Diffusion Of Colloidal Particles Research Articles

Diffusiophoresis of Macromolecules within the Framework of Multicomponent Diffusion.

Diffusiophoresis is the isothermal migration of a colloidal particle through a liquid caused by a cosolute concentration gradient. Although diffusiophoresis was originally introduced using hydrodynamics, it can also be described by employing the framework of multicomponent diffusion. This not only enables the extraction of diffusiophoresis coefficients from measured multicomponent-diffusion coefficients but also their theoretical interpretation using fundamental thermodynamic and transport parameters. This review discusses the connection of diffusiophoresis with the 2 × 2 diffusion-coefficient matrix of ternary liquid mixtures. Specifically, diffusiophoresis is linked to the cross-term diffusion coefficient characterizing diffusion of colloidal particles due to cosolute concentration gradient. The other cross-term, which describes cosolute diffusion due to the concentration gradient of colloidal particles, is denoted as osmotic diffusion. Representative experimental results on diffusiophoresis and osmotic diffusion for polyethylene glycol and lysozyme in the presence of aqueous salts and osmolytes are described. These data were extracted from ternary diffusion coefficients measured using precision Rayleigh interferometry at 25 °C. The preferential-hydration and electrophoretic mechanisms responsible for diffusiophoresis are examined. The connection of diffusiophoresis and osmotic diffusion to preferential-interaction coefficients, Onsager reciprocal relations, Donnan equilibrium and Nernst-Planck equations are also discussed.

Scaling law of correlated diffusion of colloidal particles confined to a rugged surface

Using optical microscopy and multiparticle tracking techniques, we investigate the correlated diffusion of colloidal particles over a rugged surface. Our findings demonstrate that the correlated diffusion caused by the hydrodynamic interactions of particles confined to energy landscapes displays a distinctive power-law behavior. The local energy landscape on the rugged surface reduces the long-range hydrodynamic interactions between colloidal particles. The energy landscape influences the strength of hydrodynamic interactions, but not their power-law form. The responding factor of the colloidal particles over the energy landscape to hydrodynamics decays exponentially with the potential energy minimum. We propose a scaling method, with which the correlated diffusion of colloidal particles over various energy landscapes can be scaled onto a master curve. The master curve characterizes the response of the particles over the energy landscape to the hydrodynamics. The scale factors used for the master curve allow for the calculation of the energy landscape. The findings provide physical insights into the confinement hydrodynamics and would be helpful for designing material surfaces and controlling the motion of particles on rough surfaces.

Diffusion of a chemically active colloidal particle in composite channels

Diffusion of colloidal particles in microchannels has been extensively investigated, where the channel wall is either a no-slip or a slip-passive boundary. However, in the context of active fluids, driving boundary walls are ubiquitous and are expected to have a substantial effect on the particle dynamics. By mesoscale simulations, we study the diffusion of a chemically active colloidal particle in composite channels, which are constructed by alternately arranging the no-slip and diffusio-osmotic boundary walls. In this case, the chemical reaction catalyzed by the active colloidal particle creates a local chemical gradient along the channel wall, which drives a diffusio-osmotic flow parallel to the wall. We show that the diffusio-osmotic flow can significantly change the spatial distribution and diffusion dynamics of the colloidal particle in the composite channels. By modulating the surface properties of the channel wall, we can achieve different patterns of colloidal position distribution. The findings thus propose a novel possibility to manipulate colloidal diffusion in microfluidics, and highlight the importance of driving boundary walls in dynamics of colloidal particles in microchannels.

Soft Magnetostrictive Actuator String with Cellulose Nanofiber Skin.

The formation of cellulose nanofibrous skin with a colloidal suspension is challenging due to the diffusion of colloidal particles and bacteria to the bulk and a limited supply of oxygen for bacteria in the liquid culture environment. A composite-actuating string was fabricated with magnetic nanoparticles (MNPs) and Gluconacetobacter xylinus in a solid matrix of hydrophobic microparticles. G. xylinus synthesizes a dense skin layer of cellulose nanofibers enclosing MNPs in the solid matrix to form an actuator string responsive to an external magnetic field. The nanofibrous actuator string is transformable to fit the diverse shapes of tubular structures in cross section due to its softness and plastic deformability, which reduce friction and stress against the walls of organ tissues. The nanofibrous skin string is bendable at an acute angle by magnetic actuation and is applicable as an endoscopic guidewire to reach a target deep inside a model kidney structure.

