(728a) CFD Investigations of Carbopol Mixing in the Transition Region

Mixing is a crucial step in the production of many products, ranging from hair care to pharmaceuticals. The industrial process is typically used to blend miscible liquids, dissolve soluble compounds in a liquid, to facilitate a chemical reaction, to suspend insoluble material in liquid (e.g. paint), or to emulsify immiscible liquids (e.g. mayonnaise). Optimizing the efficiency of a mixing tank is key in product production, since not only does optimization lead to a more cost effective production process, but also a higher quality product, which is crucial in the pharmaceutical and chemical industries. To optimize the mixing process, what occurs inside the tank must be well understood. This can be unrealistic using just the physical system, as tanks can have significant volumes making modeling difficult. Computational Fluid Dynamics (CFD) offers a valuable look inside the tanks. CFD is used in modeling various physical systems to analyze velocity profiles, streamlines, volume fraction distributions, and numerous other fluid and flow properties. With data gathered from computational models, the properties and behaviors of fluid domains within a mixing tank can be studied.

The characteristics of a mixing tank are determined by the regime in which the tank operates: laminar, transition, or turbulent. Mixing is typically studied and modeled in the laminar or turbulent regime, as the equations governing these regimes are well understood. Due to the complexity of transition mixing, there is minimal modeling done in the regime despite it being a common working regime for certain industries, including the pharmaceutical, agrochemical, cosmetic, and food industries.^1-4 The lack of accurate transition mixing models hinders these industries in fully understanding their processes. The inaccuracy of transition mixing models is due to CFD’s inability to predict large scale instabilities in the flow domain.⁵ Not only does the inaccuracy of transition mixing models hinder industries in optimizing their processes, but it also inhibits investigation of the behavior of this regime. Processes that typically lie in the transition regime tend to involve non-Newtonian fluids due to their complex behavior. A non-Newtonian fluid is one who’s viscosity is a nonlinear function of shear. This results in different Reynolds numbers throughout a tank, since the Reynolds number is a function of viscosity. The regime of a fluid domain is determined by the Reynolds number of the flow, with lower Reynolds numbers indicating laminar flow and higher Reynolds numbers indicating turbulent flow.

The goals of this project are to investigate the behavior of a non-Newtonian, shear thinning fluid, Carbopol, being mixed in the transition flow regime using CFD, and to adapt these computer-generated models to physical systems to increase the accuracy of the models. Since the transition regime spans a range of Reynolds numbers, three different ranges within the transition regime were modeled. These Reynolds numbers accurately span the transition regime of the A320 impeller, the impeller used in this study. Two sets of models were generated: (i) with changing impeller speed and (ii) with changing viscosity profile. This also allows for an investigation of the flow field’s behavior with changing viscosity versus changing RPM despite having the same Reynolds number. Carbopol’s viscosity can be easily modified with pH, which makes it an optimal working fluid for many industrial studies.⁶ Using data from actual systems, models were generated, analyzed, and modified using commercial CFD software to accurately represent the physical systems. The models were generated using multiphase transient flow simulations with the mixture model to allow for non-Newtonian viscosities. To compare the physical systems and the models, a portion of dyed Carbopol was added after the tanks reached steady state. Blend times and patterns were analyzed and compared across the tanks. To track the mixing in the computational model, volume fractions were used. The hope is that this work will contribute to the understanding of mixing in the transition regime.

References

(1) Rzyski, E. Mixing Time (time to homogenization) in the Transition Region of Mixing. The Chemical Engineering Journal 1985, 31, 75.

(2) Zhang, Y.; Gao, Z.; Li, Z.; Derksen, J. J. Transitional flow in a Rushton turbine stirred tank. AIChE Journal 2017, 63 (8), 3610.

(3) Machado, M. B.; Bittorf, K. J.; Roussinova, V. T.; Kresta, S. M. Transition from turbulent to transitional flow in the top half of a stirred tank. Chemical Engineering Science 2013, 98, 218.

(4) Mendoza, F.; Bañales, A. L.; Cid, E.; Xuereb, C.; Poux, M.; Fletcher, D. F.; Aubin, J. Hydrodynamics in a stirred tank in the transitional flow regime. Chemical Engineering Research and Design 2018, 132, 865.

(5) Bakker, A.; Myers, K. J.; Ward, R. W.; Lee, C. K. The Laminar and Turbulent Flow Pattern of a Pitched Blade Turbine. Trans IChemE 1996, 74.

(6) Kelly, W.; Gigas, B. Using CFD to predict the behavior of power law fluids near axial-flow impellers operating in the transitional flow regime. Chemical Engineering Science 2003, 58 (10), 2141.