Changes in the deformability of red blood cells can reveal a range of pathologies. For example, cells which have been stored for transfusion are known to exhibit progressively impaired deformability. Thus, this aspect of red blood cells has been characterized previously using a range of techniques. In this paper, we show a novel approach for examining the biophysical response of the cells with quantitative phase imaging. Specifically, optical volume changes are observed as the cells transit restrictive channels of a microfluidic chip in a high refractive index medium. The optical volume changes indicate an increase of cell's internal density, ostensibly due to water displacement. Here, we characterize these changes over time for red blood cells from two subjects. By storage day 29, a significant decrease in the magnitude of optical volume change in response to mechanical stress was witnessed. The exchange of water with the environment due to mechanical stress is seen to modulate with storage time, suggesting a potential means for studying cell storage.