Migration Of Colloidal Particles Research Articles

Temperature-induced migration of electro-neutral interacting colloidal particles

Migration of colloidal particles induced by temperature gradients is commonly referred to as thermodiffusion, thermal diffusion, or the (Ludwig-)Soret effect. The thermophoretic force experienced by a colloidal particle that drives thermodiffusion consists of two distinct contributions: a contribution resulting from internal degrees of freedom of single colloidal particles, and a contribution due to the interactions between the colloids. We present an irreversible thermodynamics based theory for the latter collective contribution to the thermophoretic force. The present theory leads to a novel “thermophoretic interaction force” (for uncharged colloids), which has not been identified in earlier approaches. In addition, an N-particle Smoluchowski equation including temperature gradients is proposed, which complies with the irreversible thermodynamics approach.A comparison with experiments on colloids with a temperature dependent attractive interaction potential over a large concentration and temperature range is presented. The comparison shows that the novel thermophoretic interaction force is essential to describe data on the Soret coefficient and the thermodiffusion coefficient.

FABRICATION OF REALISTIC TRANSPARENT POROUS MEDIA FOR 3D OBSERVATION OF INTERNAL MASS TRANSPORT

A new experimental system was developed to observe the migration of colloidal particles in saturated porous media in 3D, which is important in engineering processes such as contaminant migration and filtration. The system enables the observation of internal migration that is invisible from the outside by fabricating a porous body using a transparent material and a 3D printer. Non-artificial media with arbitrarily controlled internal pore sizes were fabricated by designing the porous media based on the results of numerical analysis on phase-separation phenomena. The refractive indices of the porous media and the interstitial liquid were matched, and a laser sheet was used to extract cross sections of the media. By reconstructing multiple cross-sectional images, it was possible to visualize the 3D migration of suspended particles. The developed system was then applied to the collective gravitational settling of fine particles in saturated porous media. The results showed that the particles selectively settled in the pore networks while repeatedly branching in the lateral direction.

Interplay of electric field and pressure-driven flow inducing microfluidic particle migration

The lateral migration of colloidal particles inside a microfluidic channel has gained attention due to being both fundamentally intriguing and applicable for particle separation, such as cancer cell isolation or extracellular vesicle purification. Applying an external electric field combined with a pressure-driven flow induces such lateral migrations. In this study, new modes of lateral particle migration have been found by experimentally investigating 6 µm particles in the co-presence of electric field and pressure-driven flow. The experiments revealed the importance of the relative strengths of electric field and pressure gradient in determining particle lateral positioning. We hypothesize that the nonuniformity of the polarization caused by the external electric field and the rotation of the particle due to the background pressure-driven flow result in these modes of transverse migration. These new migration patterns are further utilized to perform microparticle separation and, more importantly, present a novel separation modality.

Effect of gravity on colloidal particle transport in a saturated porous medium: Analytical solutions and experiments.

The colloidal particle transport process in all porous media from laboratory to nature is affected by gravity. In this paper, a mathematical model of colloidal particle migration in a saturated porous medium with the gravity effect is established by combining the gap velocity (advection) with the settling velocity (gravity effect), and an analytical solution of the particle migration problem with time variation of the particle injection intensity is obtained using an integral transformation. The correctness and rationality of the analytical solution are verified by comparing the experimental and theoretical results of the particle migration problem in the point-source transient injection mode. The analytical solution can easily analyze the colloid transport experimental data in a variety of seepage directions. Analysis of the influence of seepage velocities in three different seepage directions on particle transport parameters shows: under the same seepage direction, the peak value of the breakthrough curve increased with an increase in the seepage velocity. The dispersion, adsorption coefficient, and deposition rate decreased with an increase in the seepage velocity. Under the same seepage velocity, the peak value of the breakthrough curve from large to small was vertically downward (VD)> horizontal (H)> vertically upward (VU), the order of dispersion from large to small was vertically downward (VD)>horizontal (H) >vertically upward (VU), the order of the adsorption coefficient and deposition rate of particles from large to small was vertically upward (VU)> horizontal (H) >vertically downward (VD), and the smaller the seepage velocity, the greater the relative differences in the peak value of the breakthrough curve, dispersion, the particle adsorption coefficient, and the deposition rate in the different seepage directions. Therefore, gravity is an important mechanism of particle migration in saturated porous media. The larger the particle size and density were, the smaller the seepage velocity was and the more obvious the effect of gravity. The findings of this study can help for better understanding of colloidal transport properties in porous media under the coupled effects of gravity and hydrodynamics.