Solid-liquid transition induced by the anisotropic diffusion of colloidal particles

We numerically study the phase behaviors of colloids with anisotropic diffusion in two dimensions. It is found that the diffusion anisotropy of colloidal particles plays an important role in the phase transitions. A strong diffusion anisotropy induces the large vibration of particles, subsequently, the system goes into a disordered state. In the presence of the strong-coupling, particles with weak diffusion anisotropy can freeze into hexagonal crystals. Thus, there exists a solid-liquid transition. With the degree of diffusion anisotropy increasing, the transition points are shifted to the stronger-coupled region. A competition between the degree of diffusion anisotropy and coupling strength widens the transition region where the heterogeneous structures coexist, which results in a broad-peak probability distribution curve for the local order parameter. Our study may be helpful for the experiments related to the phase behavior in statistical physics, materials science and biophysical systems.

Diffusion of colloidal particles in model porous media.

Using video microscopy and simulations, we study the long-time diffusion of colloidal tracers in a wide range of model porous media composed of frozen colloidal matrices with different structures. We found that the diffusion coefficient of a tracer can be quantitatively determined by the structures of porous media. In particular, a universal scaling relation exists between the dimensionless diffusion coefficient of the tracer and the structural entropy of the system. This universal scaling relation is an extension of the scaling law previously discovered for the diffusion of colloidal particles in fluctuating media.

Non-Gaussian normal diffusion in low dimensional systems

Brownian particles suspended in disordered crowded environments often exhibit non-Gaussian normal diffusion (NGND), whereby their displacements grow with mean square proportional to the observation time and non-Gaussian statistics. Their distributions appear to decay almost exponentially according to “universal” laws largely insensitive to the observation time. This effect is generically attributed to slow environmental fluctuations, which perturb the local configuration of the suspension medium. To investigate the microscopic mechanisms responsible for the NGND phenomenon, we study Brownian diffusion in low dimensional systems, like the free diffusion of ellipsoidal and active particles, the diffusion of colloidal particles in fluctuating corrugated channels and Brownian motion in arrays of planar convective rolls. NGND appears to be a transient effect related to the time modulation of the instantaneous particle’s diffusivity, which can occur even under equilibrium conditions. Consequently, we propose to generalize the definition of NGND to include transient displacement distributions which vary continuously with the observation time. To this purpose, we provide a heuristic one-parameter function, which fits all time-dependent transient displacement distributions corresponding to the same diffusion constant. Moreover, we reveal the existence of low dimensional systems where the NGND distributions are not leptokurtic (fat exponential tails), as often reported in the literature, but platykurtic (thin sub-Gaussian tails), i.e., with negative excess kurtosis. The actual nature of the NGND transients is related to the specific microscopic dynamics of the diffusing particle.

Ultrasound-enhanced diffusion and streaming of colloids in porous media

Diffusion of colloidal particles in porous media is critical for the development of specially engineered colloids used to aid the recovery of oil from a petroleum reservoir. However, shielded structures, such as dead-end pores, prevent these colloids from reaching the available oil. This article examines the use of ultrasound fields as a mechanism for increasing the mobility of colloidal particles in porous media. Particle tracking of optical video microscopy experiments performed in micromodels of varying porosity are used to construct mean square displacement, from which effective diffusion coefficients and average particle velocities can be measured. We introduce an acoustic field by sweeping a phase space that consists of multiple voltages, frequencies and porosities. Our experiments show that diffusion scales linearly with voltage, while average particle velocity scales quadratically. We found that the diffusion and average velocity peaked near a frequency of ~40 kHz for porosities of 0.62, 0.76 and 0.9, suggesting the presence of a natural frequency. A second natural frequency with a value close to ~90 kHz was also observed in experiments conducted at 0.62 and 0.76. The effective diffusion at 40 kHz has a maximum value ~0.4 μm2/s, which is a factor of 5.5 times greater than in the absence of an acoustic field. Outside of the 40 kHz resonance peak, diffusion remains enhanced, with a measured coefficient of ~0.15 μm2/s. This is still a factor of 2 greater than when no acoustic field is present. Overall, our results demonstrate that ultrasound enhances the transport of colloidal particles through porous media. Future work aims to use these results as the foundation for improved modelling of acoustically stimulated transport through porous media as well as applying these results to problems related to particulate separation.

Hydrodynamic separation of colloidal particles in tubes: Effective one-dimensional approach.

