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Approach and collisions of particles with solid surfaces submerged in liquid
Date
2025
Abstract
This work evaluates the conditions under which particle-wall collisions occur, for conditions representative of seed crystals in industrial-scale crystallisation unit operations, using bespoke two-dimensional and three-dimensional immersed boundary – lattice Boltzmann method (IB-LBM) solvers. Free-moving particles are inserted into a fully developed impinging jet flow, with the initial velocity of the particle matched to the fluid velocity at the point of insertion. Perpendicular (0°) and slightly inclined (1°, 5°) impinging jets are investigated and initial particle orientation relative to the jet is varied from -5° to 90°. Critical Reynolds number values, above which particle-wall collisions occur, are obtained for a range of particle shapes representative of typical pharmaceutical crystal habits. Particle orientation and normal velocity on approach to the target surface (and at the point of collision) are investigated and discussed. A velocity profile that matches the solution for an inviscid jet is used to define the inlet velocity profile for 2D simulations to represent previous experimental work and a flat inlet velocity profile is used in the 3D simulations to better represent crystalliser conditions.
Particle approach behaviour reproduces behaviour noted in particle sedimentation work as particles rotate into their high-drag orientation on approach. High aspect ratio particles rotate more on approach to the target surface and are more influenced by particle orientation relative to the jet, while low aspect ratio particles are more influenced by jet orientation. Particle normal velocity on approach to the target surface is determined by the frontal length/area of the particle, while particle normal velocity within 0.5 𝐿𝐶 (where 𝐿𝐶 is the characteristic length of the particle) of the target surface is determined by the shape of the approaching particle face (flat, rounded or pointed). Particles with a flat frontal face are rapidly decelerated within 0.5 𝐿𝐶 of the target surface while rounded or pointed faces allow the particle to more easily pierce the near-wall flow. For particle Reynolds numbers below the critical value for collision, a secondary collision type may occur when particles gently contact the target surface due to rotation while moving tangentially to the target surface.
The particle Reynolds number 𝑅𝑒 is defined as 𝑅𝑒 =𝑢𝑤𝐿𝐶𝜈, where 𝑢𝑤 is the inlet velocity of the impinging jet, 𝐿𝐶 is the particle’s characteristic length and 𝜈 is the fluid kinematic viscosity. The particle Reynolds number is defined using the inlet velocity of the jet as it is one of the input parameters that characterises the system. As the particle Reynolds number is defined using the inlet velocity of the jet and particles slow on approach to the target surface, critical Reynolds number values increase as the initial distance between particle and target surface is increased. Particles in the 2D inviscid inlet velocity profile jet have an initial distance of 72 𝐿𝐶 and are simulated at particle Reynolds numbers of 100 to 400; particles in the 3D flat inlet velocity profile jet have an initial distance of 22.5 𝐿𝐶 and are simulated at particle Reynolds numbers of 30 to 90. The critical Reynolds number value range of 325 to 350 for 2D circular particles is comparable to previous experimental values of 250 using low aspect ratio particles at comparable distances and flow conditions.
For 3D particles inserted 22.5 𝐿𝐶 from the target surface (equivalent to a 0.225 mm distance for 10 μm seed crystal) critical Reynolds number values are higher than those achieved under typical crystalliser operating conditions. As particles rotate into their high-drag orientation on approach (raising their critical Reynolds number value) and small changes in initial particle position (relative to the jet centreline) result in a significant change in impact location, particle-wall collisions are unlikely to occur under normal crystalliser operating conditions. In the unlikely event that a particle-wall collision does occur, particles are slowed to less than 20% of their initial velocity (4% of the initial kinetic energy), even at double the critical Reynolds number required for collision, reducing the likelihood of particle attrition.
Supervisor
Frawley, Patrick
Shardt, Orest
Shardt, Orest
Description
Publisher
University of Limerick
Citation
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ORegan_2025_Approach.pdf
Adobe PDF, 2.65 MB
Funding code
Funding Information
Sustainable Development Goals
External Link
Type
Thesis
Rights
http://creativecommons.org/licenses/by-nc-sa/4.0/