Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

Roy, Mrittika; Gopalakrishnan, Ranganathan

doi:10.1080/02786826.2024.2420682

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

Journal Article · Wed Nov 13 23:00:00 EST 2024 · Aerosol Science and Technology

DOI:https://doi.org/10.1080/02786826.2024.2420682· OSTI ID:2584651

Roy, Mrittika ^[1]; Gopalakrishnan, Ranganathan ^[1]

University of Memphis, TN (United States)

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB^® codes are also provided. Extension to include translation Brownian motion is straightforward.

View Accepted Manuscript (DOE)

Research Organization:: University of Memphis, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0021206

OSTI ID:: 2584651

Journal Information:: Aerosol Science and Technology, Journal Name: Aerosol Science and Technology Journal Issue: 8 Vol. 59; ISSN 0278-6826; ISSN 1521-7388

Publisher:: Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

References (42)

Numerical solution of differential equations with colored noise Milshtein, G. N.; Tret'yakov, M. V. Journal of Statistical Physics, Vol. 77, Issue 3-4 https://doi.org/10.1007/BF02179457	journal	November 1994
On Simulating Randomly Driven Dynamic Systems Kasdin, N. Jeremy; Stankievech, Landis J. The Journal of the Astronautical Sciences, Vol. 57, Issue 1-2 https://doi.org/10.1007/BF03321506	journal	January 2009
Momentum slip correction factor for small particles in nine common gases Rader, Daniel J. Journal of Aerosol Science, Vol. 21, Issue 2 https://doi.org/10.1016/0021-8502(90)90001-e	journal	January 1990
Molecular dynamics simulation using quaternions Rapaport, D. C. Journal of Computational Physics, Vol. 60, Issue 2 https://doi.org/10.1016/0021-9991(85)90009-9	journal	September 1985
Brownian Dynamics Simulation of Rigid Particles of Arbitrary Shape in External Fields Fernandes, Miguel X.; de la Torre, José García Biophysical Journal, Vol. 83, Issue 6 https://doi.org/10.1016/S0006-3495(02)75309-5	journal	December 2002
Browndye: A software package for Brownian dynamics Huber, Gary A.; McCammon, J. Andrew Computer Physics Communications, Vol. 181, Issue 11 https://doi.org/10.1016/j.cpc.2010.07.022	journal	November 2010
Brownian dynamics determination of the bipolar steady state charge distribution on spheres and non-spheres in the transition regime Gopalakrishnan, Ranganathan; Meredith, Mark J.; Larriba-Andaluz, Carlos Journal of Aerosol Science, Vol. 63 https://doi.org/10.1016/j.jaerosci.2013.04.007	journal	September 2013
The unipolar diffusion charging of arbitrary shaped aerosol particles Gopalakrishnan, Ranganathan; Thajudeen, Thaseem; Ouyang, Hui Journal of Aerosol Science, Vol. 64 https://doi.org/10.1016/j.jaerosci.2013.06.002	journal	October 2013
Computational study of electrostatic focusing of aerosol nanoparticles using an einzel lens Ahmed, Rayhan; Gopalakrishnan, Ranganathan Journal of Aerosol Science, Vol. 137 https://doi.org/10.1016/j.jaerosci.2019.105443	journal	November 2019
Comparison of the predictions of Langevin Dynamics-based diffusion charging collision kernel models with canonical experiments Li, Li; Chahl, Harjindar Singh; Gopalakrishnan, Ranganathan Journal of Aerosol Science, Vol. 140 https://doi.org/10.1016/j.jaerosci.2019.105481	journal	February 2020
An experimentally validated model of diffusion charging of arbitrary shaped aerosol particles Li, Li; Gopalakrishnan, Ranganathan Journal of Aerosol Science, Vol. 151 https://doi.org/10.1016/j.jaerosci.2020.105678	journal	January 2021
Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling Suresh, Vikram; Gopalakrishnan, Ranganathan Journal of Aerosol Science, Vol. 155 https://doi.org/10.1016/j.jaerosci.2021.105746	journal	June 2021
The Art of Molecular Dynamics Simulation Rapaport, D. C. https://doi.org/10.1017/CBO9780511816581	book	January 2004
Diffusion- and reaction-limited cluster aggregation revisited Jungblut, Swetlana; Joswig, Jan-Ole; Eychmüller, Alexander Physical Chemistry Chemical Physics, Vol. 21, Issue 10 https://doi.org/10.1039/C9CP00549H	journal	January 2019
Symplectic quaternion scheme for biophysical molecular dynamics Miller, T. F.; Eleftheriou, M.; Pattnaik, P. The Journal of Chemical Physics, Vol. 116, Issue 20 https://doi.org/10.1063/1.1473654	journal	May 2002
Langevin dynamics for rigid bodies of arbitrary shape Sun, Xiuquan; Lin, Teng; Gezelter, J. Daniel The Journal of Chemical Physics, Vol. 128, Issue 23 https://doi.org/10.1063/1.2936991	journal	June 2008
Langevin thermostat for rigid body dynamics Davidchack, Ruslan L.; Handel, Richard; Tretyakov, M. V. The Journal of Chemical Physics, Vol. 130, Issue 23 https://doi.org/10.1063/1.3149788	journal	June 2009
Collision limited reaction rates for arbitrarily shaped particles across the entire diffusive Knudsen number range Gopalakrishnan, Ranganathan; Thajudeen, Thaseem; Hogan, Christopher J. The Journal of Chemical Physics, Vol. 135, Issue 5 https://doi.org/10.1063/1.3617251	journal	August 2011
Brownian dynamics with hydrodynamic interactions Ermak, Donald L.; McCammon, J. A. The Journal of Chemical Physics, Vol. 69, Issue 4 https://doi.org/10.1063/1.436761	journal	August 1978
