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Hashemi A, Peláez RP, Natesh S, Sprinkle B, Maxian O, Gan Z, Donev A. Computing hydrodynamic interactions in confined doubly periodic geometries in linear time. J Chem Phys 2023; 158:2882262. [PMID: 37094003 DOI: 10.1063/5.0141371] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Accepted: 03/20/2023] [Indexed: 04/26/2023] Open
Abstract
We develop a linearly scaling variant of the force coupling method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally accurate Stokes solver uses the fast Fourier transform in the periodic xy plane and Chebyshev polynomials in the aperiodic z direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the z direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly periodic geometries [Maxian et al., J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement.
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Affiliation(s)
- Aref Hashemi
- Courant Institute, New York University, New York, New York 10012, USA
| | - Raúl P Peláez
- Courant Institute, New York University, New York, New York 10012, USA
- Departamento Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, Spain
| | - Sachin Natesh
- Courant Institute, New York University, New York, New York 10012, USA
- Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Brennan Sprinkle
- Courant Institute, New York University, New York, New York 10012, USA
- Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Ondrej Maxian
- Courant Institute, New York University, New York, New York 10012, USA
| | - Zecheng Gan
- Courant Institute, New York University, New York, New York 10012, USA
- Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China
| | - Aleksandar Donev
- Courant Institute, New York University, New York, New York 10012, USA
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2
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van der Wee EB, Blackwell BC, Balboa Usabiaga F, Sokolov A, Katz IT, Delmotte B, Driscoll MM. A simple catch: Fluctuations enable hydrodynamic trapping of microrollers by obstacles. SCIENCE ADVANCES 2023; 9:eade0320. [PMID: 36888698 PMCID: PMC9995068 DOI: 10.1126/sciadv.ade0320] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Accepted: 02/01/2023] [Indexed: 06/18/2023]
Abstract
It is known that obstacles can hydrodynamically trap bacteria and synthetic microswimmers in orbits, where the trapping time heavily depends on the swimmer flow field and noise is needed to escape the trap. Here, we use experiments and simulations to investigate the trapping of microrollers by obstacles. Microrollers are rotating particles close to a bottom surface, which have a prescribed propulsion direction imposed by an external rotating magnetic field. The flow field that drives their motion is quite different from previously studied swimmers. We found that the trapping time can be controlled by modifying the obstacle size or the colloid-obstacle repulsive potential. We detail the mechanisms of the trapping and find two remarkable features: The microroller is confined in the wake of the obstacle, and it can only enter the trap with Brownian motion. While noise is usually needed to escape traps in dynamical systems, here, we show that it is the only means to reach the hydrodynamic attractor.
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Affiliation(s)
- Ernest B. van der Wee
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
| | - Brendan C. Blackwell
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
| | | | - Andrey Sokolov
- Materials Science Division, Argonne National Laboratory, Lemont, IL 60439, USA
| | - Isaiah T. Katz
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
| | - Blaise Delmotte
- LadHyX, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau 91120, France
| | - Michelle M. Driscoll
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
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3
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Verweij RW, Melio J, Chakraborty I, Kraft DJ. Brownian motion of flexibly linked colloidal rings. Phys Rev E 2023; 107:034602. [PMID: 37072967 DOI: 10.1103/physreve.107.034602] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 01/04/2023] [Indexed: 04/20/2023]
Abstract
Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on the conformation and diffusion of molecular ring polymers simultaneously are challenging due to their inherently small size. Here, we study an experimental model system for cyclic polymers, that consists of rings of flexibly linked micron-sized colloids with n=4-8 segments. We characterize the conformations of these flexible colloidal rings and find that they are freely jointed up to steric restrictions. We measure their diffusive behavior and compare it to hydrodynamic simulations. Interestingly, flexible colloidal rings have a larger translational and rotational diffusion coefficient compared to colloidal chains. In contrast to chains, their internal deformation mode shows slower fluctuations for n≲8 and saturates for higher values of n. We show that constraints stemming from the ring structure cause this decrease in flexibility for small n and infer the expected scaling of the flexibility as function of ring size. Our findings could have implications for the behavior of both synthetic and biological ring polymers, as well as for the dynamic modes of floppy colloidal materials.
