First thing Nikhil whenever you are asking a question please be more specific. At first go i was unable to understand that you are taking about capillary tube and the phenomenon of capilarity.

Consider a capillry tube put in a liquid (say water) whose length is more than the mximum possible capillary rise (Ho) and hence It contains water uto Ho and a concave miniscus whse radius is such that r(miniscus)=2*sigma/(rho*g*Ho)

 

Now as you dip the capillary into the liquid such that length of capillary above liquid surface is H (<Ho). Then water will try to come out. This will change the radius of miniscus. The new miniscus will have a radius r'(miniscus)=2*sigma/(rho*g*H). This system is still at equilibrium. So in this case there will be flatening of miniscus (Or increase in contact angle as you said) But that will never become convex to let water  come out.

I hope this description clears your doubt