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Yamamoto R, Molina JJ, Nakayama Y. Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles. SOFT MATTER 2021; 17:4226-4253. [PMID: 33908448 DOI: 10.1039/d0sm02210a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.
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Affiliation(s)
- Ryoichi Yamamoto
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan.
| | - John J Molina
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan.
| | - Yasuya Nakayama
- Department of Chemical Engineering, Kyushu University, Fukuoka 819-0395, Japan
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Spatafora-Salazar A, Lobmeyer DM, Cunha LHP, Joshi K, Biswal SL. Hierarchical assemblies of superparamagnetic colloids in time-varying magnetic fields. SOFT MATTER 2021; 17:1120-1155. [PMID: 33492321 DOI: 10.1039/d0sm01878c] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Magnetically-guided colloidal assembly has proven to be a versatile method for building hierarchical particle assemblies. This review describes the dipolar interactions that govern superparamagnetic colloids in time-varying magnetic fields, and how such interactions have guided colloidal assembly into materials with increasing complexity that display novel dynamics. The assembly process is driven by magnetic dipole-dipole interactions, whose strength can be tuned to be attractive or repulsive. Generally, these interactions are directional in static external magnetic fields. More recently, time-varying magnetic fields have been utilized to generate dipolar interactions that vary in both time and space, allowing particle interactions to be tuned from anisotropic to isotropic. These interactions guide the dynamics of hierarchical assemblies of 1-D chains, 2-D networks, and 2-D clusters in both static and time-varying fields. Specifically, unlinked and chemically-linked colloidal chains exhibit complex dynamics, such as fragmentation, buckling, coiling, and wagging phenomena. 2-D networks exhibit controlled porosity and interesting coarsening dynamics. Finally, 2-D clusters have shown to be an ideal model system for exploring phenomena related to statistical thermodynamics. This review provides recent advances in this fast-growing field with a focus on its scientific potential.
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Affiliation(s)
- Aldo Spatafora-Salazar
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA.
| | - Dana M Lobmeyer
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA.
| | - Lucas H P Cunha
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA.
| | - Kedar Joshi
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA.
| | - Sibani Lisa Biswal
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA.
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Matsuoka Y, Nakayama Y, Kajiwara T. Effects of viscoelasticity on shear-thickening in dilute suspensions in a viscoelastic fluid. SOFT MATTER 2020; 16:728-737. [PMID: 31825055 DOI: 10.1039/c9sm01736d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio 1 - β = ηp/(ηs + ηp) which measures the coupling between the polymer stress and flow: ηp and ηs are the polymer and solvent viscosity, respectively. As 1 - β increases, while the stresslet does not change significantly compared to that in the β → 1 limit, the growth rate of the normalized polymer stress with Wi was suppressed. Analysis of flow and conformation dynamics around a particle for different β reveals that at large 1 - β, polymer stress modulates flow, leading to suppression of polymer stretch. This effect of β on polymer stress development indicates complex coupling between fluid elasticity and flow, and is essential to understand the rheology and hydrodynamic interactions in suspensions in viscoelastic media.
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Affiliation(s)
- Yuki Matsuoka
- Corporate Engineering Center, Sumitomo Bakelite Co., Ltd., Shizuoka 426-0041, Japan.
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TRIPATHI DHARMENDRA, BHUSHAN SHASHI, BÉG OANWAR. ANALYTICAL STUDY OF ELECTRO-OSMOSIS MODULATED CAPILLARY PERISTALTIC HEMODYNAMICS. J MECH MED BIOL 2017. [DOI: 10.1142/s021951941750052x] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
A mathematical model is developed to analyze electro-kinetic effects on unsteady peristaltic transport of blood in cylindrical vessels of finite length. The Newtonian viscous model is adopted. The analysis is restricted under Debye–Hückel linearization (i.e., wall zeta potential [Formula: see text] 25[Formula: see text]mV) is sufficiently small). The transformed, nondimensional conservation equations are derived via lubrication theory and long wavelength and the resulting linearized boundary value problem is solved exactly. The case of a thin electric double layer (i.e., where only slip electro-osmotic velocity considered) is retrieved as a particular case of the present model. The response in pumping characteristics (axial velocity, pressure gradient or difference, volumetric flow rate, local wall shear stress) to the influence of electro-osmotic effect (inverse Debye length) and Helmholtz–Smoluchowski velocity is elaborated in detail. Visualization of trapping phenomenon is also included and the bolus dynamics evolution with electro-kinetic effects examined. A comparative study of train wave propagation and single wave propagation is presented under the effects of thickness of EDL and external electric field. The study is relevant to electrophoresis in haemotology, electrohydrodynamic therapy and biomimetic electro-osmotic pumps.