We investigate diffusion of colloidal particles carried by flow in tubes of variable diameter and under the influence of an external field. We generalize the method mapping the three-dimensional confined diffusion onto an effective one-dimensional problem to the case of nonconservative forces and use this mapping for the problem in question. We show that in the presence of hydrodynamic drag, the lowest approximation (the Fick-Jacobs approximation) may be insufficient, and inclusion of at least the first-order correction is desirable to obtain more reliable results. As a practical application, we use the method for investigation of separation of colloidal particles carried by a fluid flow according to their size, using flotation and centrifugation.

Dynamic susceptibility of a concentrated ferrofluid: The role of interparticle interactions.

The dynamic susceptibility of concentrated ferrofluids of magnetite-kerosene type is studied experimentally to clarify the effect of interparticle interactions on the magnetization reversal dynamics and the ferrofluid relaxation time spectrum. We synthesize six ferrofluid samples, four of which have the same wide particle size distribution with a high (more than 2kT) average energy of magnetic dipole interactions. These samples differ in particle concentration and dynamic viscosity. The two remaining samples have a lower content of large particles and a moderate energy of magnetic dipole interactions. For all samples, we measure the dynamic susceptibility in the weak probing field at frequencies up to 160kHz and the field amplitude dependence of the susceptibility at a frequency of 27kHz. The results show that the susceptibility dispersion at frequencies up to 10kHz is due to the rotational diffusion of colloidal particles and aggregates. Steric and hydrodynamic interparticle interactions are the main reason for the strong concentration dependence of the viscosity and so they also strongly influence the frequency dependence of the susceptibility. The influence of van der Waals and magnetic dipole interactions on the susceptibility is manifested indirectly, through the formation of multiparticle clusters. The contribution of clusters to the low-frequency susceptibility reaches 80%. Their large sizes (about 100 nm) shift the dispersion region to frequencies of 1-100Hz, depending on the temperature and particle concentration. Experiments at 27kHz demonstrate the increase in the dynamic susceptibility with increasing field amplitude. This growth is unexpected since all spectral amplitudes in the Debye function expansion of the dynamic susceptibility decrease monotonically with increasing field. To clarify the situation, the auxiliary problem of the magnetodynamics of a uniaxial particle in the alternating field is solved numerically. The Fokker-Planck-Brown rotational diffusion equation is used. It is shown that an increase in the field amplitude reduces the anisotropy barrier and the Néel relaxation time of particles and increases the dynamic susceptibility by one to two orders of magnitude compared to the weak-field limit. The calculation results are in qualitative agreement with the experimental data and allow us to propose a consistent interpretation of these data. We find that the increase in dynamic susceptibility with increasing amplitude is observed when two necessary conditions are met: (i) The suspension viscosity and the field frequency are high enough to cause the blocking of the rotational degrees of freedom of particles and aggregates and (ii) particles with a large magnetic anisotropy are present in the ferrofluid.

Spatial Cross-Correlated Diffusion of Colloids under Shear Flow.

The spatial cross-correlated diffusion of colloidal particles is often used as an essential tool to study the dynamic properties of a fluid because it directly describes the hydrodynamic interaction between two particles in a fluid. However, the experimental measurement of cross-correlated diffusion can be substantially modified by even a weak shear flow. In this work, the effect of a shear flow on spatial cross-correlated diffusion is demonstrated using experimental measurements that show a clear dependence on pair angles. An analytical solution is proposed to explain the experimental observations. A numerical simulation is performed to systemically demonstrate the influence of shear flow on spatial cross-correlated diffusion. The results of the experiment, theoretical analysis, and numerical simulation agree well with each other. Therefore, this research provides a sensitive experimental method to determine the weak shear flow in any quasi-two-dimensional fluid systems.

Simulations of the dynamic deposition of colloidal particles from a volatile sessile drop

HypothesisThe deposition of particles from a volatile liquid drop atop a substrate is primarily governed by the advection and diffusion of the particles in the liquid. Colloidal particles may further coagulate and adsorb to the substrate during the deposition process. The external geometry and the internal composition of the particulate deposit are then determined by an interplay between these four mechanisms. SimulationWe simulate the process of deposition by solving the governing transport equations. We explore the interplay between the different mechanisms mentioned above. In particular, we study the contribution of the diffusion of colloidal particles and aggregates to the morphology of the deposit, which was neglected in a previous study. FindingsThe rates of diffusion and coagulation of each specific aggregate are dependent on its size. Hence, the transport equation uniquely correlates to each population of aggregates. The overall transport problem, alongside the rates of particle and aggregate adsorption and liquid evaporation, determines the geometry of the deposit. Moreover, the local rate of particle coagulation determines the internal composition of the different aggregate populations in the deposit. Our results appear to be in qualitative agreement with previous experimental findings.