Salt-induced diffusiophoresis of a nonionic micelle: Roles of salting out and proximity to surfactant cloud point

• Salt-induced diffusiophoresis is the migration of a colloidal particle in water caused by a salt concentration gradient. • Tyloxapol micelle was identified as model particle with surface properties governed by polyethylene glycol (PEG) chains. • Na 2 SO 4 was chosen because it is a common salt and a strong salting-out agent according to Hofmeister series. • Gradient of Na 2 SO 4 drives micelle diffusiophoresis from high to low salt concentration due to PEG preferential hydration. • Near surfactant cloud point, diffusiophoresis becomes dominant mechanism responsible for micelle transport. Salt-induced diffusiophoresis is the migration of colloidal particles in water caused by salt concentration gradients. A widespread example of colloidal particles is represented by those with interfacial properties governed by polyethylene glycol (PEG) functionalities. Since salting-out salts strongly affect PEG-water interactions, their gradients are expected to generate diffusiophoresis of PEG-based particles. In this work, diffusiophoresis of nonionic micelles of tyloxapol, a polyoxyethylene surfactant, was characterized in the presence of Na 2 SO 4 . Specifically, multicomponent-diffusion coefficients were measured at 25 °C for the ternary tyloxapol-Na 2 SO 4 -water system using Rayleigh interferometry. These transport data, together with measurements of cloud points and dynamic-light-scattering diffusion coefficients, were used to determine the effect of salt concentration on micelle mobility, salt-induced micelle diffusiophoresis and salt osmotic diffusion induced by micelle gradients. It was found that gradients of Na 2 SO 4 induce micelle diffusiophoresis from high to low salt concentration. Moreover, diffusiophoresis becomes the dominant mechanism responsible for micelle transport near surfactant cloud point due to increase in both micelle size and osmotic compressibility with salt concentration. A hydration model was employed to theoretically describe salt salting-out effect on micelle diffusiophoresis and salt osmotic diffusion. This work is the first report showing salt-induced diffusiophoresis of a neutral PEG-based colloidal particle and characterizing its magnitude near miscibility gaps.

Liquid Optothermoelectrics: Fundamentals and Applications.

Liquid thermoelectricity describes the redistribution of ions in an electrolytic solution under the influence of temperature gradients, which leads to the formation of electric fields. The thermoelectric field is effective in driving the thermophoretic migration of charged colloidal particles for versatile manipulation. However, traditional macroscopic thermoelectric fields are not suitable for particle manipulations at high spatial resolution. Inspired by optical tweezers and relevant optical manipulation techniques, we employ laser interaction with light-absorbing nanostructures to achieve subtle heat management on the micro- and nanoscales. The resulting thermoelectric fields are exploited to develop new optical technologies, leading to a research field known as liquid optothermoelectrics. This Invited Feature Article highlights our recent works on advancing fundamentals, technologies, and applications of optothermoelectrics in colloidal solutions. The effects of light irradiation, substrates, electrolytes, and particles on the optothermoelectric manipulations of colloidal particles along with their theoretical limitations are discussed in detail. Our optothermoelectric technologies with the versatile capabilities of trapping, manipulating, and pulling colloidal particles at low optical power are finding applications in microswimmers and nanoscience. With its intricate interfacial processes and tremendous technological promise, optothermoelectrics in colloidal solutions will remain relevant for the foreseeable future.

Combined electrokinetic and shear flows control colloidal particle distribution across microchannel cross-sections.

