Node buffer size has a big influence on performance of Mobile Opportunistic Networks (MONs). This is mainly because each node should temporarily cache packets to deal with the intermittently connected links. In this paper, we study fundamental bounds on node buffer size below which the network system can not achieve the expected performance. Given the condition that each link has the same probability p to be active, and q to be inactive during each time slot, there exits a critical value pc from a percolation perspective. If p > pc, the network is in the supercritical case, there is an achievable upper bound on the buffer size of nodes, independent of the inactive probability q. When p < pc, the network is in the subcritical case, and there exists a closed-form solution for buffer occupation, which is independent of the size of the network.