The liquid ring pump is widely used in various industries, such as chemical and power industries. Numerical methods are expected to reduce the cost of product development by replacing much of the experimental testing with numerical analysis testing. The flow in a liquid ring pump exhibits a drastically changing gas-liquid interface. Due to this characteristic, the Moving Particle Semi-Implicit (MPS) method [1], a representative particle-based approach, is considered well suited for its simulation. In previous research applying the MPS method to simulate the gas phase in liquid ring pumps [2], gas backflow through the axial clearance was ignored due to the 2D simulation framework. Therefore, a gap model accounting for this gas backflow was developed in this research. The main idea of the gap model is to model the gas backflow as a mass transfer process governed by local pressure differences. First, a simplified piston model was adopted to validate the gap model by comparing theoretical solutions with simulation results. Then, the gap model was applied to the simulation of liquid ring pumps and validated by comparing experimental and simulation results. In turbulence modeling, the large eddy simulation (LES) turbulence model for particle methods developed by Arai et al. [3] was adopted. The improved free surface detection method developed by Shibata et al. [4] was used for wall treatment to determine the impeller and casing surface particles. For moving impeller surface particles, the normal vector was calculated using the weighted average of relative position vectors from the fluid particle to neighboring impeller surface particles. For stationary casing wall particles, the normal vector was calculated directly using the normalized position vector with respect to the casing center. These normal vectors were used to compute the dimensionless wall distance y+ for fluid particles, which determines whether a fluid particle belongs to the viscous sublayer, logarithmic layer, or outer layer.