Figure 4 displays the degradation ratio of salicylic acid in the polymeric microchannel reactors as a function of the inlet concentration for different flow rates and reactor dimensions. All the reactors show the same trend. As previously observed, higher degradation is reported for lower flow rates. Furthermore, degradation decreases with inlet concentration. The degradation ratio is closely linked to the salicylic acid adsorbed amount because the photocatalytic reaction occurs on the surface of the catalyst. An inlet concentration of 4 mg/l seems sufficient to saturate the catalyst surface (all catalytic sites of the catalyst surface are occupied) due to the low total catalyst surface (*A*_{cat}=140–210 mm^{2}). A further increase in salicylic acid concentration does not affect the actual catalyst surface concentration and therefore results in the diminution of the degradation ratio at higher inlet concentrations.

Figure 4 Degradation of salicylic acid in the polymeric microchannel reactors with different dimensions as a function of the inlet concentration at different flow rates (*Q*). The lines are drawn to guide the eye. Geometrical characteristics of the reactors: *κ*=3000 m^{-1} and *A*_{cat}=210 mm^{2} for R2, *κ*=3333 m^{-1} and *A*_{cat}=175 mm^{2} for R1.5, *κ*=4000 m^{-1} and *A*_{cat}=140 mm^{2} for R1, *κ*=2670 m^{-1} and *A*_{cat}=210 mm^{2} for R0.75, *κ*=2000 m^{-1} and *A*_{cat}=280 mm^{2} for R4. *κ* corresponds to the specific catalyst surface area per volume unit of liquid treated inside the reactor and *A*_{cat} to the total catalyst surface.

Degradation performances are also affected by microchannel size. Under the same experimental conditions, the highest photocatalytic degradation is obtained in the reactor R2 which possesses the largest channel width and the lowest channel height among the reactors studied. In addition, the degradation ratio cannot be directly related to the total catalyst surface (*A*_{cat}) and also to the specific catalyst surface area (*κ*). For instance, there is a large difference in the degradation ratio between the microchannel reactors R2 and R0.75 while they display the same catalyst surface. In the same way, degradation is relatively low for reactor R1 while it gets the highest specific catalyst surface area. Note that, usually, a larger surface area should be an advantage in using the photocatalyst [1, 7]. This is not the case in the present study. We are aware, however, that the residence time in the reactors can affect photocatalytic performances. For a flow rate of 2 ml/h, residence times are equal to 63, 94, 126, 141, and 252 s, for reactors R1, R1.5, R2, R0.75, and R4, respectively. The values of the residence time are unable to fully explain the photocatalytic behavior because the highest residence time is reported for reactor R4 while it displays the lowest photocatalytic activity. In addition, there is a large difference in the degradation ratio between the microchannel reactors R2 and R0.75 while they posses approximately the same residence time. To summarize, the effect of the reactor dimensions appears and the different sizes of the channel are responsible for the differences of activity observed.

All previous experiments were performed with reactors having a constant microchannel length (*L*=70 mm). Additional series of measurements are made to test the effect of the channel length. Experiments are then performed with microchannel reactors with different lengths. The reactors used are similar in width and height to R0.75 (*w*=1.5 mm and *h*=0.75 mm) and R4 (*w*=2 mm and *h*=1 mm). In Figure 5 the evolution of the degradation ratio as a function of the channel length is reported for a variety of experimental conditions. For the different reactors, a similar evolution can be observed. Degradation increases with the microchannel length, which is explained by the rise of the residence time of the reactants in the reactor. The degradation ratio *X* follows a linear increase as a function of the microchannel length *L*. The slopes of the curves are 0.0053 and 0.0076 mm^{-1} for R4 and R0.75, respectively. These slopes depend on both the inlet concentration and the reactor dimensions (channel width and height).

Figure 5 Degradation ratio (*X*) of salicylic acid as a function of the microchannel length (*L*) for different inlet concentrations (*C*_{in}) and polymeric reactors. The reactors used are similar in width and height to R0.75 (*w*=1.5 mm and *h*=0.75 mm) and R4 (*w*=2 mm and *h*=1 mm). The lines represent the best linear fits given by *X*=0.0076 *L* + 0.0097 (R^{2}=0.992) for R0.75, and *X*=0.0053 *L*-0.0026 (R^{2}=0.996) for R4.

For an optimal design of the microchannel reactors, it is important to obtain a relation between the degradation ratio *X* and the geometrical dimensions of the channel (*w, h*, and *L*) in order to reproduce the experimental results, i.e., *X*(R2) > *X*(R1.5) > *X*(R1) > *X*(R0.75) > *X*(R4). It was previously observed that *X* increases with the channel width *w* and length *L* (Figures 4 and Figure 5) while it decreases with the channel height *h* (Figure 4). For this reason, a dimensionless geometrical parameter, which reads as *wL*/*h*^{2}, is introduced. The product *wL* highlights the uniform light irradiation over the entire catalyst surface. It is then considered that the bottom of the channel covered with TiO_{2} can be photoactivated. The actual illuminated catalyst surface becomes equal to *wL*. In addition, the term in 1/*h*^{2} is necessary to take into account the diffusion of salicylic acid from the solution to the actual illuminated catalyst surface (mass transfer limitation). In a precedent study, we demonstrated that some external mass transfer limitation occurs in our experimental system [19]. For the special case of microchannel reactors, Commenge et al. [33] showed that in the case of heterogeneous reactions limited by mass transfer, the characteristic time for the operation (diffusion limited) varies with the square of the channel height (*h*^{2}).

