Captive bubbles are commonly used to determine how interfacial films of pulmonary surfactant respond to changes in surface area, achieved by varying hydrostatic pressure. Although assumed to be isothermal, the gas phase temperature (Tg) would increase by >100°C during compression from 1 to 3 atm if the process were adiabatic. To determine the actual change in temperature, we monitored pressure (P) and volume (V) during compressions lasting <1 s for bubbles with and without interfacial films and used P · V to evaluate Tg. P · V fell during and after the rapid compressions, consistent with reductions in n, the moles of gas phase molecules, because of increasing solubility in the subphase at higher P. As expected for a process with first-order kinetics, during 1 h after the rapid compression P · V decreased along a simple exponential curve. The temporal variation of n moles of gas was determined from P · V >10 min after the compression when the two phases should be isothermal. Back extrapolation of n then allowed calculation of Tg from P · V immediately after the compression. Our results indicate that for bubbles with or without interfacial films compressed to >3 atm within 1 s, the change in Tg is <2°C.
Optimal control of a fed-batch reactor with overflow metabolism
