Anisotropic diffusion of spherical particles in closely confining microchannels

Bridging Macroscopic Diffusion and Microscopic Cavity Escape of Brownian and Active Particles in Irregular Porous Networks

While irregular and geometrically complex pore networks are ubiquitous in nature and industrial processes, there is no universal model describing nanoparticle transport in these environments. 3D super-resolution nanoparticle tracking was employed to study the motion of passive (Brownian) and active (self-propelled) species within complex networks, and universally identified a mechanism involving successive cavity exploration and escape. In all cases, the long-time ensemble-averaged diffusion coefficient was proportional to a quantity involving the characteristic length scale and time scale associated with microscopic cavity exploration and escape (D ∼ r2/ttrap), where the proportionality coefficient reflected the apparent porous network connectivity. For passive nanoparticles, this coefficient was always lower than expected theoretically for a random walk, indicating reduced network accessibility. In contrast, the coefficient for active nanomotors, in the same pore spaces, aligned with the theoretical value, suggesting that active particles navigate "intelligently" in porous environments, consistent with kinetic Monte Carlo simulations in networks with variable pore sizes. These findings elucidate a model of successive cavity exploration and escape for nanoparticle transport in porous networks, where pore accessibility is a function of motive force, providing insights relevant to applications in filtration, controlled release, and beyond.

Nanomotor-enhanced transport of passive Brownian particles in porous media

Artificial micro/nanomotors are expected to perform tasks in interface-rich and species-rich environments for biomedical and environmental applications. In these highly confined and interconnected pore spaces, active species may influence the motion of coexisting passive participants in unexpected ways. Using three-dimensional super-resolution single-nanoparticle tracking, we observed enhanced motion of passive nanoparticles due to the presence of dilute well-separated nanomotors in an interconnected pore space. This enhancement acted at distances that are large compared to the sizes of the particles and cavities, in contrast with the insignificant effect on the passive particles with the same dilute concentration of nanomotors in an unconfined liquid. Experiments and simulations suggested an amplification of hydrodynamic coupling between self-propelled and passive nanoparticles in the interconnected confined environment, which enhanced the effective energy for passive particles to escape cavities through small holes. This finding represents an emergent behavior of confined nanomotors and suggests new strategies for the development of antifouling membranes and drug delivery systems.

pH-Mediated Size-Selective Adsorption of Gold Nanoparticles on Diblock Copolymer Brushes

Precise control of nanoparticles at interfaces can be achieved by designing stimuli-responsive surfaces that have tunable interactions with nanoparticles. In this study, we demonstrate that a polymer brush can selectively adsorb nanoparticles according to size by tuning the pH of the buffer solution. Specifically, we developed a facile polymer brush preparation method using a symmetric polystyrene-b-poly(2-vinylpyridine) (PS-b-P2VP) block copolymer deposited on a grafted polystyrene layer. This method is based on the assembly of a PS-b-P2VP thin film oriented with parallel lamellae that remains after exfoliation of the top PS-b-P2VP layer. We characterized the P2VP brush using X-ray reflectivity and atomic force microscopy. The buffer pH is used to tailor interactions between citrate-coated gold nanoparticles (AuNPs) and the top P2VP block that behaves like a polymer brush. At low pH (∼4.0) the P2VP brushes are strongly stretched and display a high density of attractive sites, whereas at neutral pH (∼6.5) the P2VP brushes are only slightly stretched and have fewer attractive sites. A quartz crystal microbalance with dissipation monitored the adsorption thermodynamics as a function of AuNP diameter (11 and 21 nm) and pH of the buffer. Neutral pH provides limited penetration depth for nanoparticles and promotes size selectivity for 11 nm AuNP adsorption. As a proof of concept, the P2VP brushes were exposed to various mixtures of large and small AuNPs to demonstrate selective capture of the smaller AuNPs. This study shows the potential of creating devices for nanoparticle size separations using pH-sensitive polymer brushes.

Colloidal Stochastic Resonance in Confined Geometries

We investigate the dynamical properties of a colloidal particle in a double cavity. Without external driving, the particle hops between two free-energy minima with transition mean time depending on the system's entropic and energetic barriers. We then drive the particle with a periodic force. When the forcing period is set at twice the transition mean time, a statistical synchronization between particle motion and forcing phase marks the onset of a stochastic resonance mechanism. Comparisons between experimental results and predictions from the Fick-Jacobs theory and Brownian dynamics simulation reveal significant hydrodynamic effects, which change both resonant amplification and noise level. We further show that hydrodynamic effects can be incorporated into existing theory and simulation by using an experimentally measured particle diffusivity.