Collectivity in diffusion of colloidal particles: from effective interactions to spatially correlated noise

The collectivity in the simultaneous diffusion of many particles, i.e. the interdependence of stochastic forces affecting different particles in the same solution, is a largely overlooked phenomenon with no well-established theory. Recently, we have proposed a novel type of thermodynamically consistent Langevin dynamics driven by spatially correlated noise (SCN) that can contribute to the understanding of this problem. This model draws a link between the theory of effective interactions in binary colloidal mixtures and the properties of SCN. In the current article, we review this model from the perspective of collective diffusion and generalize it to the case of multiple (N > 2) particles. Since our theory of SCN-driven Langevin dynamics has certain issues that could not be resolved within this framework, in this article we also provide another approach to the problem of collectivity. We discuss the multi-particle Mori–Zwanzig model, which is fully microscopically consistent. Indeed, we show that this model supplies a lot of information, complementary to the SCN-based approach, e.g. it predicts the deterministic dynamics of the relative distance between the particles, it provides an approximation for non-equilibrium effective interactions and predicts the collective sub-diffusion of tracers in the group. These results provide the short-range, inertial limit of the earlier model and agree with its predictions under some general conditions. In this article we also review the origin of SCN and its consequences for a variety of physical systems, with emphasis on the colloids.

Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed.

Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.

Selective transport control on molecular velcro made from intrinsically disordered proteins.

The selectivity and speed of many biological transport processes transpire from a 'reduction of dimensionality' that confines diffusion to one or two dimensions instead of three. This behaviour remains highly sought after on polymeric surfaces as a means to expedite diffusional search processes in molecular engineered systems. Here, we have reconstituted the two-dimensional diffusion of colloidal particles on a molecular brush surface. The surface is composed of phenylalanine-glycine nucleoporins (FG Nups)--intrinsically disordered proteins that facilitate selective transport through nuclear pore complexes in eukaryotic cells. Local and ensemble-level experiments involving optical trapping using a photonic force microscope and particle tracking by video microscopy, respectively, reveal that 1-µm-sized colloidal particles bearing nuclear transport receptors called karyopherins can exhibit behaviour that varies from highly localized to unhindered two-dimensional diffusion. Particle diffusivity is controlled by varying the amount of free karyopherins in solution, which modulates the multivalency of Kap-binding sites within the molecular brush. We conclude that the FG Nups resemble stimuli-responsive molecular 'velcro', which can impart 'reduction of dimensionality' as a means of biomimetic transport control in artificial environments.

Diffusion of colloidal particles in swimming suspensions

Previously, we have proposed to analyse the hydrodynamic interactions in a suspension of swimmers with respect to an effective hydrodynamic diffusion coefficient, which only considers the fluctuating motion caused by the stirring of the fluid. In this work, we study the diffusion of colloidal particles immersed in a bath of swimmers. To accurately resolve the many-body hydrodynamic interactions responsible for this diffusion, we use a direct numerical simulation scheme based on the smooth profile method. We consider a squirmer model for the self-propelled swimmers, as it accurately reproduces the flow field generated by real microorganisms, such as bacteria or spermatozoa. We show that the diffusion coefficients of the colloids are comparable with the effective diffusion coefficients of the swimmers, provided that the concentration of swimmers is high enough. At low concentrations, the difference in the way colloids and swimmers react to the flow leads to a reduction in the diffusion coefficient of the colloids. This is clearly seen in the appearance of a negative-correlation region for the velocity-correlation function of the colloids, which does not exist for the swimmers.

Correlated Diffusion of Colloidal Particles near a Liquid-Liquid Interface

Optical microscopy and multi-particle tracking are used to investigate the cross-correlated diffusion of quasi two-dimensional colloidal particles near an oil-water interface. The behaviors of the correlated diffusion along longitudinal and transverse direction are asymmetric. It is shown that the characteristic length for longitudinal and transverse correlated diffusion are particle diameter and the distance from particle center to the interface, respectively, for large particle separation . The longitudinal and transverse correlated diffusion coefficient and are independent of the colloidal area fraction when , which indicates that the hydrodynamic interactions(HIs) among the particles are dominated by HIs through the surrounding fluid for small . For high area fraction , the power law exponent for the spatial decay of begins to decrease, which suggests the HIs are more contributed from the 2D particle monolayer self for large .

