The fluid and solid mechanics of particle wall collisions were investigated for entrained coal gasifier applications. Critical velocity was used to characterize the conditions required for the reacted coal particles to stick to the wall. The critical velocity was derived from a viscoelastic model. Based on this method, the sticking probability was determined for simulated char particles from different coal specific gravity and size fractions. In this method, particles that exceeded the critical velocity were predicted to adhere, while those below it were predicted to rebound. This study showed that the sticking efficiency based on the critical velocity was closer to the predictions based on the temperature of the critical viscosity and critical angle than the predictions based on the temperature of the critical viscosity alone. However, there was a significant difference in the predictions between the "rules based criterion" and the critical velocity methodology for the sticking efficiency calculations of the larger size fractions for higher specific gravity fractions (SG3 and SG4). Nevertheless, the critical velocity methodology in this work is the first attempt to address the influence of both the ash and the carbon on the particle properties responsible for the inertial behavior of char particles within an entrained flow gasifier. Provided that the remaining uncertainty of the measurements of the particle compressive yield strength and the modulus of elasticity versus temperature is addressed in correlation to the measured viscosity and surface tension, this method could be a practical alternative in determining sticking efficiency.