Recent experimental observations on combined electrokinetic and shear flows of colloidal suspensions in rectangular cross-section microfluidic channels have shown unusual cross-stream colloidal particle migration and dynamic assembly. Although a new electrophoresis-induced lift force has been postulated to cause the lateral migration of colloidal particles, little is known about how fluid properties and flow conditions impact this force and therefore subsequent colloidal particle migration. Furthermore, no experimental quantification of this electrophoresis-induced lift force is available. We report several key advances by demonstrating that the kinematic viscosity of the fluid can be used to modulate the spatial distribution of particles over the entire microchannel cross-section, with suppression of the colloidal particle migration observed with increase in fluid kinematic viscosity. Colloidal particle migration of ∼10 μm from not only the top and bottom microchannel walls but also from the side walls is shown with the corresponding electrophoresis-induced lift force of up to ∼30 fN. The breadth of flow conditions tested capture the channel Reynolds number in the 0.1-1.1 range, with inertial migration of colloidal particles shown in flow regimes where the migration was previously thought to be ineffective, if not for the electrophoresis-induced lift force. The ability of the electrophoresis-induced lift force to migrate colloidal particles across the entire microchannel cross-section establishes a new paradigm for three-dimensional control of colloidal particles within confined microchannels.

Decision-making at a T-junction by gradient-sensing microscopic agents

Active navigation in food searching, survival, and mating has led to the evolution of diverse strategies in natural living systems. We study navigation of microscopic gradient-sensing agents that orient among possible paths via sensing of a diffusible substance's concentration, first with experiments on colloidal particle migration along concentration gradients by diffusiophoresis. We treat particle exit time as a mean first passage time (MFPT) problem and show that a separatrix concentration gradient determines path taking statistics. We confirm numerically that an MFPT discontinuity hinders microscopic agents in following the shortest path.

Soft lithography with liquid marbles

The soft lithography process with water marbles immersed into the PDMS matrix is demonstrated. Near-surface cavities, decorated with the toroidal residues, built of the colloidal particles, initially coating the marbles, are formed in the course of evaporation of water filling the liquid marbles. Water liquid marbles coated with lycopodium, polyethylene and polytetrafluoroethylene particles remained attached to the PDMS/air interface from below due to the capillary bridges. The analysis of the equilibrium of a liquid marble supported by the capillary bridge is suggested. Thermal fields arising from cross-linking of PDMS and evaporation of water from liquid marbles are explored. The migration of colloidal particles coating the marbles towards the contact line in the course of water evaporation is reported and analyzed. Migration of particles is related to the “coffee-stain effect”. Mechanical properties of the PDMS samples stamped with the liquid marbles are reported.

Dynamics of colloidal particles in microchannels under combined pressure and electric potential gradients

Dynamics of charged sub-micron or colloidal particles in a microfluidic device through cross-stream migration under combined pressure gradients and electric potential gradients was demonstrated using confocal microscopy. The microfluidic device was a rectangular cross-section poly(dimethylsiloxane) or PDMS microchannel sealed with a borosilicate glass lid to form a hybrid PDMS-glass device. We postulate that the reported particle migration may arise in response to electrophoretic particle slip, i.e., the difference between the particle and fluid velocities, due to the applied electric potential gradient across the microchannel. Colloidal particle migration was observed either towards or away from the microchannel walls depending on the relative directions for the applied potential and pressure gradients. When pressure gradient driving the fluid flow and potential gradient were applied in the same direction, colloidal particles migrate away from the microchannel walls. In the case of opposite directions for the pressure and potential gradients, colloidal particles migrate towards the microchannel walls and subsequently assemble into distinct bands next to both the bottom glass and top PDMS walls. The results reported here demonstrate that the particle dynamics due to electrophoresis in Poiseuille flow within a microchannel result in non-uniform spatial distributions of colloidal particles via cross-stream migration, with the ability to assemble particles into distinct band structures at channel walls. Such manipulation, once fully realized, could lead to several microfluidics applications in material synthesis, particle separation, and biosensing.

Discussions on the driving mechanism of postdepositional migration of 241Am and 137Cs in organomineral sediments (Lake Krugloe, Tomsk region, Russia).

