Balloon compliance fixture correction

A balloon compliance fixture correction removes the volume response of tubing, connectors, fluid and other apparatus from a measured balloon volumetric compliance. It is a correction to a defined measurement arrangement. The pressure reference and the state of the apparatus must match between characterization and use.

For a quasistatic experiment in which fixture and balloon experience the same pressure increment, writeA separately characterized fixture supplies $C_f$. A rigid termination can provide one control configuration, but changing tubing or trapped gas between the control and balloon runs changes the correction itself.

For an original example, $C_{\mathrm{meas}}=2.00$ and $C_f=0.50\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$ give $C_b=1.50\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$. Assigning the whole measured response to the balloon would overestimate it by one third relative to the corrected value. Independent standard uncertainties $0.05$ and $0.04\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$ give $u(C_b)=\sqrt{0.05^2+0.04^2}\approx 0.0640\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$. Correlated inputs instead require the term $-2\mathrm{Cov}(C_{\mathrm{meas}},C_f)$ in the variance.^[ref]

Trapped gas explains one nonlinear contribution. For an isothermal gas pocket with $p_{\mathrm{abs}}{V}_g$ constant, its local stored-volume response is $-d{V}_g/dp=V_g/p_{\mathrm{abs}}$. A $20\mu \mathrm{L}$ pocket at $100\mathrm{kPa}$ absolute pressure contributes $0.20\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$. Absolute pressure is required here; substituting gauge pressure into the gas law would be wrong.

A manufacturer's diameter-versus-pressure chart, such as Nipro's Thouzer chart, reports a different observable from injected volume.^[ref] Such a chart does not measure the fixture's stored volume. Comparing a measured volume curve with it requires the balloon geometry and apparatus correction, rather than treating diameter compliance and whole-system volume compliance as identical.

During flow, different parts of the fixture can have different pressures. The simple additive quasistatic model then needs a dynamic extension, consistent with the balloon inflation hydraulic time constant. Loading history and hysteresis must also match before two response curves can be subtracted.