Solid-liquid suspensions

Apart from the above mentioned classification, i.e. laminar, transitional and turbulent regime, fluid mixing in stirred vessels has also been generally classified into the single phase flow and multi-phase flow concerning the number of mixing phases. General information about the single phase flow in stirred vessels has been discussed above, and as it is widely encountered in a variety of industries, it is necessary to introduce briefly the multiphase flow in stirred vessels, e.g. solid/liquid, gas/liquid, and solid/gas/liquid. Due to the additional effects associated with the discrete phase, e.g. interactions between particle-fluid and particle-particle collisions, considerable complexity of the turbulent (time-dependent) flow structure is induced in the multi-phase mixing in stirred vessels (Nienow, 1997b).

Solid suspensions in liquids find a wide range of industrial applications in chemical reaction, pharmaceuticals, catalytic, crystallization, sterilization, and mineral industries. Depending on the density of solid particles, the solid particles may settle at the tank base (_d _l), or float on the liquid surface (_d _l). In order to achieve good heat and mass transfer, or chemical reaction between the liquid phase and solid particles, the settling or floating solid particles need to be lifted off the tank base or be drawn down from the liquid top surface. The particles are then distributed to different regions within the stirred vessel. Either inadequate or overmixing of solid suspensions in liquids causes poor product quality or poor energy efficiency.

16 Considering the suspension of settling particles, three levels have been classified in terms of the degree of solid suspensions: 1) on-bottom motion; 2) just complete suspension; 3) uniform suspension (Paul et al., 2004), as shown in Fig. 2.4. The just complete suspension (impeller speed of Njs,) is a critical state which could satisfy the requirement in most industrial applications, because under this condition the total surface of solid particles is sufficiently exposed to the liquid phase. The uniform solid distribution which requires much higher impeller speed of above Njs are desirable in some industries such as crystallizers and polymerization reactors, and non-uniform solid distribution may lead to unacceptably high local supersaturating levels and subsequent non-uniformity in crystal growth (Atiemo-Obeng et al., 2004).

(a) (b) (c)

Figure 2.4. Degree of solid suspension (Paul et al., 2004): (a) Partial suspension; (b) Complete suspension; (c) Uniform suspension.

Extensive studies on characterizing the value of Njs have been carried out since the empirical correlation for Njs was proposed in the pioneering work of Zwietering (1958), and these studies have been reviewed by Jafari et al. (2012) and Tadhavi et al. (2011). However, none of the developed correlations are universally applicable, as the values of Njs from different theoretical models vary over a wide range (Bohnet and Niesmak, 1980). The Zwietering

17 criterion, i.e. no particle remains stationary on the bottom of the tank for longer than 1-2 s, is still the most widely used criterion.

Comparing with the theoretical models for the values of Njs, a localized hydrodynamic approach provides a more efficient basis for design since it enables a detailed description of the multiphase flow structures. The dilute solid suspensions, with the solid loading ranging from 0.02 vol% to 2.5 vol%, have been widely investigated using the well-established optical techniques such as LDV and PIV (Nouri and Whitelaw, 1992; Guiraud et al., 1997; Micheletti and Yianneskis, 2004; Montante et al., 2012). However, these techniques cannot be applied to dense solid concentrations due to the opacity of the systems. Solid dynamics at low solid concentrations have little effect on the liquid phase and hence, the liquid flow in dilute solid-liquid suspensions presents high similarity to the flow field of the single phase (Mersmann et al. 1998; Montante, G., 2012). However, with increasing solid particles, the effect of solid particles on the liquid phase is no longer negligible. Large drop in liquid velocities in the presence of particles of 2.5 vol% has been reported (Nouri and Whitelaw, 1992; Micheletti and Yianneskis, 2004).

So far, attempts at local measurements have been mainly limited to the investigation of mean axial solid-concentration profiles at low to medium solid loadings using intrusive conductivity or capacitance probes (Godfrey and Zhu, 1994; Brunazzi et al., 2004; Špidla et al., 2005).

Both the radial and axial solid distributions at solid loading of 20 vol%, using the probe method, were measured by Yamazaki and Miyanami (1986). The probe methods, however, give limited information and cannot be used to probe the local hydrodynamics of suspensions in detail or to measure the 3-D distribution of both liquid and solid. Recently, the radioactive particle tracer method has been used to measure the flow fields of both phases; solid

18 distributions at high solid loadings of up to 40 wt% were reported by Guida et al. (2009, 2010) using the Positron Emission Particle Tracking (PEPT) measurement, and the Computer Automated Radioactive Particle Tracking (CARPT) technique based on gamma-ray emissions has been developed (Rammohan et al., 2001; Guha et al., 2007). CFD modelling has been widely employed for simulating the solid-liquid suspensions in stirred vessels, as reviewed by Sommerfeld and Decker (2004) and Sardeshpande and Ranade (2012). Direct Numerical Simulations (DNS), Large Eddy Simulations (LES), and Eulerian-Lagrangian approches were used to handle dilute systems (~ 5 vol%) in a limited range of works due to computationally expensive cost (Derksen, 2003; Sbrizzai et al., 2006). The multi-fluid Eulerian-Eulerian model has been most widely used to model high solid concentrations (Tamburini et al. 2011;

Khopkar et al., 2006). However, validations reported in the literature have been restricted to dilute systems (Montante and Magelli, 2005; Khopkar et al., 2006; Micale et al., 2004;

Altway et al., 2001).

Mixing features become more complicated concerning solid suspensions in liquids exhibiting non-Newtonian behaviour, for example, in the process of particulate food mixtures such as fruit particles in yoghurt. This area has been scarcely investigated in the previous research.

The just suspended impeller speed, Njs, for solid suspensions in shear-thinning liquids was measured in few studies (Kushalkar and Pangarkar, 1995; Wu and Pullum, 2001; Ibrahim and Nienow, 2010). Attempt at the detailed local information of solid suspensions in a Bingham liquid has been made numerically by Derksen (2009) using a Lattice-Boltzmann method.

However, due to the lack of experimental data for the solid suspensions in viscoplastic liquids in stirred vessels, a one-dimensional single phase planar channel flow was performed instead to validate the CFD predictions. In summary, there are still outstanding issues that have not

19 been addressed concerning the accurate CFD modelling of solid-liquid suspensions due to the complex interactions between the phases and within the solid particles.