4.4 Calculation, characterization, and correction of mass flow
The mass flow \(Q_{ij}\) between chamber \(i\) and \(j\) depends on the pressures on both sides of the air passage and the air passage itself (Figure S3 and 8). Empirical formulas \cite{Joshi.2021b,Joshi.2021,Cheng.2018,Jungong.2008,Kawashima.2004,KUROSHITA_2002} and the lumped-parameter resistance model \cite{Stanley.2021} (mathematically similar to empirical formulas) have conveniently approximated the flow function of an air passage, which, however, work well only when the pressure on one side remains constant. In our actuator, the pressures in both chambers change rapidly. So we use a data-driven flow \(Q\) function for higher accuracy.