(371a) Towards the Combination of Modeling Strategies for Solid-Liquid Mixing

Solid-liquid mixing is a topic that has not been completely explored due to the variety of challenges it faces. These challenges include the occurrence of complex flow patterns in the tank, which may be due to its geometry, to turbulence or rheological phenomena therein, as well as to the intrinsic multiscale nature of solid-liquid flows. In particular, it remains unclear how the interaction between turbulence or rheology and the particle collisions impact the flow patterns and critical mixing parameters such as the impeller torque, the just-suspension speed (N_js) and the dispersion characteristics. To shed light on these issues related to solid-liquid mixing, numerical and experimental work is essential.

The seminal paper of Tsuji [1] discusses and establishes that solid-fluid modeling strategies can be classified by the scale, macro, meso or micro, within which the fluid and the solid phases are modeled. This allows for a better understanding of the strengths and weaknesses of these methods, both in terms of precision and modeling hypotheses, as well as numerical challenges such as computational time. With these strengths and weaknesses in mind, more than one method can be integrated into a multiscale strategy. The development of a new drag correlation by Beetstra et al. [2] and its application to solid-liquid modeling is a prime example of the relevance of such an approach.

In the recent years, many numerical models have been used to simulate solid-fluid flows. A non-extensive list of these methods include the Eulerian-Eulerian [3] and Eulerian-Lagrangian approaches [4], the combination of CFD and the Discrete Element Method (CFD-DEM) [5], the Quadrature Method of Moment (QMOM) [6], the Multiphase Particle In Cell Methods (MP-PIC) [7, 8], Stokesian Dynamics [9] and DNS [10]. Despite their relative potential, many of these methods have not come of age and their use for the study of solid-liquid mixing flows is still rather limited.

In this work, we present the challenges linked with the physics of solid-liquid and its modeling. We classify the models available in the literature on the basis of their modeling scale. The principles behind each model are briefly explained in order to give a better understanding of their strengths, weaknesses and regime of applicability in terms of particle concentration and length scale. The potential combination of these models into multiscale modeling strategies is discussed.

This work is the first step towards the development of new multiscale strategies for the efficient modeling of solid-liquid mixing, with the aim of gaining a better understanding of the governing phenomena and underlying physics.

 References

[1] Y. Tsuji, Multi-scale modeling of dense phase gas-particle flow, Chem Eng Sci, 62 (2007) 3410-3418.

[2] R. Beetstra, M.A. van der Hoef, J.A.M. Kuipers, Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres, Aiche J, 53 (2007) 489-501.

[3] D. Guha, P.A. Ramachandran, M.P. Dudukovic, J.J. Derksen, Evaluation of large eddy simulation and Euler-Euler CFD models for solids flow dynamics in a stirred tank reactor, Aiche J, 54 (2008) 766-778.

[4] T. Srinivasa, S. Jayanti, An Eulerian/Lagrangian study of solid suspension in stirred tanks, Aiche J, 53 (2007) 2461-2469.

[5] Z.Y. Zhou, S.B. Kuang, K.W. Chu, A.B. Yu, Discrete particle simulation of particle-fluid flow: model formulations and their applicability, J Fluid Mech, 661 (2010) 482-510.

[6] R.O. Fox, P. Vedula, Quadrature-Based Moment Model for Moderately Dense Polydisperse Gas-Particle Flows, Industrial & Engineering Chemistry Research, 49 (2010) 5174-5187.

[7] D.M. Snider, An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows, J Comput Phys, 170 (2001) 523-549.

[8] P.J. O’Rourke, D.M. Snider, An improved collision damping time for MP-PIC calculations of dense particle flows with applications to polydisperse sedimenting beds and colliding particle jets, Chem Eng Sci, 65 (2010) 6014-6028.

[9] J. Brady, G. Bossis, Stokesian Dynamics, Annual Reviews in Fluid Mechanics, 20 (1988) 111-157.

[10] J.J. Derksen, Direct numerical simulations of aggregation of monosized spherical particles in homogeneous isotropic turbulence, Aiche J, 58 (2012) 2589-2600.