A core of bottom sediments from Lake Krugloe located within the 30km influence zone of the Siberian Chemical Plant (located in the city of Seversk "Tomsk-7") was studied to determine scales and rates of migration of artificial radionuclides 137Cs and 241Am in organomineral sediment. It was found that the main portion of 137Cs and 241Am was contained in the sediment interval above 10cm. This means that the horizon of 10cm corresponds to 1950-the time of the start of widespread tests of nuclear weapons. The 210Pbex dates also confirm that this particular horizon was formed in the 1950s. Pore waters in the core above the 10cm horizon are in oxidizing conditions. The depth of the oxidized/reduced boundary was determined from the distribution of redox-sensitive elements Fe and U dissolved in the pore solution. The core distribution of 137Cs is a slightly sloping step, with the lower edge at the 10cm level. The smearing of the lower boundary of this distribution showing the scale of 137Cs migration made it possible to estimate the diffusion mobility of 137Cs. Its diffusion coefficient turned out to be of the order of 10-8cm2s-1. As shown by measurements, the scale of migration of 241Am and the scale of migration of 137Cs have similar values. Theoretical analysis carried out in this work shows that the most probable mechanism of 137Cs and 241Am migration in the pore solution of lake sediment is the migration of colloidal particles to which these radionuclides are strongly bound. Calculation of the diameter of such particles by the Stokes-Einstein formula shows that they have submicron dimensions (d≈ 400nm). No evidence was found that the change in redox conditions in the sediment had an effect on migration of Am ions in pore solution.

Dynamic properties of polydisperse colloidal particles in the presence of thermal gradient studied by a modified Brownian dynamic model

Aggregation and migration of colloidal particles under the thermal gradient widely exists in nature and many industrial processes. In this study, dynamic properties of polydisperse colloidal particles in the presence of thermal gradient were studied by a modified Brownian dynamic model. Other than the traditional forces on colloidal particles, including Brownian force, hydrodynamic force, and electrostatic force from other particles, the electrostatic force from the asymmetric ionic diffusion layer under a thermal gradient has been considered and introduced into the Brownian dynamic model. The aggregation ratio of particles (RA), the balance time (tB) indicating the time threshold when becomes constant, the porosity (), fractal dimension (Df) and distributions of concentration (DISC) and aggregation (DISA) for the aggregated particles were discussed based on this model. The aggregated structures formed by polydisperse particles are less dense and the particles therein are loosely bonded. Also it showed a quite large compressibility as the increases of concentration and interparticle potential can significantly increase the fractal dimension. The thermal gradient can induce two competitive factors leading to a two-stage migration of particles. When , the unsynchronized aggregation is dominant and the particles slightly migrate along the thermal gradient. When , the thermophoresis becomes dominant thus the migrations of particles are against the thermal gradient. The effect of thermophoresis on the aggregate structures was found to be similar to the effect of increasing particle concentration. This study demonstrates how the thermal gradient affects the aggregation of monodisperse and polydisperse particles and can be a guide for the biomimetics and precise control of colloid system under the thermal gradient. Moreover, our model can be easily extended to other more complex colloidal systems considering shear, temperature fluctuation, surfactant, etc.

Splitting and separation of colloidal streams in sinusoidal microchannels.

The control of the distribution of colloidal particles in microfluidic flows plays an important role in biomedical and industrial applications. A particular challenge is to induce cross-streamline migration in laminar flows, enabling the separation of colloidal particles according to their size, shape or elasticity. Here we show that viscoelastic fluids can mediate cross-streamline migration of deformable spherical and cylindrical colloidal particles in sinusoidal microchannels at low Reynolds numbers. For colloidal streams focused into the center of the channel entrance this leads to a symmetric stream-splitting and separation into four substreams. The degree of stream splitting and separation can be controlled via the flow rates, viscoelasticity of the focusing fluid, and the spatial microchannel modulation with an upper limit when reaching the microchannel walls. We demonstrate that this effect can be used to separate flexible particles of different size and shape. This methodology of cross-stream migration has thus great potential for the passive separation of colloids and cells in microfluidic channels.

