On the interaction of turbulence with nucleation and growth in reaction crystallisation

Abstract

The objective of this work is to investigate the interaction of turbulence with the nonlinear processes of particle nucleation and growth that occur in reaction crystallisation, also known as precipitation. A validated methodology for coupling the population balance equation with direct numerical simulation of turbulent flows is employed for simulating an experiment conducted by Schwarzer et al. (Chem. Engng Sci., vol. 61, no. 1, 2006, pp. 167–181), where barium sulphate nanoparticles are formed by mixing and reaction of barium chloride and sulphate acid in a T-mixer, with the spatial resolution resolved down to the Kolmogorov scale. A unity Schmidt number is assumed, since at present it is not possible to resolve the Batchelor scale for realistic Schmidt numbers (order of 1000 or more). The probability density function, filtered averages and spatial distribution of time and length scales are all examined in order to shed light on the interplay of turbulence and precipitation. Separate Damköhler numbers are defined for nucleation and growth and both are found to be close to unity, indicating that the process is neither mixing nor kinetics controlled. The nucleation length scales are also evaluated and compared with the Kolmogorov scale to show the importance of resolving nucleation bursts. In addition, zones of different rate-determining mechanisms are identified. The ultimate aim of precipitation is to obtain control over the product particle size distribution, and the present study elucidates the synergistic or competing roles of mixing, nucleation and growth on the process outcome and discusses the implications for modelling.

Machine-Learning-Enabled Ligand Screening for Cs/Sr Crystallizing Separation

“…The linear growth rate G L is derived as , G L = normald L normald t = k normala 3 k v S h D AB K SP M ( SR − 1 ) ρ C L C where L is the particle diameter. Sh , k v , and ρ C represent the Sherwood number, volume shape factor, and crystal density, respectively.…”

Crystal Nucleation and Growth: Supersaturation and Crystal Resilience Determine Stickability

“…The nucleation rate ( B N ) was calculated using the model presented by Tang et al: B normalN = 1.5 D AB ( K SP SN A ) 7 / 3 γ CL k T V normalm .25em exp [ − 16 3 true( γ CL k T true) 3 V normalm 2 ( ν ⁢ ln SR ) 2 ] where all parameters are listed in Table . We also applied the growth model in the form presented by Tang et al First, the linear growth rate, G L = d L /d t , was expressed as G normalL = k normala 3 k v S h D AB K SP M ( SR − 1 ) ρ …”

“…The nucleation rate ( B N ) was calculated using the model presented by Tang et al: where all parameters are listed in Table . We also applied the growth model in the form presented by Tang et al First, the linear growth rate, G L = d L /d t , was expressed as where L c is the size of a critically stable nucleus (in meters) at the specific supersaturation: The volumetric growth rate is then expressed as …”

“…(5) where all parameters are listed in Table 2. We also applied the growth model in the form presented by Tang et al 30 First, the linear growth rate, G L = dL/dt, was expressed as…”

“…Experimental Conditions InvestigatedThe nucleation rate (B N ) was calculated using the model presented by Tang et al:30 …”