The oscillatory flow reactor (OFR) has been widely investigated during the last two decades as a novel platform for achieving efficient and uniform mixing at average shear rates up to one order of magnitude lower than the standard stirred tank reactor (STR) [1]. The OFR consists of a tubular device containing evenly spaced baffles which are transversely assembled to a periodically oscillating flow. The mixing is achieved by the interaction of the fluid with the constrictions, which may be designed with different configurations according to the application [2].
The novel OFR presented in this work was designed with smooth periodic constrictions and differs from the typical integral baffle configuration in the cross-section format, which is rectangular rather than circular. This new feature was developed to improve the suspension and the flow of solid particles in continuous processing operations, such as crystallization. In order to characterize the mixing efficiency of this device, residence time distribution (RTD) experiments with liquid solutions and solid suspensions were conducted by monitoring the response of a pulse tracer for each system. A face-centered composite experiment was designed through a design of experiments (DoE) approach to assess the effects of different hydrodynamic conditions on the axial dispersion coefficients of liquids and solids.
Experimental Section
The OFR used in this work consists of a 3.3 m long Perspex® plate-like reactor, with an internal diameter of 8 mm in the straight section and 3.3 mm in the constriction, and a total volume of 145 mL. A continuous net flow of deionized water was injected into the reactor by a peristaltic pump and oscillated by a linear motor. At time zero, a pulse tracer of 2 mL was quickly injected at 25 cm downstream of the water inlet. A 0.4 g/L aqueous solution of indigo carmine was used as liquid tracer and a 40 % (m/m) suspension of PVC particles with a mean diameter of 160 mm was used as solid tracer. The concentration of tracer was measured in the reactor outlet by a spectrometer at the wavelengths of 654 nm and 655 nm for the liquid and the solid tracers, respectively. The axial dispersion coefficients were determined by fitting the experimental data from RTD experiments to a plug flow with axial dispersion model [3].
A full factorial experiment was designed with Minitab® to assess the effect of three factors, the net flow rate, Q, the frequency of oscillation, f, and the amplitude of oscillation, x0, on two response variables, the axial dispersion coefficient of liquids, DL, and the axial dispersion coefficient of solids, DS. Each factor was studied at two levels: 15.6 and 109.5 ml/min for Q, 3 and 6 Hz for f, and 12.9 and 22.5 mm for x0. In coded units, the low level is defined as –1 and the high level is defined as +1. Each combination of factors was performed in triplicate. This design was augmented with centre and axial points and turned into a face-centered composite design in order to build a second order model for each response variable. Each term of this model is either linear, square or an interaction between factors and has an associated coefficient that delivers the best fit between the model and the experimental data.
Results and Discussion
A second-order model was developed in Minitab® so as to predict DL and DS with different levels of Q, f and x0. The significance of each term of the model was determined by comparison of the p-value of each term to the significance level of 95 %. The p-value measures the evidence against the null hypothesis, which states that there is no association between the term and the response.
A backward stepwise elimination technique was applied to select the significant terms, and to eliminate the insignificant terms from the model. To keep the model hierarchy, a linear term remained in the model when an interaction or square effect of that term was found significant. After this procedure, the residuals versus fitted values plots were checked for nonrandom patterns. It was found that the scatter of the residuals around the zero residuals line is wider as the value of the fits increases, which indicates nonconstant variances. A Box-Cox transformation of the data with λ=0 was used to stabilize these variances.
The linear terms of Q and x0, the square term of f and the interaction term between Q and f were found significant for both the response variables. Also, the interaction term between Q and x0 was found significant for DL, but not for DS. However, this term as a p-value of only 0.043, meaning that with a confidence interval 96 %, instead of 95 %, this term would not be considered significant.
The final regression models for the transformed responses of DL and DS are described by the following equations, in coded units:
ln(DL) = –7.3549 +0.4507Q –0.0216f +0.2961x0 –0.3160f2 +0.1955Q f–0.0858Qx0
ln(DS) = –7.4966 +0.3292Q –0.0151f +0.3800x0 –0.3229f2 +0.1531Qf
These models have coefficients of determination of 89.5 % and 88.2 %, respectively. Also, the p-values for the lack-of-fit were found to be more than 0.05 for both the models, so there is no evidence that the models do not fit the data with a confidence interval of 95 %.
The regression coefficients of both models have the same order of magnitude and the same signal, meaning that the direction and the strength of each factor is very similar for both DL and DS. Moreover, the positive effects of Q and x0, implied by the positive signal of their coefficients, are consistent with previous studies [3]. The contour plots also show similar trends for both models. Therefore, one can conclude that liquid solutions and solid suspensions have identical dispersion performances in this reactor.
Conclusions
A novel OFR with smooth periodic constrictions and a rectangular cross-section was developed. RTD experiments with liquid solutions and solid suspensions were performed to determine DL and DS in this device. A face-centered composite experiment was designed and a second-order model was built so as to predict DL and DS with different levels of Q, f and x0.
The novel OFR used in this work was found to have similar axial dispersion performances with liquid solutions and solid suspensions. This is of paramount importance for multiphase systems such as crystallization where the migration of molecules between a supersaturated solution and crystalline particles takes place throughout the whole nucleation and growth steps.
The models obtained for both DL and DS might be further improved by the addition of other significant variables that were not considered in this study, namely the pressure drop. This might be object of future work.
Acknowledgments
This work was financially supported by: I) POCI-01-0145-FEDER-016816 (PTDC/QEQ-PRS/3787/2014) funded by the Project 9471 – Reforçar a Investigação, o Desenvolvimento Tecnológico e a Inovação (Project 9471 – RIDTI), by the European Regional Development Fund (ERDF) and by national funds through Fundação para a Ciência e a Tecnologia I.P. (FCT); II) IF exploratory project [IF/01087/2014] funded by FCT; III) POCI-01-0145-FEDER-006939 (Laboratory for Process Engineering, Environment, Biotechnology and Energy – UID/EQU/00511/2013) funded by ERDF, through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI) and by national funds, through FCT; IV) NORTE‐01‐0145‐FEDER‐000005 – LEPABE-2-ECO-INNOVATION, supported by North Portugal Regional Operational Programme (NORTE 2020), under the Portugal 2020 Partnership Agreement, through ERDF. P. Cruz gratefully acknowledges doctoral scholarship [SFRH/BD/119391/2016] from FCT. A. Ferreira is an Investigador FCT.
References
[1] X. Ni, J. A. Cosgrove, A. D. Arnott, C. A. Greated, and R. H. Cumming, “On the measurement of strain rate in an oscillatory baffled column using particle image velocimetry,” Chem. Eng. Sci., vol. 55, no. 16, pp. 3195–3208, 2000.
[2] J. R. McDonough, A. N. Phan, and A. P. Harvey, “Rapid process development using oscillatory baffled mesoreactors – A state-of-the-art review,” Chem. Eng. J., vol. 265, pp. 110–121, 2015.
[3] M. Zheng and M. Mackley, “The axial dispersion performance of an oscillatory flow meso-reactor with relevance to continuous flow operation,” Chem. Eng. Sci., vol. 63, pp. 1788–1799, 2008.
See more of this Group/Topical: Applications of Particle Technology for Pharmaceuticals