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Affiliation(s)
- Ruben W Verweij
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Julio Melio
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Indrani Chakraborty
- Department of Physics, Birla Institute of Technology and Science, Pilani-K K Birla Goa Campus, Zuarinagar, Goa 403726, India
| | - Daniela J Kraft
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
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Cichocki B, Szymczak P, Żuk PJ. Generalized Rotne-Prager-Yamakawa approximation for Brownian dynamics in shear flow in bounded, unbounded, and periodic domains. J Chem Phys 2021; 154:124905. [PMID: 33810690 DOI: 10.1063/5.0030175] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Inclusion of hydrodynamic interactions is essential for a quantitatively accurate Brownian dynamics simulation of colloidal suspensions or polymer solutions. We use the generalized Rotne-Prager-Yamakawa (GRPY) approximation, which takes into account all long-ranged terms in the hydrodynamic interactions, to derive the complete set of hydrodynamic matrices in different geometries: unbounded space, periodic boundary conditions of Lees-Edwards type, and vicinity of a free surface. The construction is carried out both for non-overlapping as well as for overlapping particles. We include the dipolar degrees of freedom, which allows one to use this formalism to simulate the dynamics of suspensions in a shear flow and to study the evolution of their rheological properties. Finally, we provide an open-source numerical package, which implements the GRPY algorithm in Lees-Edwards periodic boundary conditions.
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Affiliation(s)
- Bogdan Cichocki
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Piotr Szymczak
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Paweł J Żuk
- Department of Biosystems and Soft Matter, Institute of Fundamental and Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
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Abstract
3D printing (also called "additive manufacturing" or "rapid prototyping") is able to translate computer-aided and designed virtual 3D models into 3D tangible constructs/objects through a layer-by-layer deposition approach. Since its introduction, 3D printing has aroused enormous interest among researchers and engineers to understand the fabrication process and composition-structure-property correlation of printed 3D objects and unleash its great potential for application in a variety of industrial sectors. Because of its unique technological advantages, 3D printing can definitely benefit the field of microrobotics and advance the design and development of functional microrobots in a customized manner. This review aims to present a generic overview of 3D printing for functional microrobots. The most applicable 3D printing techniques, with a focus on laser-based printing, are introduced for the 3D microfabrication of microrobots. 3D-printable materials for fabricating microrobots are reviewed in detail, including photopolymers, photo-crosslinkable hydrogels, and cell-laden hydrogels. The representative applications of 3D-printed microrobots with rational designs heretofore give evidence of how these printed microrobots are being exploited in the medical, environmental, and other relevant fields. A future outlook on the 3D printing of microrobots is also provided.
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Affiliation(s)
- Jinhua Li
- Center for Advanced Functional Nanorobots, Department of Inorganic Chemistry, University of Chemistry and Technology Prague, Technická 5, Prague 6, 16628, Czech Republic.
| | - Martin Pumera
- Center for Advanced Functional Nanorobots, Department of Inorganic Chemistry, University of Chemistry and Technology Prague, Technická 5, Prague 6, 16628, Czech Republic. and Future Energy and Innovation Laboratory, Central European Institute of Technology, Brno University of Technology, Purkyňova 656/123, Brno, CZ-61600, Czech Republic and Department of Chemistry and Biochemistry, Mendel University in Brno, Zemedelska 1, CZ-613 00, Brno, Czech Republic and Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
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Sprinkle B, van der Wee EB, Luo Y, Driscoll MM, Donev A. Driven dynamics in dense suspensions of microrollers. SOFT MATTER 2020; 16:7982-8001. [PMID: 32776032 DOI: 10.1039/d0sm00879f] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We perform detailed computational and experimental measurements of the driven dynamics of a dense, uniform suspension of sedimented microrollers driven by a magnetic field rotating around an axis parallel to the floor. We develop a lubrication-corrected Brownian dynamics method for dense suspensions of driven colloids sedimented above a bottom wall. The numerical method adds lubrication friction between nearby pairs of particles, as well as particles and the bottom wall, to a minimally-resolved model of the far-field hydrodynamic interactions. Our experiments combine fluorescent labeling with particle tracking to trace the trajectories of individual particles in a dense suspension, and to measure their propulsion velocities. Previous computational studies [B. Sprinkle et al., J. Chem. Phys., 2017, 147, 244103] predicted that at sufficiently high densities a uniform suspension of microrollers separates into two layers, a slow monolayer right above the wall, and a fast layer on top of the bottom layer. Here we verify this prediction, showing good quantitative agreement between the bimodal distribution of particle velocities predicted by the lubrication-corrected Brownian dynamics and those measured in the experiments. The computational method accurately predicts the rate at which particles are observed to switch between the slow and fast layers in the experiments. We also use our numerical method to demonstrate the important role that pairwise lubrication plays in motility-induced phase separation in dense monolayers of colloidal microrollers, as recently suggested for suspensions of Quincke rollers [D. Geyer et al., Phys. Rev. X, 2019, 9(3), 031043].