Universal scaling of correlated diffusion of colloidal particles near a liquid-liquid interface

In this letter, we investigate the correlated diffusion of colloidal particles in quasi two-dimensional monolayer near an oil-water interface for different distance between the interface and the particle monolayer z. It is found that there is a transition in the behavior of the correlated diffusion from the bulk dominated to the interface dominated with decreasing z or increasing inter-particle separation r. With a scaling method proposed by us, the correlated diffusion can be scaled onto a master curve which captures the characters of this transition. The scale factors and the master curve allow the calculation of the distance z, which are in agreement with the one-particle measurements.

Mechanisms for Anomalous Diffusion in a Nematic Environment

Mechanisms for anomalous diffusion of colloidal particles in a nematic environment are theoretically investigated. It is shown that thermal fluctuations of the nematic director may couple to the translational and orientational motions of particles, which leads to anomalous diffusion. Both superdiffusion, when the mean square displacement increases with the time faster than linearly, and subdiffusion, when this dependence is slower than linear, are possible. For micrometer-sized particles, the anomalous diffusion effects are expected on millisecond time scales.

Effect of Gravity Modulation on the Onset of Ferroconvection in a Densely Packed Porous Layer

The stability of a horizontal porous layer of a ferromagnetic fluid heated from below is studied when the fluid layer is subject to a time-periodic body force. Modified Darcy law is used to describe the fluid motion. The effect of gravity modulation is treated by a perturbation expansion in powers of the amplitude of modulation. The stability of the system, characterized by a correction Rayleigh number, is determined as a function of the frequency of modulation, magnetic parameters, and Vadasz number. It is found that subcritical instability is possible for low frequency g-jitter and that the magnetic and g-jitter mechanisms work against each other for small and moderate values of frequency of modulation. The effect of Vadasz number is shown to be reinforcing the influence of gravity modulation for small and moderate values of frequency. The magnetic, porous and modulation effects disappear altogether for sufficiently large values of the frequency of modulation. Keywords-Ferromagnetic fluid, Gravity modulation, Perturbation method, Porous layer, Stability. Gupta and Gupta (3) investigated thermal instability in a layer of ferromagnetic fluid subject to coriolis force and permeated by a vertical magnetic field. It is substantiated that overstability cannot occur if the Prandtl number is greater than unity. Gotoh and Yamada (4) investigated the linear convective instability of a ferromagnetic fluid layer heated from below and confined between two horizontal ferromagnetic boundaries. The Galerkin technique is used and the Legendre polynomials are taken as the trial functions. It is shown that the magnetization of the boundaries and the nonlinearity of fluid magnetization reduce the critical Rayleigh number and the effects of magnetization and buoyancy forces are shown to compensate each other. Blums (5) examined the possibility of having convection in ferromagnetic fluids as a result of magneto- diffusion of colloidal particles which give rise to non-uniform magnetization. Stiles and Kagan (6) examined the thermoconvective instability of a horizontal layer of ferrofluid in a strong vertical magnetic field. Their work also questioned the satisfactory agreement claimed to exist between the experiments and the theoretical model of Finlayson which has been generalized by them. Odenbach (7) investigated the convective flow generated by the interaction of a magnetic field gradient with a gradient in magnetization in a magnetic fluid. This gradient was caused by the diffusion of the magnetic particles in the field gradient. Aniss et al. (8) investigated the effect of a time-sinusoidal magnetic field on the onset of convection in a horizontal magnetic fluid layer heated from above. The Floquet theory is used to determine the convective threshold for free-free and rigid-rigid cases. The possibility to produce a competition between the harmonic and subharmonic modes at the onset of convection is discussed. Abraham (9) investigated the Rayleigh-Benard problem in a micropolar ferromagnetic fluid layer in the presence of a vertical uniform magnetic field analytically. It is shown that the micropolar ferromagnetic fluid layer heated from below is more stable as compared with the classical Newtonian ferromagnetic fluid. The effect of radiative heat transfer on ferroconvection has been studied by Maruthamanikandan (10) using the linear stability analysis. Consideration is given to two asymptotic cases, viz., transparent and opaque layers of fluid. The critical values marking the onset of convection are obtained using the Galerkin technique. Bajaj (11) considered thermosolutal convection in magnetic fluids in the presence of a vertical magnetic field and bifrequency vertical vibrations. The regions of parametric instability have been obtained using the Floquet theory. Ramanathan and Muchikel (12) investigated the effect of temperature-dependent viscosity on ferroconvective instability in a porous medium. It is found that the stationary mode of instability is