Kinetics of migration of colloidal particles in meat muscles in the absence and presence of a proteolytic enzyme to simulate non-motile bacteria penetration

In this study, migration rate and spatial distribution of colloidal particles with and without proteolytic enzymes were studied after injection in pork loin muscle cubes for 5days at 25°C to simulate behavior of non-motile bacteria. Samples were monitored daily by light microscopy and confocal laser scanning microscopy and particle distribution and movement analyzed by image analysis (MATLAB®). The extent of proteolytic activity was assessed by determining the tyrosine content in muscle tissue. Results showed that particles diffused from the injection hot spot into the inner structure of the meat (1.35±0.99×10−12 to 2.39±2.02×10−12m2/s). Upon addition of protease, the migration rate increased, i.e. the particle distribution became more widespread due to proteolysis of meat proteins reducing resistance to mass transfer. Results indicate that particles are able to diffuse into the densely packed fiber structure of meat muscles, which is contrary to the long held belief that such penetration may not occur in the absence of extensive proteolysis or mechanical damage of tissue.

Printing small dots from large drops.

Printing of droplets of pure solvents containing suspended solids typically leads to a ring stain due to convective transport of the particles toward the contact line during evaporation of the solvent. In mixtures of volatile solvents, recirculating cells driven by surface tension gradients are established that lead to migration of colloidal particles toward the center of the droplet. In favorable cases, a dense disk of particles forms with a diameter much smaller than that of the droplet. In the latter stages of drying, convective transport of the particles radially toward the contact line still occurs. Two strategies are described to fix the distribution of particles in a compact disk much smaller than the initial diameter of the drying droplet. First, a nanoparticulate clay is added to induce an evaporation-driven sol-gel transition that inhibits convective flow during the latter stages of drying. Second, a nonadsorbing polymer is added to induce depletion flocculation that restricts particle motion after the particles have been concentrated near the center of the droplet. The area of the resulting deposit can be as little as 10% of the footprint of the printed droplet.

A new numerical investigation of some thermo-physical properties on unsteady MHD non-Darcian flow past an impulsively started vertical surface

The behaviour of unsteady non-Darcian magnetohydrodynamic fluid flow past an impulsively started vertical porous surface is investigated. The effect of thermophoresis due to migration of colloidal particles in response to a macroscopic temperature gradient is taken into account. It is assumed that both dynamic viscosity and thermal conductivity are linear functions of temperature. The governing equations are non-dimensionalized by using suitable similarity transformation which can unravel the behaviour of the flow at short time and long time periods. A novel iteration scheme, called bivariate spectral local linearization method is developed for solving the corresponding systems of highly non-linear partial differential equations. The results of the numerical solutions obtained are presented graphically and analyzed for the effects of the various important parameters entering into the problem on velocity, temperature, and concentration field within the boundary layer.

Saturated Hydraulic Conductivity Changes with Time and Its Prediction at SAR and Salinity in Quevedo Region Soils

Darcy’s law is applied to describe the steady flow processes in which the flux remains constant with time along the conducting system. Due to the dispersion and migration of colloidal particles and lodging in the soil pores the reduction in hydraulic conductivity occurs with time in particular when the soil and the percolating solution are affected by electrolyte concentration. Hence, the aim of this study is to find empirical equations that can be used to predict the flux with time. Data for the effluent volume versus time (up to 6 hours) which was collected for three soils (located at Quevedo-Los Rios region) treated by two salt solutions (5 and 50 meq/l) with different SAR values were used to test certain mathematical forms of equations. Only four empirical equations were found to perfectly fit the data (flux vs time) whereas, fitting the calculated and measured data of the hydraulic conductivity for all soils produced regression factors R2 ≥ 0.99. So, these equations can be applied to predict the hydraulic conductivity and to characterize the flow process at saturated conditions of the studied soils with great confidence. The Hoerl function model was the best of all equations for application as the fitting degrees were almost perfect for all studied soils at 5 and 50 meq/l. It was observed for all equations that one of the fitting parameters would always represent the initial hydraulic conductivity (Kos) that was evaluated graphically at zero time by extrapolation.

