In this work, a Domain-distributed Physics Informed Neural Network(PINN) is used to solve an unsteady, incompressible two-phase flow problem, where data on interface position generated from the numerical simulation is also used as training data. This framework uses a Volume of Fluid (VOF) approach to advect the interface. The network outputs velocity, pressure, and volume fraction for input points randomly sampled from the domain. The knowledge of the interface position is utilized in sampling the points for training. The domain close to the interface is refined well to capture the fluid-fluid interface's effects accurately. The accuracy of the PINN model is validated by comparison with results from a CFD-based numerical model and published data. The PINN framework is then advanced into a distributed architecture, called Distributed physics-informed neural network(DPINN), where the network's architecture is distributed across the problem domain. The effects of the different parameters involved in the distributed PINN architecture, such as the width of each sub-domain and the size of local networks, are investigated. The significance of weighting the various terms in the DPINN loss function is demonstrated well in this work. The solution will converge well only when the loss terms involved in the loss function of the network are normalized. Two different types of domain distributions were tested to achieve a reasonably good approximation to the results from numerical methods.