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Mahapatra P, Pal SK, Ohshima H, Gopmandal PP. Electrohydrodynamics of diffuse porous colloids. SOFT MATTER 2024; 20:2840-2862. [PMID: 38456335 DOI: 10.1039/d3sm01759a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/09/2024]
Abstract
The present article deals with the electrohydrodynamic motion of diffuse porous particles governed by an applied DC electric field. The spatial distribution of monomers as well as the charge distribution across the particle are considered to follow sigmoidal distribution involving decay length. Such a parameter measures the degree of inhomogeneity of the monomer distribution across the particle. The diffuse porous particles resemble several colloidal entities which are often seen in the environment as well as in biological and pharmaceutical industries. Considering the impact of bulk pH and ion steric effects, we modelled the electrohydrodynamics of such porous particulates based on the modified Boltzmann distribution for the spatial distribution of electrolyte ions and the Poisson equation for electric potential as well as the conservation of mass and momentum principles. We adopt regular perturbation analysis with weak field assumption and the perturbed equations are solved numerically to calculate the electrophoretic mobility and neutralization fraction of the particle charge during its motion as well as fluid collection efficiency. We further deduced the closed form relation between the drag force experienced by the charged porous particle and the fluid collection efficiency. In addition to the numerical results, we further derived the closed form analytical results for all the intrinsic parameters indicated above derived within the Debye-Hückel electrostatic framework and homogeneous distribution of monomers within the particle for which the decay length vanishes. The deduced mathematical results as indicated above will be useful to analyze several electrostatic and hydrodynamic features of a wide class of porous particulate and environmental entities.
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Affiliation(s)
- Paramita Mahapatra
- Department of Mathematics, National Institute of Technology Durgapur, Durgapur-713209, India.
| | - S K Pal
- Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - H Ohshima
- Faculty of Pharmaceutical Sciences, Tokyo University of Science, Noda, Chiba, Japan
| | - Partha P Gopmandal
- Department of Mathematics, National Institute of Technology Durgapur, Durgapur-713209, India.
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Mahapatra P, Ohshima H, Gopmandal PP. Effect of hydrodynamic slip on the electrophoresis of hydrophobic spherical particles in a solution of general electrolytes. Colloid Polym Sci 2022. [DOI: 10.1007/s00396-022-05018-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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3
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Liu J, Chai Z, Shi B. Diffuse-interface lattice Boltzmann modeling of charged particle transport in Poiseuille flow. Phys Rev E 2022; 106:015306. [PMID: 35974528 DOI: 10.1103/physreve.106.015306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Accepted: 06/24/2022] [Indexed: 06/15/2023]
Abstract
In this paper, we developed a coupled diffuse-interface lattice Boltzmann method (DI-LBM) to study the transport of a charged particle in the Poiseuille flow, which is governed by the Navier-Stokes equations for fluid field and the Poisson-Boltzmann equation for electric potential field. We first validated the present DI-LBM through some classical benchmark problems, and then investigated the effect of electric field on the lateral migration of the particle in the Poiseuille flow. The numerical results show that the electric field has a significant influence on the particle migration. When an electric field in the vertical direction is applied to the charged particle initially located above the centerline of the channel, the equilibrium position of the particle would drop suddenly as the electric field is larger than a critical value. This is caused by the wall repulsion due to lubrication, the inertial lift related to shear slip, the lift owing to particle rotation, the lift due to the curvature of the undisturbed velocity profile, and the electric force. On the other hand, when an electric field in the horizontal direction is adopted, the equilibrium position of the particle would move toward the centerline of the channel with the increase of the electric field.