Lateral migration and focusing of colloidal particles and DNA molecules under viscoelastic flow

Much difficulty has been encountered in manipulating small-scale materials, such as submicron colloidal particles and macromolecules (e.g., DNA and proteins), in microfluidic devices since diffusion processes due to thermal (Brownian) motion become more pronounced with decreasing particle size. Here, we present a novel approach for the continuous focusing of such small-scale materials. First, we successfully focused fluorescent submicron polystyrene (PS) beads along equilibrium positions in microchannels through the addition of a small amount water-soluble polymer [500 ppm poly(ethylene oxide) (PEO)]. Lateral migration velocity significantly depends upon the viscoelastic effect (Weissenberg number: Wi) and the aspect ratio of particle size to channel height (a/h). Interestingly, focusing using viscoelastic flows was also observed for flexible DNA molecules (λ-DNA and T4-DNA), which have radii of gyration (R(g)) of approximately 0.69 μm and 1.5 μm, respectively. This small-scale material manipulation using medium viscoelasticity will contribute to the design of nanoparticle separation and genomic mapping devices.

Gel electrophoresis in suspensions of charged spherical particles

Gel-electrophoresis, the migration of colloidal particles through a polymer gel in response to an applied electric field, is investigated theoretically in this study. It is a very powerful technique widely used in soft matter science. Both the short range steric effect (due to the direct contact friction between the gel and the migrating particles) and the long range hydrodynamic effect (due to the hydrodynamic force of the gel exerted upon the liquid suspension) are considered with the particle mobility calculated as the product of the predictions from these two approaches separately. Brinkman fluid is assumed to model the polymer gel and Kuwabara's unit cell model is employed to represent the suspension of particles. A pseudo-spectral method is adopted to solve the resulting general electrokinetic equations. We find, among other things, that the deformation of ion clouds surrounding the particles due to the convection flow within the porous gels deters the particle motion significantly, as an induced electric field opposite to the applied electric field is generated, an effect referred to as the polarization effect here. The higher the surface potential of the particle is, the more significant the reduction of mobility due to this polarization effect. Local extrema are observed in the mobility profiles with varying double layer thickness around κa = 1, where κ is the reciprocal of Debye length, and a is the particle radius, as the polarization effect manifests itself there in general. The presence of the gel retards the particle motion in general. The poorer the permeability is, the more severe the reduction. On the other hand, the more concentrated the particle suspension is, the slower the particle motion in general, due to the hindrance effect between neighboring particles. Moreover, the involvement of polarization and overlapping effects of the double layer further complicates the electrophoretic behavior of the particle, which is discussed in detail. Excellent agreement is obtained between the results reported here and the experimental data available in the literature for gold nanoparticles in dilute suspensions. The current study greatly extends the theoretical analysis scope of gel-electrophoresis from previous dilute suspensions only to concentrated ones as well, which are encountered frequently in practical applications in biological and biochemical fields, as well as other fields involving soft matters such as colloids and polymer gels.

The Migration of Styrene Butadiene Latex during the Drying of Coating Suspensions: When and How Does Migration of Colloidal Particles Occur?

Surface elemental compositions of model latex clay coatings on an impervious substrate consolidated under various conditions were measured using the XPS technique, in order to clarify when and how colloidal latex particles migrate to the surface during drying. Under similar drying conditions, surface carbon content decreased with the addition of a water-soluble polymer to the coating colors, while remaining virtually unchanged for coatings of different coat weights made with a given color, indicating that surface carbon content variation is mainly caused by migration of latex rather than of water-soluble polymer. The results also showed that for coatings made with a given suspension, surface carbon content decreased with increasing delay time between coating and heating. For coatings frozen during consolidation and dried by sublimation, surface carbon content increased with increasing drying time before freezing. These results suggest that for the model coatings studied, latex migration mainly occurs after coating application before capillary formation during the initial drying stage when coatings are in the liquid phase, contradicting both the conventional capillary transport and boundary wall migration mechanisms. An alternative mechanism which attributes latex migration to surface trapping effect and to higher Brownian mobility of the smaller latex particles compared with pigment appears to provide a systematically consistent explanation to those phenomena. The new particle migration mechanism implies that segregation of colloidal particles is a ubiquitous phenomenon that would occur not only during the drying of paper coatings but also during consolidation of colloidal films containing particles of different sizes. This is of great importance in the control of surface compositions of nanocomposite coatings.