For a constant value of the flow rate and the inlet salicylic acid concentration, the degradation ratio can be reported as a function of *wL*/*h*^{2}. Each experimental point corresponds to a given microchannel reactor. In Figure 6, the degradation ratios from the data of Figure 4 (reactors R2, R1.5, R1, R0.75, and R4) are plotted against the dimensionless geometrical ratio *wL*/*h*^{2}, for several flow rates *Q* and inlet concentrations *C*_{in}. In all cases, a similar evolution can be observed. For a fixed value of *Q* and *C*_{in}, the data points fall on a single line indicating that *X* increases linearly with *wL*/*h*^{2}. Based on 12 sets of experimental data the following equation is obtained to correlate the degradation ratio in terms of length, width, and height of the microchannel. The equation can be written as:

Figure 6 Degradation of salicylic acid as a function of the dimensions of the microchannel reactors (*wL*/*h*^{2}) for different inlet concentrations (*C*_{in}) and flow rates (*Q). w* refers to the channel width, *L* to the channel length, and *h* to the channel height. The lines represent the best linear fits given by *X*=*a* (*wL*/*h*^{2}).

Applying this linear fit to the data of Figure 6 gives the values of the proportionality factor *a*. All the results are reported in . A majority of regression coefficients are better than 0.986. For a constant flow rate, the proportionality factor (*a*) does not depend on the inlet salicylic acid concentration. For *Q*=10 ml/h, all the values equal 0.0002 regardless of the inlet concentration. As the flow rate decreases below 10 ml/h the average values become *a*=0.00042±0.00005 and *a*=0.0003 for flow rates of 4 ml/h and 2 ml/h, respectively. However, the values slightly vary with the flow rate because they range from 0.0002 to 0.0005. Considering all the data, the average proportionality factor is equal to *a*=0.00031±0.00009. A single value of *a* represents well the experimental degradation ratios for all flow rates and inlet concentrations.

Table 2 Parameters obtained from the linear fit *X*=*a* (*wL*/*h*^{2}).

The linear fits are performed with the data from Figure 6. R^{2} is the regression coefficient.

The linear relationship between the degradation ratio and the dimensionless geometrical parameter indicates that the change in the photocatalytic activity, at a given flow rate and concentration, is fully determined by the dimensions of the microchannel. It is clear that despite its simplicity the empirical relation captures the essential physics of the photocatalytic degradation in a rectangular microchannel reactor in the presence of mass transfer limitation. Owing to the high degree of correspondence for a wide variety of configurations, Eq. (5) can be used to predict the photodegradation behavior as a function of key geometrical parameters such as microchannel length, width, and height. To increase the photocatalytic efficiency, a microchannel with a high value of the ratio *wL*/*h*^{2} has to be used. For this purpose a channel with large width and length coupled with a low height is highly recommended.

However, it is anticipated that the dimensions of the channel are not the major parameter in order to significantly enhance the degradation. Other parameters such as light intensity (*I*), flow rate (*Q*), and inlet concentration (*C*_{in}) may be more appropriate. Furthermore, all these operating parameters do not have the same relative effect, with some having a more pronounced impact. A method for analysis consists of evaluating the sensitivity of each parameter by calculating the elasticity criteria [34]. Elasticity is a measure of the incremental percentage change in the variable *X* with respect to an incremental percentage change in another variable *Y*:

The calculation of the elasticity of the degradation with respect to the light intensity is performed using experimental data previously obtained by our groups [19, 20]. The experiments were conducted in reactor R1.5 at different light intensities ranging from 1 to 2.8 mW/cm^{2}. presents the values of the elasticity of the degradation with respect to the key operating parameters *Y* (*I, Q, C*_{in}, or *wL*/*h*^{2}). The two parameters having a great influence (elasticity equal to approx. 0.6–0.7) are the light intensity and the flow rate. As expected, the light intensity is the major factor in photocatalytic reactions, because electron-hole pairs are produced by light energy. It is also demonstrated that the flow rate make a significant contribution to the degradation ratio. The two other parameters (*C*_{in} and *wL*/*h*^{2}) have a lower influence (elasticity equal to 0.3–0.2). The reactor dimensions, with an elasticity value of 0.24, are a much less sensitive parameter. An elasticity value equals to 0.24 means that an increase of 10% of the dimensionless geometrical ratio *wL*/*h*^{2} leads to an increase of 2.4% of the degradation ratio.

Table 3 Values of the elasticity of the degradation with respect to key operating parameters.

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