, resulting in stronger surface tension and stickier bubbles. Other factors such as the PH level of the water and the temperature can also impact the stickiness of bubbles.
The length of time that bubbles stay stuck together varies depending on factors such as the quality of the soap, external conditions, and the size of the bubbles. Generally, smaller bubbles will stay stuck together for a longer period than larger bubbles. Bubbles may also pop or separate due to changes in the environment.
Yes, the phenomenon of bubbles sticking together can be explained by the principles of surface tension and the properties of soap molecules. When two bubbles come in contact, their surface tension combines, creating a larger surface area and causing them to stick together. This can be observed in many other substances with surface tension, such as water droplets on a surface.