**Figure 5**
(*a*) Temporal changes in the transmission of visible light through the transmission cell as a function of time during the solution exchange (from the dyed solution to deionized water) in the cell. Normalized transmission is defined as *T*(*t*)/(*T*_{max} − *T*_{min}), where *T*(*t*) is the measured transmission as a function of time, *t* (*i.e.* *t* = 0 when deionized water was injected), and *T*_{max} and *T*_{min} are maximum and minimum transmission values (*i.e.* through deionized water and the dyed solution), respectively. Four data sets are plotted for different flow settings (from 0.6 to 8 ml min^{−1}). (*b*) Relationship between the observed exchange time, *t*_{1/2}, and the inverse flow rate. The exchange time, *t*_{1/2}, is defined by the relation *T*(*t*_{1/2}) = (*T*_{max} − *T*_{min})/2, and calculated based on the best fit to the data using equation (2). The solid blue line represents the best fit through the data using equation (3). The data were also fit to a model without the 0.25 ml min^{−1} data (dashed cyan line) to confirm that the slope parameter is not controlled by one outlier. |