Dear Sir,
  Liquid also flows from high concentration to low concentration. Since the liquid column above A is more than that of B, a higher density of the liquid is expected at A (since pressure above A is more). So again, the liquid should flow to B.
  But, gravity pulls B towards A. This might counterbalance the former statement. But I do not know if it is true.
If required, I can also prove that liquid flows from high pressure to low pressure with practical example.
Akash Anand Here is the thing, only maintaining potential difference is not enough, we always need a path to flow, if there is no path then fluid wont flow. The condition that you have given, in static condition fluid wont flow at all, in beginning it was not static, so it will follow in a complex path. But once static condition reached then there wont be any flow.
Akash Anand And the movement you are talking will increase the potential energy of the liquid. Without any external work we cant gain any energy.