Use of conductivity data

a) Time-delay measurements

The time-delay measurements for the OPP experiments were used to determine t0, the

time when the osmotic perturbation occurred. A value of tP(the time when the cell

pressure starts changing) was obtained from the unculled data by taking a linear regression of points in the first 1/3-1/2 of the water phase (see Fig. 3.8). From the time-delay tD, we have:

t0 = tP - tD. (4.1)

One may ask: does the measured time-delay give information about the ULe thickness present in an OPP experiment? In §3.6.2 it was demonstrated that, in simulated data, a relationship exists between the ULe thickness δULEsimand the time-delay tDsim. This

suggests that a relationship may also exist between the measured time-delay tD and

the ULe thickness δULE presentin an OPP experiment. If there is a consistent tD vs.

Since the value of δULE is unknown, the relationship between tD and δULE cannot be

examined directly. It may then be asked whether the simulated data can be used instead to infer δULE in an OPP experiment. However, this will only be possible if:

a) the simulated curve fits the initial curvature and water phase of the observed data exactly (i.e. tDsim = tD)

b) the relationship between the ULe thickness and the time-delay in both observed and simulated data are consistent across different cells.

It may be shown that (a) is rarely achieved and that (b) is false, thus limiting the usefulness of tD as a general predictive tool for the ULE thickness. To show this, the

relationships between tDsim and δULEsim, and between tD and δULEsim,for fits to two OPP

data sets from different cells, were examined. δULEsim in this case is used as a

hypothetical proxy for δULE. δULEsim wasfixed at different values, the data fitted by optimizing Lp, ps, σ and t0, and tDsim and tD calculated. t0 must be optimized since tD is

affected by δULEsim, and tP in Eq. (4.1) changes by a lesser amount than t0 for fits to the

data.

It was found that for a small range of δULEsimvalues (3-7 x 10-5m), the δULEsim vs. tD

and δULEsim vs. tDsim relationships for fits to two data sets from different cells were

linear (Fig. 4.7). However, the slope of these relationships differed between δULEsim

vs. tD and δULEsimvs. tDsim (in each Fig. 4.7b and Fig. 4.7c), as predicted, due to

differences in the slopes of the water phases between simulated and observed data. The slope of these relationships also differed between the two data sets (Fig. 4.7b & Fig. 4.7c). The δULEsim vs. tDsim relationship for simulations where the data is not fitted

but different values of δULE were chosen and used to generate different relaxation

curves (Fig. 4.7a), was linear but with a different slope again.

These results confirm that (a) and (b) above are not true and that there is no method for inferring the ULe thickness in CPP experiments from available data. Therefore,

δULE should be treated as an additional parameter to be optimized for fits using the

UL model. Use of the measured time-delay was limited to determination of t0 for OPP

For OPP Run 9 of Cell 3 0.0 0.2 0.4 0.6 0.8 1.0 3 4 5 6 7 T im e- d el ay ( s ) (b)

For OPP Run 9 of Cell 4

0.0 0.4 0.8 1.2 1.6 3 4 5 6 7

Simulated ULe thickness (x10-5 m)

T im e- d el ay ( s ) (c)

For simulated OPP curves which vary depending on ULe thickness 0.0 0.2 0.4 0.6 0.8 1.0 1.2 3 4 5 6 7 Si m u a lte d ti m e -d e la y (s ) (a)

Fig. 4.7 Showing time-delay vs. ULe thickness (δULEsim) relationships. (a) For simulated curves which

change with δULEsim. In (b) and (c), the pink line indicates δULEsim plotted against tD for observed OPP

b) Ramp time measurements

The relationship between the ramp time and time-delay was examined by imposing a ramp in the external solute concentration in simulated OPP data and calculating the time-delay from the output P-t curve. The model showed a correlation between the ramp time and time-delay, as expected since they are both dependent on t0 (Fig. 4.8).

However, as the main component of the ramp time is the mixing time (§4.2.2b) which may vary between runs and have no relation to t0, this correlation would not

necessarily be observed in the observed data.

When measured ramp times and time-delays were plotted for the observed data (Fig. 4.9), it was found that only cell 4 exhibited a correlation between these two factors. For cells 2 and 3 the ramp times were similar for each OPP run (Table 4.7).

Considering these patterns in the measured ramp times, the latter was not suitable for use as an input into the model. It was decided that for model fits to OPP experiments without a bubble (e.g. for Cell 4), the ramp time will be considered a free parameter to be optimized along with the membrane parameters (in a similar way that the ULe thickness was considered an additional free parameter for OPP experiments with bubbles). Since the ramp time and ULe thickness can’t be simultaneously optimized due to their correlation (the ramp time is correlated with the time-delay which in turn is dependent on the ULe thickness), the ULe thickness will be fixed at average values found for fits to the OPP experiments with a bubble, and the ramp times then

estimated using the model. This is because for a given cell geometry and the same external flow rate and external solution, one would expect the ULe thickness to be more or less a constant value for each cell.

There is a lack of sufficient information available on how the external concentration changes over time. The conductivity data in Fig. 4.2 suggests that the change in external concentration (or shape of the concentration exchange function) is non-linear and is not actually a ramp. Consequently, different representations for this exchange function (linear and exponential) will also be explored (see §4.7).

Ramp time vs. time-delay for OPP simulations 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 1 2 3 4 Ramp time (s) T im e- d el ay ( s ) 5

Fig. 4.8 Showing a correlation between ramp times and time-delays for simulated OPP data using the UL model.

Ram p tim e vs. Tim e-delay for 3 cells

0.0 0.2 0.4 0.6 0.8 1.0 1.50 1.70 1.90 2.10 2.30 2.50 Ram p tim e (s) T im e- d elay ( s)

Fig. 4.9 Ramp times vs. time-delays for observed OPP data for Cell 2 (▲), Cell 3(■), and Cell 4 (♦).