2D Marangoni Effect due to Evaporation of Solute

Dear Community,

I am trying to solve Marangoni effect due to evaporation of solute. I have closely followed the model example in which the Marangoni effect is due to the thermal gradients.

Here is what I would like to know.

1. How to define the weak term in my model? I have tried using "-test(u)*k*cx"
Also, I don't understand weak term properly :( and what do these test functions mean?
2. I think, one can also use boundary stress instead of weak term. I defined my boundary stress as "-k*cx". When I try to solve I have convergence problems. Any thoughts?

also, I really appreciate if some one can give me an intuitive understanding of weak term.

PS: k is the evaporation rate and cx is the gradient in c (i.e.) dc/dx

thanks
Sathish.