## 3 Influence Factors of \(R_{s}\)  
### Influence of Environmental Factors on \(R_{s}\)  
#### 3.1.1 Water Flow Rate  
Many studies have reported a several-fold increase in \(R_{s}\) values under water turbulence state compared to those under static state [32; 40; 41; 42; 43]. The summary of \(R_{s}\) values from 23 previous studies are presented in Figure 3. The further statistical analysis of data revealed a substantial positive correlation between water flow rate and the \(R_{s}\) values due to the rise in diffusion rate and the decrease of WBL thickness by increasing turbulence [13; 21; 26; 27; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59]. Not surprisingly, however, a significant variability was observed in the \(R_{s}\)/A values, ranging from \(4.73\times 10^{-5}\) to \(1.63\times 10^{-1}\) L/cm\({}^{2}\)/d at flow rate from unstirring to 16.75 cm/s since different pH values, various temperatures, and diverse analytes were used in the calibration experiments from the literature [44; 53; 57; 58]. With regard to the influence of water flow rate on the \(R_{s}\) values, researchers deduced a common view that the variation of the \(R_{s}\) values with flow rate is controlled by the thickness of WBL because the fixed \(R_{s}\) values for different analytes were obtained at a given flow rate [60]. By considering that the total resistances to mass transfer were equivalent to the sum of the resistances for transport through the WBL, the membrane, and the sorbent, the effect of mass transfer through the WBL on the \(R_{s}\) of polar organic compounds can be understood more comprehensively as it is expressed in Equation (7) [61; 62]. When transport through the membrane was only via the pore, Equation (7) could be presented as Equation (8):  
\[\frac{1}{k_{o}}=\frac{A}{R_{s}}=\frac{1}{k_{w}}+\frac{1}{K_{mw}k_{m}}+\frac{1} {K_{bw}k_{b}} \tag{7}\]  
\[\frac{1}{k_{o}}=\frac{\delta_{w}}{D_{w}}+\frac{\delta_{m}\varrho^{2}}{\partial k _{m}}+\frac{1}{K_{bw}k_{b}} \tag{8}\]  
where \(k_{o}\) is the overall mass transport coefficient (MTC); \(k_{w}\), \(k_{m}\), and \(k_{b}\) are the MTC for the WBL, the membrane, and the biofilm, respectively; \(A\) is the exposure surface area of the sampling device; \(K_{mw}\) and \(K_{bw}\) are the partition coefficient of the membrane water and the biofilm water, respectively; \(\theta\)is the tortuosity; and \(\varPhi\) is the membrane porosity. It was very clear from Equations (7) and (8) that the \(\delta_{w}\) value had a negative relationship with the \(R_{s}\), indicating that the WBL is one of key effect factors on the \(R_{s}\). Figure 3: Summary of the \(R_{s}\) (L/cm\({}^{2}\)/d) of the POCIS determined in previous studies at different water flow rates: (**a**) distribution of the \(R_{s}\) with water flow rate; (**b**) statistical analysis of the \(R_{s}\) (the \(R_{s}\) values were normalized to the unit surface area of the passive sampler, and the data source was from 23 previous studies). In general, the enhanced water turbulence could cause an increase of analyte diffusion and a reduction of WBL thickness without taking account of the influence of temperature, pH, and salinity on \(R_{s}\)[48; 63]. Nevertheless, when the WBL thickness reduced to a certain extent, where further increase in flow rate would no longer affect the \(R_{s}\) values, the components of membrane and/or pore characteristics should dominate the \(R_{s}\)[55]. Numerous experiments have been carried out under laboratory conditions to explore the cumulative dynamics of samplers controlled by water membrane interface. It was found that there was a large deviation in the \(R_{s}\) values obtained under in situ and laboratory conditions for the same pollutant [26; 49; 52]. This variability was mainly due to the diverse environmental conditions that have been poorly explored.