Electrophoresis of a colloidal particle embedded in electrolyte saturated porous media

Bhattacharyya, S.; De, Simanta; Gopmandal, Partha P.

doi:10.1016/j.ces.2014.07.044

Cited by 20 publications

(15 citation statements)

References 19 publications

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“…Interestingly, this describes experimentally observed transitions from a mean velocity that is linear in the electric-field strength at low field strengths to one that becomes highly nonlinear at high field strengths, albeit with a mechanical compliance factor that changes sign with the particle size. However, high electric-field strengths also manifest in non-linear electrokinetics 7 , and it is presently unknown when and how to distinguish these. Yet another body of work has addressed the electric-fieldinduced dynamics of particles that are permanently adhered to or entrapped in hydrogel networks 1,18,26 ; these studies complement an extensive microrheology literature 25 .…”

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confidence: 99%

“…These furnished a strong foundation for testing more intricate computations that account for non-linear electrostatics and relaxation effects. For example, Bhattacharyya et al 7 adopted a direct discretization methodology (finite-volume) to capture the polarization and relaxation effects for bare particles in uncharged gels, also addressing non-linear effects arising from strong electric fields. A very similar study, using the same direct-solution methodology, was undertaken by Bhattacharyya and De 6 for charged gels and strong electric fields.…”

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confidence: 99%

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Electrokinetics of nanoparticle gel-electrophoresis

Hill

2016

Soft Matter

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Gel-electrophoresis has been demonstrated in recent decades to successfully sort a great variety of nanoparticles according to their size, charge, surface chemistry, and corona architecture. However, quantitative theoretical interpetations have been limited by the number and complexity of factors that influence particle migration. Theoretical models have been fragmented and incomplete with respect to their counterparts for free-solution electrophoresis. This paper unifies electrokinetic models that address complex nanoparticle corona architectures, corona and gel charge regulation (e.g., by the local pH), multi-component electrolytes, and non-linear electrostatics and relaxation effects. By comprehensively addressing the electrokinetic aspects of the more general gel-electrophoresis problem, in which short-ranged steric interactions are significant, a stage is set to better focus on the physicochemical and steric factors. In this manner, it is envisioned that noparticle gelelectrophoresis may eventually be advanced from a nanoparticle-characterization tool to one that explicitly probes the short-ranged interactions of nanoparticles with soft networks, such as synthetic gels and biological tissues. In this paper, calculations are undertaken that identify a generalized Hückel limit for nanoparticles in low-conductivity gels, and a new Smoluchowski limit for polyelectrolyte-coated particles in high-conductivity gels that is independent of the gel permeability. Also of fundamental interest is a finite, albeit small, electrophoretic mobility for uncharged particles in charged gels. Electrophoretic mobilities and drag coefficients (with electroviscous effects) for nanoparticles bearing non-uniform coronas show that relaxation effects are typically weak for the small nanoparticles (radius ≈ 3-10 nm) to which gel-electrophoresis has customarily been applied, but are profound for the larger nanoparticles (radius 40 nm in low conductivity gels) to which passivated gel-electrophoresis experiments have recently been applied. To demonstrate its practical application, the model is applied to (pH charge regulating) carboxylated polystyrene nanospheres in low-density passivated agarose gels (weak steric effects). This furnishes a new theoretical interpretation of literature data for which a finite diffuse-layer-thickness, pH-charge regulation, high charge, and relaxation effects dominate over the steric influences.

