1. "By plotting it is 'obvious', that for r=0 this is always negative (so r
must decrease to have a chance to fullfill F=0."
The above point you mentioned should be understood as
when R3=r=0, this means that the gravity factor is ignored, so it is now
irrelavant that whether liquid is above vapour or vapour is above liquid.
Bcoz If gravity is zero then the problem, instead of a vertical through flow
becomes a horizental flow problem. which is always stable thats why we have
sigma<0, for all l=lambda.
For lambda = 10^3 and 10^4 compute solutions for F=0 with an initial
guess of r = -2*lambda which then defines a line equation
Lin := lambda -> -1.591517842027199990210998791356366512040*lambda
This means that for large l=lambda the system is marignally stable, i.e., sigma=0
for large lambda. to me thats fine.