Achieving reliability in bulk solids mixing processes is key to meeting product quality requirements in a wide range of industries but physical trial-and-error optimization is time consuming and expensive. Altair EDEM enables the efficient virtual optimization of bulk solid mixing equipment and process operation.
Simulation files used in this example can be downloaded here:
A step-by-step tutorial for setting up a simple mixing simulation in EDEM can be found here.
EDEM simulations can provide otherwise difficult to obtain insight into the mechanics of mixing systems including the internal flow field and the spatial-temporal evolution of mixture uniformity as shown below:
The convection in bulk solids mixing systems can be analyzed using the instantaneous particle velocity or using time-averaged continuum fields such as the momentum density field shown in Figure 1. The latter is computed from the discrete particle data using EDEM's continuum analysis functionality and is useful for convection analysis of transient or cyclic mixing systems.
Figure 1 Instantaneous particle velocity and time-averaged momentum density field in a paddle mixer
The spatial-temporal evolution of mixture component concentrations can be analyzed by performing virtual sampling using EDEM bins as shown in Figure 2. The concentrations are computed from the total particle mass by type within the bin, which can be exported from EDEM into a comma delimited file. It is possible to bin other particle properties and the number of particles, particle velocity and particle residence time are of relevance to mixing.
Figure 2 EDEM bins in a paddle mixer simulation and corresponding mass fractions of blue particles in each bin
The temporal evolution of mixture uniformity can be computed from binned particle data using the Relative Standard Deviation (RSD) of mixture component concentrations in a population of bins as shown in Figure 3. A rectilinear grid of bins can be generated in EDEM using the Grid Bin Group option and the concentrations can be computed from exported binned particle mass as before. An RSD value of 0 corresponds to the perfectly mixed state and a value of 1 to the fully segregated state.
Figure 3 An EDEM grid bin group in a paddle mixer and the RSD evolution of the blue particle concentrations within the bins
The uniformity of binary mixtures can be computed more accurately from the binned particle data using the Lacey mixing index [1] defined in Equations 1 to 4 where is the Lacey mixing index,
is the total number of bins,
is the average number of particles of type 1 per bin,
is the number of particles in bin i,
is the number of particles of type 1 in bin i and
is the proportion of type 1 particles in the system. An example result is shown in Figure 4. A Lacey index value of 0 corresponds to the perfectly segregated state and a value of 1 to the randomly mixed state. An EDEMpy script for automatically computing the Lacey mixing index from EDEM simulation data is available here.
Figure 4Temporal evolution of the Lacey mixing index in a paddle mixer
If the two mixture components have equal mass fractions and similar particle size distributions it is also possible to quantify the mixture uniformity using the particle contacts-based Segregation Index [2] defined in Equation 5 where is the number of contacts between particle types i and j. A value of 0 corresponds to the perfectly mixed state and a value of 2 to the fully segregated state. Unlike the Lacey Mixing index, the Segregation Index is not sampling-based and is therefore not sensitive to the statistical effects of sample population size. The calculation can be performed externally to EDEM from exported particle contacts data or using the EDEMpy script available here.
Figure 5 Temporal evolution of the Segregation Index in a paddle mixer
For ternary and higher order mixtures the mixture uniformity can be quantified by using multi-component mixing indices such as the one proposed by Cho et al. [3] or by lumping components together to reduce the mixture to a binary one.
Modelling bulk solids mixing processes is simple with EDEM’s intuitive Graphical User Interface (GUI) as shown below:
To learn more about EDEM functionality please review our E-learning.
Producing fit for purpose EDEM models requires calibration and the below article provides an overview of the methodology and the available tools.
For examples of virtual optimization of bulk solids mixing processes with EDEM, please see the below webinars.
- Continuous Pharmaceutical Powder Mixing Process Modelling
- Modelling Pharmaceutical Manufacturing Processes Using Particle Simulation
EDEM can also be combined with machine learning, CAD and automation tools in the Altair portfolio to optimize mixer design and operation more efficiently. For more information, please see the below articles.
- Combining Machine Learning and Simulation for Continuous Mixing Optimization
- Combining AI and simulation for Bin Blending Optimization
References
[1] Gu, Z. and Chen, J. J. J. (2015) ‘A probabilistic analysis of some selected mixing indices’, Chemical Engineering Research and Design. Institution of Chemical Engineers, 93(April), pp. 293–303. doi: 10.1016/j.cherd.2014.04.014.
[2] Marigo, M. et al. (2012) ‘A numerical comparison of mixing efficiencies of solids in a cylindrical vessel subject to a range of motions’, Powder Technology. Elsevier B.V., 217, pp. 540–547. doi: 10.1016/j.powtec.2011.11.016.
[3] Cho, M., Dutta, P. and Shim, J. (2017) ‘A non-sampling mixing index for multicomponent mixtures’, Powder Technology. Elsevier B.V., 319, pp. 434–444. doi: 10.1016/j.powtec.2017.07.011.