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confidence: 99%

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confidence: 99%

Electrokinetics of nanoparticle gel-electrophoresis

Hill

2016

Soft Matter

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“…The Brinkman model is considered as a hydrodynamic continuum and can be characterized by the Darcy permeability coefficient. In the literature, an extension was made to the Brinkman model adding a term representing the electrokinetic transport phenomena inside the porous medium [19–26]. Tsai et al.…”

Section: Introductionmentioning

confidence: 99%

“…Bhattacharyya et al. [24] studied the electrophoresis problem of a colloidal particle embedded in the electrolyte‐saturated chargeless Brinkman medium in the presence of an electric field. They determined the velocity of the spherical particle through the balance of drag and electric forces as a function of charge density of the particle, permeability of the medium, and Debye‐layer thickness.…”

Section: Introductionmentioning

confidence: 99%

Transient electrophoresis of a conducting spherical particle embedded in an electrolyte‐saturated Brinkman medium

2021

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In this study, the time‐dependent electrophoretic motion of a conducting spherical particle embedded in an arbitrary electrolyte solution saturated porous medium is investigated. The porous medium is uniformly charged and the embedded hard particle is charged with constant ζ‐potential or constant surface charge density. The unsteady modified Brinkman equation with an electric force term, which governs the fluid velocity field, is used to model the porous medium and is solved by Laplace's transform technique. An analytical expression for the electrophoretic velocity of the spherical particle is obtained in Laplace transform domain as a function of the relevant parameters, and its inversion is obtained through numerical techniques. Also, in this study, the steady‐state electrophoretic velocity is obtained analytically as linear functions of ζ‐potential (or surface density charge) and the fixed charge density. The steady‐state electrophoretic velocity is displayed graphically for various relevant parameters and compered with the available data in the literature. Also, the numerical values of the transient electrophoretic velocity are plotted versus the nondimensional elapsed time and discussed for different values of the Debye length parameter, density ratio, permeability of the porous medium, and for high and nonconducting particles.

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“…Although the Brinkman equation is semiempirical in nature, it fits well with the experimental data in general and is regarded as the standard approach describing the fluid flow through a porous media. It was further extended to cover the corresponding electrokinetic transport phenomena inside the porous media, with an extra consideration of the electrical driving force . Feng et al studied the motion of a chargeless sphere near planar confining boundaries in a fiber matrix modelled as Brinkman's medium.…”

Section: Introductionmentioning

confidence: 99%

Start‐up Brinkman electrophoresis of a dielectric sphere for Happel and Kuwabara models

Saad

2018

Math Methods in App Sciences

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The starting electrophoresis in a charged porous continuum response of a homogeneous suspension of spherical particles to the sudden application of an external electric field is analyzed semianalytically through the use of a unit cell model. The electric double layer in the porous Brinkman medium surrounding each sphere is assumed to be thin but finite, and the effect of dynamic electroosmosis within it is included. The field equation for the fluid outside the double layers is solved based on the unit cell model under the start-up Brinkman model. Expressions of the time-dependent electrophoretic and settling velocities of the particle in the Laplace transform as functions of the permeability, the relative mass density, the electrokinetic particle radius, and the volume fraction of the particles are performed for two different boundary conditions at the fictitious surface of the cell. Numerical results indicate that the timescale for the development of electrophoresis and sedimentation is small for a high permeability, an assemblage of spheres through a dielectric porous medium with a higher particle volume fraction and a smaller particle to porous fluid density ratio; the electrophoretic mobility is a monotonically increasing function of the electrokinetic radius of the sphere at any instant. The start-up of electrophoretic mobility decreases with an increase in the particle volume fraction at a small value of the particle-to-medium density ratio, but it may increase as the particle volume fraction increases at a large value of this density. The particle interaction effect in a swarm on the time-dependent electrophoresis is much smaller than that on the starting sedimentation of the particles. The detailed comparison of the results of the cell model with different boundary conditions at the virtual surface of the cell is obtained and illustrated graphically.

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Electrophoresis of a colloidal particle embedded in electrolyte saturated porous media

Cited by 20 publications

References 19 publications

Electrokinetics of nanoparticle gel-electrophoresis

Electrokinetics of nanoparticle gel-electrophoresis

Transient electrophoresis of a conducting spherical particle embedded in an electrolyte‐saturated Brinkman medium

Start‐up Brinkman electrophoresis of a dielectric sphere for Happel and Kuwabara models

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