Polydisperse particulate solids mixing and segregation: nonstationary Markov chains

Area of Science:

• Particle science and engineering
• Statistical mechanics
• Chemical engineering

Background:

• Understanding particle dynamics in agitated beds is crucial for process design.
• Polydisperse particulate solids exhibit complex movement patterns under external forces.
• Markov chain analysis offers a probabilistic framework for modeling such systems.

Purpose of the Study:

• To investigate the feasibility of using Markov chains to analyze interparticulate translocations.
• To model the behavior of a binary mixture of spherical particles under vertical vibration.
• To quantitatively evaluate particle mobilities within agitated beds.

Main Methods:

• A binary mixture of spherical particles was subjected to vertical sine wave vibration.
• The system's behavior was analyzed using nonstationary Markov chains with singly stochastic transition matrices.
• Transition probability elements were calculated from initial and final occupancy vectors and compared with tracer particle estimations.

Main Results:

• The agitated binary mixture of particles exhibited behavior consistent with a nonstationary Markov chain.
• Calculated transition probabilities from occupancy vectors agreed well with tracer particle estimations.
• The method allowed for quantitative evaluation of particle mobilities throughout the bed.

Conclusions:

• Markov chain analysis is a feasible and effective method for studying interparticulate translocations in agitated beds.
• The nonstationary Markov chain model accurately describes particle dynamics in vibrated polydisperse systems.
• This approach provides a quantitative tool for assessing particle mobility, aiding in process optimization.