# Soap bubbles

1. The problem statement, all variables and given/known data

We have got two bubbles with r1 and r2at p0=1bar and T0=20°C, made of two different soapy waters. We pierce them with a straw with length l=5cm and r0=2mm. There are 2g of air inside the system. (Surface tensions are γ1= 0,025 N/m2, γ2= 0,01 N/m2)
a) What are the stationary states and determine the shape of the membranes on both sides.
b) What are the radiuses before we pierce the system with a straw if the bubbles fall with the same velocity? (Use linear law for resistance)

a) So I assume that the stationary states are when the bubbles have the same radius, otherwise the other stationary state is when one is full and the other is empty (just a membrane on the straw). This is because the system wants lower energies (E=γ1*S1+γ2*S1)

Is there a formula to determine the right shape or is enough if I say that on one side is a bubble on the other is half a sphere? I tried to find shape with formulas F=2γ*(2∏r)*cosθ=pinside*S but I have problems, because I dont know the angle and the pressure inside.

b) Fg-Fbuoyancy-Fresistance=m*a=m*dv/dt
=mg-ρgV-6∏rηv=m*dv/dt from here on I don’t have a clue how to cope with it.