**9. Methodology**

The following materials were obtained from Sigma Aldrich (Munich, Germany) and were used without any further purification: AAm (99.8%) and AMPS (99%). Ammonium persulfate or APS (98%) was obtained from Tecsiquim (State of Mexico, Mexico). AMPSNa preparation is reported elsewhere [21]. The molar ratio of the monomers (1:1) was constant with a total initial concentration of 10.6% wt. The initial concentration of APS was kept constant at 0.5% wt. Polymerization progress was followed in an Anton Paar® MCR 301 Rheometer with a concen‐ tric cylinder geometry (CC27/CX) coated with polytetrafluoroethylene. A batch of reagents was prepared and then divided into seven samples that were polymerized at different shear rates as shown in **Table 1**.


**Table 1.** Set of AAm and AMPSNa copolymerization experiments at 60°C.

In relation to the CFD simulation, the geometry and the grid were constructed in Gambit®. The dimension of the geometry described the Parr® batch reactor used in the experimental work. Geometrically, the computational model is composed by a cylinder in whose interior a stirrer with rectangular impeller blades is located.

After designing the grid, sensitivity analysis was carried out to compare the velocity field magnitude in two grids with different cell sizes. The first grid (M200k) contains 201,927 cells, while the second (M400k) holds 482,312 cells. Pure water was used for both simulations.

Afterwards, Fluent® simulations were run to select a turbulence and stirring model. Experi‐ mental validation of the computational model was done by injecting 1 mL of 1 M sodium hydroxide solution (tracer). The response of the tracer was quantified with the multiparametric device OAKTON® PC 2700.

To correlate the shear rate and the stirrer speed in a batch stirred reactor, Eqs. (29) and (30) are used. This allows the comparison of stirring between the two systems used in this work, the reactor and the rheometer.

Impact of Fluid Flow on Free Radical Polymerization in a Batch Reactor http://dx.doi.org/10.5772/64156 277

$$
\dot{\gamma} = 0.10725 \text{\AA} N^{1.4} \tag{29}
$$

$$N = \left(\frac{\dot{\mathcal{V}}}{0.107255}\right)^{\frac{1}{1.4}}\tag{30}$$

where *γ*˙ is the shear rate [s−1] and *N* [rpm] is the stirrer speed. This relation was studied theoretically and experimentally by Sanchez, see [22]. The Re number was used to verify the turbulence.

$$Re = 117.39 \cdot N \tag{31}$$

**Figure 3.** Work route for simulations of stirred tanks in Fluent®.

( ) ' ''

\* '

( ) \* ''

The following materials were obtained from Sigma Aldrich (Munich, Germany) and were used without any further purification: AAm (99.8%) and AMPS (99%). Ammonium persulfate or APS (98%) was obtained from Tecsiquim (State of Mexico, Mexico). AMPSNa preparation is reported elsewhere [21]. The molar ratio of the monomers (1:1) was constant with a total initial concentration of 10.6% wt. The initial concentration of APS was kept constant at 0.5% wt. Polymerization progress was followed in an Anton Paar® MCR 301 Rheometer with a concen‐ tric cylinder geometry (CC27/CX) coated with polytetrafluoroethylene. A batch of reagents was prepared and then divided into seven samples that were polymerized at different shear

**Experiment C1 C2 C3 C4 C5 C6 C7** Shear rate [s−1] 10 30 60 90 120 150 200

In relation to the CFD simulation, the geometry and the grid were constructed in Gambit®. The dimension of the geometry described the Parr® batch reactor used in the experimental work. Geometrically, the computational model is composed by a cylinder in whose interior a stirrer

After designing the grid, sensitivity analysis was carried out to compare the velocity field magnitude in two grids with different cell sizes. The first grid (M200k) contains 201,927 cells, while the second (M400k) holds 482,312 cells. Pure water was used for both simulations.

Afterwards, Fluent® simulations were run to select a turbulence and stirring model. Experi‐ mental validation of the computational model was done by injecting 1 mL of 1 M sodium hydroxide solution (tracer). The response of the tracer was quantified with the multiparametric

To correlate the shear rate and the stirrer speed in a batch stirred reactor, Eqs. (29) and (30) are used. This allows the comparison of stirring between the two systems used in this work, the

**Table 1.** Set of AAm and AMPSNa copolymerization experiments at 60°C.

with rectangular impeller blades is located.

**9. Methodology**

276 Modeling and Simulation in Engineering Sciences

rates as shown in **Table 1**.

device OAKTON® PC 2700.

reactor and the rheometer.

*f fc c* 0 1 *J dp p* = - (26)

*fff JJJ* = + (27)

*f f fc c* 0 1 *J J dp p* =+ - (28)

The number 117.39 was calculated for the reactor filled with liquid water (viscosity of 0.001 Pa·s and density of 998.2 kg/m3 ) and by using the geometrical dimension of the system.

The methodology used for the simulations is presented in **Figure 3**. The diagram contains the experimental test used to validate the simulation model.
