A phenomenological, semi-theoretical model is proposed for predicting the size of thickness of the bubble-depleted region, or bubble hole , in the frontal vicinity of a large cap bubble rising through a swarm of otherwise uniformly dispersed small bubbles. The model lays its theoretical basis on the axial pressure distribution in the very front of the cap nose which modifies the hydrostatic pressure gradient in the absence of the cap. The consequence of this pressure modification is interpreted as a local variation/increase in the effective buoyancy acting on the swarm bubbles being overtaken by the cap; the bubble rise velocity increases as the vertical distance between the bubble and the cap decreases and, under sufficient pressure gradient, it reaches the cap rise velocity. The bubble-hole thickness is estimated in essence as the bubble-cap distance along the cap central axis in this limiting state. Experiments are conducted in a two-dimensional column to measure the hole size over a wide range of swarm gas holdups. Different liquids, including sodium sulfite and glycerin solutions, are used: the former as an electrolyte solution favors the formation and prevalence of smaller bubbles, thus for examining the bubble-size effect; the latter leads to a smaller increase in the local pressure gradient due to viscous action. The present model is found to be only capable of predicting the qualitative trends exhibited by the experimental data but to severely underestimate the extent of the bubble hole.