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Affiliation(s)
- Jiao Liu
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Zhenhua Chai
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
- Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan 430074, China
- Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Baochang Shi
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
- Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan 430074, China
- Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
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4
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Nonlinear electrophoresis of colloidal particles. Curr Opin Colloid Interface Sci 2022. [DOI: 10.1016/j.cocis.2022.101587] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Barman SS, Bhattacharyya S. Finite ion size and ion permittivity effects on gel electrophoresis of a soft particle. Colloids Surf A Physicochem Eng Asp 2022. [DOI: 10.1016/j.colsurfa.2021.128088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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Barman SS, Bhattacharyya S, Gopmandal PP, Ohshima H. Impact of charged polarizable core on mobility of a soft particle embedded in a hydrogel medium. Colloid Polym Sci 2020. [DOI: 10.1007/s00396-020-04751-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Kumar B, De S, Gopmandal PP, Sinha RK, Ohshima H. Electrophoresis of dielectric and immiscible-liquid-layer-encapsulated colloids in aqueous media. Phys Rev E 2020; 102:042618. [PMID: 33212703 DOI: 10.1103/physreve.102.042618] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2020] [Accepted: 10/04/2020] [Indexed: 11/07/2022]
Abstract
In this paper we consider the electrophoresis of a functionalized nanoparticle in electrolyte solution. The undertaken particle is comprised of a rigid inner core encapsulated with a layer of dielectric liquid (e.g., oil or lipid layer), which is immiscible to the bulk aqueous medium. The peripheral liquid layer of the undertaken nanoparticle contains mobile charges due to presence of solubilized surfactants. The mobile electrolyte ions can penetrate across the peripheral layer depending on the difference in the Born energy of the both phases. Such types of nanoparticles have received substantial attention due to their widespread applications in biomedical research. The electric double layer (EDL) is governed by the linearized Poisson-Boltzmann equation under a low potential limit and the electroosmotic flow field is governed by modified Stokes equation. We adopt the flat-plate formalism to obtain the closed analytical expression for the electrophoretic mobility of the undertaken particle under a thin EDL approximation. The dependence of electrophoretic mobility on the pertinent parameters is also illustrated.
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Affiliation(s)
- Binod Kumar
- Department of Mathematics, National Institute of Technology Patna, Patna-800005, India
| | - Simanta De
- Department of Mathematics, University of Gour Banga, Malda-732103, India
| | - Partha P Gopmandal
- Department of Mathematics, National Institute of Technology Durgapur, Durgapur-713209, India
| | - R K Sinha
- Department of Mathematics, National Institute of Technology Patna, Patna-800005, India
| | - H Ohshima
- Faculty of Pharmaceutical Sciences, Tokyo University of Science, Noda, Chiba, Japan
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Electrophoresis of composite soft particles with differentiated core and shell permeabilities to ions and fluid flow. J Colloid Interface Sci 2019; 558:280-290. [PMID: 31593861 DOI: 10.1016/j.jcis.2019.09.118] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2019] [Revised: 09/27/2019] [Accepted: 09/28/2019] [Indexed: 11/20/2022]
Abstract
Within the framework of analytical theories for soft surface electrophoresis, soft particles are classically defined by a hard impermeable core of given surface charge density surrounded by a polyelectrolyte shell layer permeable to both electroosmotic flow and ions from background electrolyte. This definition excludes practical core-shell particles, e.g. dendrimers, viruses or multi-layered polymeric particles, defined by a polyelectrolytic core where structural charges are distributed and where counter-ions concentration and electroosmotic flow velocity can be significant. Whereas a number of important approximate expressions has been derived for the electrophoretic mobility of hard and soft particles, none of them is applicable to such generic composite core-shell particles with differentiated ions- and fluid flow-permeabilities of their core and shell components. In this work, we elaborate an original closed-form electrophoretic mobility expression for this generic composite particle type within the Debye-Hückel electrostatic framework and thin double layer approximation. The expression explicitly involves the screening Debye layer thickness and the Brinkman core and shell hydrodynamic length scales, which favors so-far missing analysis of the respective core and shell contributions to overall particle mobility. Limits of this expression successfully reproduce results from Ohshima's electrophoresis theory solely applicable to soft particles with or without hard core.
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Kumar B, Gopmandal PP, Sinha RK, Ohshima H. Electrophoresis of hydrophilic/hydrophobic rigid colloid with effects of relaxation and ion size. Electrophoresis 2019; 40:1282-1292. [DOI: 10.1002/elps.201800427] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2018] [Revised: 01/04/2019] [Accepted: 01/24/2019] [Indexed: 11/09/2022]
Affiliation(s)
- Binod Kumar
- Department of MathematicsNational Institute of Technology PatnaPatna India
| | - Partha P. Gopmandal
- Department of MathematicsNational Institute of Technology PatnaPatna India
- Department of MathematicsNational Institute of Technology DurgapurDurgapur India
| | - R. K. Sinha
- Department of MathematicsNational Institute of Technology PatnaPatna India
| | - H. Ohshima
- Faculty of Pharmaceutical SciencesTokyo University of ScienceNoda Chiba Japan
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Khair AS. Strong Deformation of the Thick Electric Double Layer around a Charged Particle during Sedimentation or Electrophoresis. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:876-885. [PMID: 28759725 DOI: 10.1021/acs.langmuir.7b01897] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The deformation of the electric double layer around a charged colloidal particle during sedimentation or electrophoresis in a binary, symmetric electrolyte is studied. The surface potential of the particle is assumed to be small compared to the thermal voltage scale. Additionally, the Debye length is assumed to be large compared to the particle size. These assumptions enable a linearization of the electrokinetic equations. The particle appears as a point charge in this thick-double-layer limit; the distribution of charge in the diffuse cloud surrounding it is determined by a balance of advection due to the particle motion, Brownian diffusion of ions, and electrostatic screening of the particle by the cloud. The ability of advection to deform the charge cloud from its equilibrium state is parametrized by a Péclet number, Pe. For weak advection (Pe ≪ 1), the cloud is only slightly deformed. In contrast, the cloud can be completely stripped from the particle at Pe ≫ 1; consequently, electrokinetic effects on the particle motion vanish in this regime. Therefore, in sedimentation the drag limits to Stokes' law for an uncharged particle as Pe → ∞. Likewise, the particle velocity for electrophoresis approaches Huckel's result. The strongly deformed cloud at large Pe is predicted to generate a concomitant increase in the sedimentation field in a dilute settling suspension.
