Determination of the effective molar volume of C1 and C2

Formaldehyde ($C_1$) and Glycolaldehyade ($C_2$) are in equilibrium with hydrated oligomers. We derive an average molar volume for dissolved $C_1$ and $C_2$, considering that hydrated monomers strongly dominate larger oligomers and non-hydrated forms.

For $C_1$, Winkelman et al. 2000 find $\rho_{C1}-\rho_{H2O}=(0.051-6.8*10^{-5}*T)*W$ where $W$ is the weight fraction. At 313 K, $\rho_{C1}-\rho_{H2O}=0.03*W$. For concentrations around 1M, $W\approx \mu_{C1} c_{C1}$. We have $v_{C1}=\mu_{C1}(1-0.03)=0.0029 L.mol^{-1}$.

Fitting Permeability parameters

For every dataset, the unknown parameters to be fitted are $\bar{P}_{H2O}, \bar{P}_{X}$, which are related to corresponding $P's$ through the geometric dependence $P=\bar{P} A_{red}$.

The fitting procedure finds parameters that minimize the error for the data $V_A$ and $V_B$ simultaneously. The amplitude of the noise prevents an accurate determination of the initial condition, and we therefore test a variety of initial conditions and use the estimation of $\bar{P}$ for those conditions that minimize the error.

Transport of C2

Let us first define the functions to construct the model as outlined above

Volume data, C2 8M small (even-numbered droplets), 0.8M large (odd-numbered droplets), 40 C

Results even

Results odd droplet positions

Transport coefficients water

Transport coefficients C2

Ratios

Plots

Dimensionless Transport Ratio