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Affiliation(s)
- Brennan Sprinkle
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
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Yang T, Sprinkle B, Guo Y, Qian J, Hua D, Donev A, Marr DWM, Wu N. Reconfigurable microbots folded from simple colloidal chains. Proc Natl Acad Sci U S A 2020; 117:18186-18193. [PMID: 32680965 PMCID: PMC7414297 DOI: 10.1073/pnas.2007255117] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
To overcome the reversible nature of low-Reynolds-number flow, a variety of biomimetic microrobotic propulsion schemes and devices capable of rapid transport have been developed. However, these approaches have been typically optimized for a specific function or environment and do not have the flexibility that many real organisms exhibit to thrive in complex microenvironments. Here, inspired by adaptable microbes and using a combination of experiment and simulation, we demonstrate that one-dimensional colloidal chains can fold into geometrically complex morphologies, including helices, plectonemes, lassos, and coils, and translate via multiple mechanisms that can be varied with applied magnetic field. With chains of multiblock asymmetry, the propulsion mode can be switched from bulk to surface-enabled, mimicking the swimming of microorganisms such as flagella-rotating bacteria and tail-whipping sperm and the surface-enabled motion of arching and stretching inchworms and sidewinding snakes. We also demonstrate that reconfigurability enables navigation through three-dimensional and narrow channels simulating capillary blood vessels. Our results show that flexible microdevices based on simple chains can transform both shape and motility under varying magnetic fields, a capability we expect will be particularly beneficial in complex in vivo microenvironments.
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Affiliation(s)
- Tao Yang
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO 80401
| | - Brennan Sprinkle
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
| | - Yang Guo
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO 80401
| | - Jun Qian
- State Key Laboratory of Radiation Medicine and Protection, School for Radiological and Interdisciplinary Sciences, Soochow University, 215123 Suzhou, China
| | - Daoben Hua
- State Key Laboratory of Radiation Medicine and Protection, School for Radiological and Interdisciplinary Sciences, Soochow University, 215123 Suzhou, China
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
| | - David W M Marr
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO 80401;
| | - Ning Wu
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO 80401;
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Paul S, Bhattacharyya D, Ray DS. Clusterization of self-propelled particles in a two-component system. Phys Rev E 2020; 101:012611. [PMID: 32069557 DOI: 10.1103/physreve.101.012611] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Indexed: 11/07/2022]
Abstract
We consider a mixture of active solute molecules in a suspension of passive solvent particles comprising a thermal bath. The solute molecules are considered to be extended objects with two chemically distinct heads, one head of which having chemical affinity towards the solvent particles. The coupled Langevin equations for the solvent particles along with the equations governing the dynamics of active molecules are numerically simulated to show how the active molecules self-assemble to form clusters which remain in dynamic equilibrium with the free solute molecules. We observe an interesting crossover at an intermediate time in the variation of the order parameter with time when the temperature of the bath is changed signifying the differential behavior of clusterization below and above the crossover time associated with a transition between a thermodynamic and a quasithermodynamic regime. Enthalpy-entropy compensation in the formation of clusters below the crossover is demonstrated.
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Affiliation(s)
- Shibashis Paul
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | | | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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9
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Chen X, Zhou C, Wang W. Colloidal Motors 101: A Beginner's Guide to Colloidal Motor Research. Chem Asian J 2019; 14:2388-2405. [DOI: 10.1002/asia.201900377] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 04/09/2019] [Indexed: 12/24/2022]
Affiliation(s)
- Xi Chen
- School of Materials Science and EngineeringHarbin Institute of Technology (Shenzhen) G 908, HIT Campus, Xili University Town Shenzhen Guangdong China
| | - Chao Zhou
- School of Materials Science and EngineeringHarbin Institute of Technology (Shenzhen) G 908, HIT Campus, Xili University Town Shenzhen Guangdong China
| | - Wei Wang
- School of Materials Science and EngineeringHarbin Institute of Technology (Shenzhen) G 908, HIT Campus, Xili University Town Shenzhen Guangdong China
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10
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Sprinkle B, Donev A, Bhalla APS, Patankar N. Brownian dynamics of fully confined suspensions of rigid particles without Green's functions. J Chem Phys 2019; 150:164116. [PMID: 31042913 DOI: 10.1063/1.5090114] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a Rigid-Body Fluctuating Immersed Boundary (RB-FIB) method to perform large-scale Brownian dynamics simulations of suspensions of rigid particles in fully confined domains, without any need to explicitly construct Green's functions or mobility operators. In the RB-FIB approach, discretized fluctuating Stokes equations are solved with prescribed boundary conditions in conjunction with a rigid-body immersed boundary method to discretize arbitrarily shaped colloidal particles with no-slip or active-slip prescribed on their surface. We design a specialized Split-Euler-Maruyama temporal integrator that uses a combination of random finite differences to capture the stochastic drift appearing in the overdamped Langevin equation. The RB-FIB method presented in this work only solves mobility problems in each time step using a preconditioned iterative solver and has a computational complexity that scales linearly in the number of particles and fluid grid cells. We demonstrate that the RB-FIB method correctly reproduces the Gibbs-Boltzmann equilibrium distribution and use the method to examine the time correlation functions for two spheres tightly confined in a cuboid. We model a quasi-two-dimensional colloidal crystal confined in a narrow microchannel and hydrodynamically driven across a commensurate periodic substrate potential mimicking the effect of a corrugated wall. We observe partial and full depinning of the colloidal monolayer from the substrate potential above a certain wall speed, consistent with a transition from static to kinetic friction through propagating kink solitons. Unexpectedly, we find that particles nearest to the boundaries of the domain are the first to be displaced, followed by particles in the middle of the domain.