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Affiliation(s)
- Aditya S Khair
- Department of Chemical Engineering, Carnegie Mellon University , Pittsburgh, Pennsylvania 15213, United States
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Bhattacharyya S, Majee PS. Electrophoresis of a polarizable charged colloid with hydrophobic surface: A numerical study. Phys Rev E 2017; 95:042605. [PMID: 28505837 DOI: 10.1103/physreve.95.042605] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2016] [Indexed: 06/07/2023]
Abstract
We consider the electrophoresis of a charged colloid for a generalized situation in which the particle is considered to be polarizable and the surface exhibits hydrophobicity. The dielectric polarization of the particle creates a nonlinear dependence of the electrophoretic velocity on the applied electric field, and the core hydrophobicity amplifies the fluid convection in the Debye layer. Thus, a linear analysis is no longer applicable for this situation. The present analysis is based on the numerical solution of the nonlinear electrokinetic equations based on the Navier-Stokes-Nernst-Planck-Poisson equations coupled with the Laplace equation for the electric field within the dielectric particle. The hydrophobicity of the particle may influence its electric polarization by enhancing the convective transport of ions. The nonlinear effects, such as double-layer polarization and relaxation, are also influenced by the hydrophobicity of the particle surface. The present results compare well for a lower range of the applied electric field and surface charge density with the existing results for a perfectly dielectric particle with a hydrophobic surface based on the first-order perturbation analysis due to Khair and Squires [Phys. Fluids 21, 042001 (2009)PHFLE61070-663110.1063/1.3116664]. Dielectric polarization creates a reduction in particle electrophoretic velocity, and its impact is strong for a moderate range of Debye length. A quantitative measure of the nonlinear effects is demonstrated by comparing the electrophoretic velocity with an existing linear model.
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Affiliation(s)
- Somnath Bhattacharyya
- Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
| | - Partha Sarathi Majee
- Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
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Yeh PH, Hsu JP, Tseng S. Influence of polyelectrolyte shape on its sedimentation behavior: effect of relaxation electric field. SOFT MATTER 2014; 10:8864-8874. [PMID: 25283952 DOI: 10.1039/c4sm01351d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The sedimentation of an isolated, charged polyelectrolyte (PE) subjected to an applied field is modeled theoretically, taking into account the variation of its shape. In particular, the effects of double-layer relaxation, effective charge density, and strength of the induced relaxation electric field are examined. We show that the interaction of these effects yields complex and interesting sedimentation behaviors. For example, the behavior of the electric force acting on a loosely structured PE can be different from that on a compactly structured one; the former is dominated mainly by the convective fluid flow. For thick double layers, electric force has a local maximum as the Reynolds number varies, but tends to increase monotonically with increasing Reynolds number if the layer is thin. The drag factor is found to behave differently from literature results. The shape of a PE significantly influences its sedimentation behavior by affecting the amount of counterions attracted to its interior and the associated local electric field. Interestingly, a more stretched PE has a higher effective charge density but experiences a weaker electric force.
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Affiliation(s)
- Pin-Hua Yeh
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617.
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Electrokinetics of a charged permeable porous aggregate in an aqueous medium. Colloids Surf A Physicochem Eng Asp 2013. [DOI: 10.1016/j.colsurfa.2013.04.056] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Advective flow of non-homogeneous permeable sphere in an electrical field. Colloids Surf A Physicochem Eng Asp 2012. [DOI: 10.1016/j.colsurfa.2012.03.042] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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