The rate of engulfment of nominal 8.0 mum soda-lime glass particles into plasticized polystyrene substrate was measured using field emission scanning electron microscopy (FESEM). Initially, after the particles were deposited onto the substrates, a finite-size contact radius was observed. The degree of embedment appears consistent with estimates made using the JKR formalism. However, over time, the particle appears to become engulfed into the substrate. Initially, the engulfment rate is rather slow. However, as the particle becomes more engulfed, the rate of engulfment appears to increase until the particle is halfway submerged. After that, the engulfment rate appears to decrease, leaving the caps of the particles still visible after several months. It is proposed that the variations in the engulfment rate can be understood if it is assumed that the particle is at terminal velocity in a viscous medium, as determined by a Stokes' law drag force opposing the z-component of a surface force pushing the particle into the substrate.