The following publication describes a measurement method for determining the oxygen transfer rate in shaking flasks:
Online respiration activity measurement (OTR, CTR, RQ) in shake flasks
T. Anderlei; W. Zang; M. Papaspyrou; J. Buechs;
Biochem Eng J. (2004); Vol. 17, No. 3, pp 187-194
Experimentally you can make up several shake flasks with different filling volumes in parallel. If you get different results, then oxygen transfer could be the cause.