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Affiliation(s)
- DHARMENDRA TRIPATHI
- Department of Mechanical Engineering, Manipal University, Jaipur 303007, India
| | - SHASHI BHUSHAN
- Department of Mechanical Engineering, Manipal University, Jaipur 303007, India
| | - O. ANWAR BÉG
- Fluid Mechanics, Bio-Propulsion and Nano-Systems, Department of Mechanical and Aeronautical Engineering, Salford University, Newton Building, The Crescent, Salford M54WT, England, UK
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Deng M, Li Z, Borodin O, Karniadakis GE. cDPD: A new dissipative particle dynamics method for modeling electrokinetic phenomena at the mesoscale. J Chem Phys 2016; 145:144109. [DOI: 10.1063/1.4964628] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Mingge Deng
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - Zhen Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - Oleg Borodin
- Electrochemistry Branch, Sensors and Electron Devices Directorate, U.S. Army Research Laboratory, Adelphi, Maryland 20783, USA
| | - George Em Karniadakis
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
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Hernández-Ortiz JP, de Pablo JJ. Self-consistent description of electrokinetic phenomena in particle-based simulations. J Chem Phys 2015; 143:014108. [PMID: 26156466 PMCID: PMC4491022 DOI: 10.1063/1.4923342] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2015] [Accepted: 06/22/2015] [Indexed: 11/14/2022] Open
Abstract
A new computational method is presented for study suspensions of charged particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins, and porous particles embedded in a continuum electrolyte. A self-consistent Langevin description of the particles is adopted in which hydrodynamic and electrostatic interactions are included through a Green's function formalism. An Ewald-like split is adopted in order to satisfy arbitrary boundary conditions for the Stokeslet and Poisson Green functions, thereby providing a formalism that is applicable to any geometry and that can be extended to deformable objects. The convection-diffusion equation for the continuum ions is solved simultaneously considering Nernst-Planck diffusion. The method can be applied to systems at equilibrium and far from equilibrium. Its applicability is demonstrated in the context of electrokinetic motion, where it is shown that the ionic clouds associated with individual particles can be severely altered by the flow and concentration, leading to intriguing cooperative effects.
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Affiliation(s)
- Juan P Hernández-Ortiz
- Departamento de Materiales y Minerales, Universidad Nacional de Colombia, Sede Medellín, Medellín, Colombia
| | - Juan J de Pablo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
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Du D, Toffoletto F, Biswal SL. Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:043306. [PMID: 24827363 DOI: 10.1103/physreve.89.043306] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2013] [Indexed: 06/03/2023]
Abstract
Typically the force between paramagnetic particles in a uniform magnetic field is described using the dipolar model, which is inaccurate when particles are in close proximity to each other. Instead, the exact force between paramagnetic particles can be determined by solving a three-dimensional Laplace's equation for magnetostatics under specified boundary conditions and calculating the Maxwell stress tensor. The analytical solution to this multi-boundary-condition Laplace's equation can be obtained by using a solid harmonics expansion in conjunction with the Hobson formula. However, for a multibody system, finite truncation of the Hobson formula does not lead to convergence of the expansion at all points, which makes the approximation physically unrealistic. Here we present a numerical method for solving this Laplace's equation for magnetostatics. This method uses a smoothed representation to replace all the boundary conditions. A two-step propagation is used to dramatically accelerate the calculation without losing accuracy. Using this method, we calculate the force between two paramagnetic particles in a uniform and a rotational external field and compare our results with other models. Furthermore, the many-body effects for three-particle, ten-particle, and 24-particle systems are examined using the same method. We also calculate the interaction between particles with different magnetic susceptibilities and particle diameters. The Laplace's equation solver method described in this article that is used to determine the force between paramagnetic particles is shown to be very useful for dynamic simulations for both two-particle systems and a large cluster of particles.
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Affiliation(s)
- Di Du
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
| | - Frank Toffoletto
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Sibani Lisa Biswal
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
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