Nanoparticle collisions in the gas phase in the presence of singular contact potentials Ouyang, Hui; Gopalakrishnan, Ranganathan; Hogan, Christopher J. The Journal of Chemical Physics, Vol. 137, Issue 6 https://doi.org/10.1063/1.4742064	journal	August 2012
A fourth-order numerical integrator for stochastic Langevin equations Hershkovitz, Eli The Journal of Chemical Physics, Vol. 108, Issue 22 https://doi.org/10.1063/1.476380	journal	June 1998
An elementary singularity-free Rotational Brownian Dynamics algorithm for anisotropic particles Ilie, Ioana M.; Briels, Wim J.; den Otter, Wouter K. The Journal of Chemical Physics, Vol. 142, Issue 11 https://doi.org/10.1063/1.4914322	journal	March 2015
New Langevin and gradient thermostats for rigid body dynamics Davidchack, R. L.; Ouldridge, T. E.; Tretyakov, M. V. The Journal of Chemical Physics, Vol. 142, Issue 14 https://doi.org/10.1063/1.4916312	journal	April 2015
Brownian dynamics of confined rigid bodies Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar The Journal of Chemical Physics, Vol. 143, Issue 14 https://doi.org/10.1063/1.4932062	journal	October 2015
On the representatation of orientation space Evans, Denis J. Molecular Physics, Vol. 34, Issue 2 https://doi.org/10.1080/00268977700101751	journal	August 1977
Singularity free algorithm for molecular dynamics simulation of rigid polyatomics Evans, Denis J.; Murad, Sohail Molecular Physics, Vol. 34, Issue 2 https://doi.org/10.1080/00268977700101761	journal	August 1977
Determination of the Transition Regime Collision Kernel from Mean First Passage Times Gopalakrishnan, Ranganathan; Hogan, Christopher J. Aerosol Science and Technology, Vol. 45, Issue 12 https://doi.org/10.1080/02786826.2011.601775	journal	December 2011
The Collision Rate of Nonspherical Particles and Aggregates for all Diffusive Knudsen Numbers Thajudeen, Thaseem; Gopalakrishnan, Ranganathan; Hogan, Christopher J. Aerosol Science and Technology, Vol. 46, Issue 11 https://doi.org/10.1080/02786826.2012.701353	journal	November 2012
The Bipolar Diffusion Charging of Nanoparticles: A Review and Development of Approaches for Non-Spherical Particles Gopalakrishnan, Ranganathan; McMurry, Peter H.; Hogan,, Christopher J. Aerosol Science and Technology, Vol. 49, Issue 12 https://doi.org/10.1080/02786826.2015.1109053	journal	October 2015
Analytical expression for the rotational friction coefficient of DLCA aggregates over the entire Knudsen regime Corson, James; Mulholland, George W.; Zachariah, Michael R. Aerosol Science and Technology, Vol. 52, Issue 2 https://doi.org/10.1080/02786826.2017.1390544	journal	November 2017
High potential, near free molecular regime Coulombic collisions in aerosols and dusty plasmas Chahl, Harjindar Singh; Gopalakrishnan, Ranganathan Aerosol Science and Technology, Vol. 53, Issue 8 https://doi.org/10.1080/02786826.2019.1614522	journal	May 2019
Modeling nanoparticle charge distribution in the afterglow of non-thermal plasmas and comparison with measurements Suresh, Vikram; Li, Li; Redmond Go Felipe, Joshua Journal of Physics D: Applied Physics, Vol. 54, Issue 27 https://doi.org/10.1088/1361-6463/abf70c	journal	April 2021
JAX, M.D. A framework for differentiable physics* Schoenholz, Samuel S.; Cubuk, Ekin D. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2021, Issue 12 https://doi.org/10.1088/1742-5468/ac3ae9	journal	December 2021
Isotropic Rotational Brownian Motion Furry, W. H. Physical Review, Vol. 107, Issue 1 https://doi.org/10.1103/PhysRev.107.7	journal	July 1957
Angular velocity of a nonspherical body undergoing rotational Brownian motion Hubbard, Paul S. Physical Review A, Vol. 15, Issue 1 https://doi.org/10.1103/PhysRevA.15.329	journal	January 1977
Rotational Brownian Motion Hubbard, Paul S. Physical Review A, Vol. 6, Issue 6 https://doi.org/10.1103/PhysRevA.6.2421	journal	December 1972
Rotational Brownian Motion. II. Fourier Transforms for a Spherical Body with Strong Interactions Hubbard, Paul S. Physical Review A, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevA.8.1429	journal	September 1973
Algorithm for rigid-body Brownian dynamics Gordon, Dan; Hoyles, Matthew; Chung, Shin-Ho Physical Review E, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevE.80.066703	journal	December 2009
Coulomb-influenced collisions in aerosols and dusty plasmas Gopalakrishnan, Ranganathan; Hogan, Christopher J. Physical Review E, Vol. 85, Issue 2 https://doi.org/10.1103/PhysRevE.85.026410	journal	February 2012
Calculating the rotational friction coefficient of fractal aerosol particles in the transition regime using extended Kirkwood-Riseman theory Corson, James; Mulholland, George W.; Zachariah, Michael R. Physical Review E, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevE.96.013110	journal	July 2017
Stochastic Problems in Physics and Astronomy Chandrasekhar, S. Reviews of Modern Physics, Vol. 15, Issue 1 https://doi.org/10.1103/RevModPhys.15.1	journal	January 1943
Runge-Kutta Algorithm for the Numerical Integration of Stochastic Differential Equations Kasdin, N. Jeremy Journal of Guidance, Control, and Dynamics, Vol. 18, Issue 1 https://doi.org/10.2514/3.56665	journal	January 1995

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