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Affiliation(s)
- Brennan Sprinkle
- Engineering Science and Applied Math, Northwestern University, Evanston, Illinois 60208, USA
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Amneet Pal Singh Bhalla
- Department of Mechanical Engineering, San Diego State University, San Diego, California 92182, USA
| | - Neelesh Patankar
- McCormick School of Engineering, Northwestern University, Evanston, Illinois 60208, USA
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Spyrogianni A, Karadima KS, Goudeli E, Mavrantzas VG, Pratsinis SE. Mobility and settling rate of agglomerates of polydisperse nanoparticles. J Chem Phys 2018; 148:064703. [PMID: 29448768 DOI: 10.1063/1.5012037] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO2 agglomerates in water is investigated and their settling rate in infinitely dilute suspensions is calculated by a Brownian dynamics algorithm tracking the agglomerate translational and rotational motion. The corresponding friction matrices are obtained using the HYDRO++ algorithm [J. G. de la Torre, G. del Rio Echenique, and A. Ortega, J. Phys. Chem. B 111, 955 (2007)] from the Kirkwood-Riseman theory accounting for hydrodynamic interactions of primary particles (PPs) through the Rotne-Prager-Yamakawa tensor, properly modified for polydisperse PPs. Agglomerates are generated by an event-driven method and have constant mass fractal dimension but varying PP size distribution, mass, and relative shape anisotropy. The calculated diffusion coefficient from HYDRO++ is used to obtain the agglomerate mobility diameter dm and is compared with that from scaling laws for fractal-like agglomerates. The ratio dm/dg of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant dm and mean dp, the agglomerate settling rate, us, increases with increasing PP geometric standard deviation σp,g (polydispersity). A linear relationship between us and agglomerate mass to dm ratio, m/dm, is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the us of agglomerates consisting of polydisperse PPs is then derived, us=1-ρfρpg3πμmdm (ρf is the density of the fluid, ρp is the density of PPs, μ is the viscosity of the fluid, and g is the acceleration of gravity), valid for agglomerates for which the characteristic rotational time is considerably shorter than their settling time. Our calculations demonstrate that the commonly made assumption of monodisperse PPs underestimates us by a fraction depending on σp,g and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO2 agglomerates in water.
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Affiliation(s)
- Anastasia Spyrogianni
- Department of Mechanical and Process Engineering, ETH Zurich, Zurich 8092, Switzerland
| | - Katerina S Karadima
- Department of Chemical Engineering, University of Patras, Patras 26504, Greece
| | - Eirini Goudeli
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Vlasis G Mavrantzas
- Department of Mechanical and Process Engineering, ETH Zurich, Zurich 8092, Switzerland
| | - Sotiris E Pratsinis
- Department of Mechanical and Process Engineering, ETH Zurich, Zurich 8092, Switzerland
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12
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Sprinkle B, Balboa Usabiaga F, Patankar NA, Donev A. Large scale Brownian dynamics of confined suspensions of rigid particles. J Chem Phys 2017; 147:244103. [DOI: 10.1063/1.5003833] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Brennan Sprinkle
- McCormick School of Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | - Florencio Balboa Usabiaga
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, New York 10010, USA
| | - Neelesh A. Patankar
- McCormick School of Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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