Real-space imaging of nanoparticle transport and interaction dynamics by graphene liquid cell TEM

Thermal motion of colloidal nanoparticles and their cohesive interactions are of fundamental importance in nanoscience but are difficult to access quantitatively, primarily due to the lack of the appropriate analytical tools to investigate the dynamics of individual particles at nanoscales. Here, we directly monitor the stochastic thermal motion and coalescence dynamics of gold nanoparticles smaller than 5 nm, using graphene liquid cell (GLC) transmission electron microscopy (TEM). We also present a novel model of nanoparticle dynamics, providing a unified, quantitative explanation of our experimental observations. The nanoparticles in a GLC exhibit non-Gaussian, diffusive motion, signifying dynamic fluctuation of the diffusion coefficient due to the dynamically heterogeneous environment surrounding nanoparticles, including organic ligands on the nanoparticle surface. Our study shows that the dynamics of nanoparticle coalescence is controlled by two elementary processes: diffusion-limited encounter complex formation and the subsequent coalescence of the encounter complex through rotational motion, where surface-passivating ligands play a critical role.

Protein Transport through Nanopores Illuminated by Long-Time-Scale Simulations

The transport of molecules through nanoscale confined space is relevant in biology, biosensing, and industrial filtration. Microscopically modeling transport through nanopores is required for a fundamental understanding and guiding engineering, but the short duration and low replica number of existing simulation approaches limit statistically relevant insight. Here we explore protein transport in nanopores with a high-throughput computational method that realistically simulates hundreds of up to seconds-long protein trajectories by combining Brownian dynamics and continuum simulation and integrating both driving forces of electroosmosis and electrophoresis. Ionic current traces are computed to enable experimental comparison. By examining three biological and synthetic nanopores, our study answers questions about the kinetics and mechanism of protein transport and additionally reveals insight that is inaccessible from experiments yet relevant for pore design. The discovery of extremely frequent unhindered passage can guide the improvement of biosensor pores to enhance desired biomolecular recognition by pore-tethered receptors. Similarly, experimentally invisible nontarget adsorption to pore walls highlights how to improve recently developed DNA nanopores. Our work can be expanded to pressure-driven flow to model industrial nanofiltration processes.

Channel-length dependence of particle diffusivity in confinement

Understanding the diffusive behavior of particles and large molecules in channels is of fundamental importance in biological and synthetic systems, such as channel proteins, nanopores, and nanofluidics. Although theoretical and numerical modelings have suggested some solutions, these models have not been fully supported with direct experimental measurements. Here, we demonstrate that experimental diffusion coefficients of particles in finite open-ended channels are always higher than the prediction based on the conventional theoretical model of infinitely long channels. By combining microfluidic experiments, numerical simulations, and analytical modeling, we show that diffusion coefficients are dependent not only on the radius ratio but also on the channel length, the boundary conditions of the neighboring reservoirs, and the compressibility of the medium.

Height distribution and orientation of colloidal dumbbells near a wall

Geometric confinement strongly influences the behavior of microparticles in liquid environments. However, to date, nonspherical particle behaviors close to confining boundaries, even as simple as planar walls, remain largely unexplored. Here, we measure the height distribution and orientation of colloidal dumbbells above walls by means of digital in-line holographic microscopy. We find that while larger dumbbells are oriented almost parallel to the wall, smaller dumbbells of the same material are surprisingly oriented at preferred angles. We determine the total height-dependent force acting on the dumbbells by considering gravitational effects and electrostatic particle-wall interactions. Our modeling reveals that at specific heights both net forces and torques on the dumbbells are simultaneously below the thermal force and energy, respectively, which makes the observed orientations possible. Our results highlight the rich near-wall dynamics of nonspherical particles and can further contribute to the development of quantitative frameworks for arbitrarily shaped microparticle dynamics in confinement.

Electroviscous effect for a confined nanosphere in solution

A charged colloidal particle suspended in an electrolyte experiences electroviscous stresses arising from motion-driven electrohydrodynamic phenomena. Under certain conditions, the additional contribution from electroviscous drag forces to the total drag experienced by the moving particle can lead to measurable deviations of particle diffusion coefficients from values predicted by the well known Stokes-Einstein relation that describes diffusive behavior of small particles in an unbounded charge-free fluid. In this study, we investigate the role of electroviscous stresses on nanoparticle diffusion in confined geometries using both simulations and experiment. We compare our experimental measurements with the results of a numerically solved continuum model based on the Poisson-Nernst-Planck-Stokes system of equations and find good agreement between experiment and theory. Depending on the radius of the counterion species in solution and the degree of confinement, we find that the viscous drag on polystyrene nanoparticles can be augmented by approximately 10-25% compared to the values predicted by pure hydrodynamic models in the absence of free charge in the fluid. This enhancement corresponds approximately to a 5-10% increase compared to the electroviscous contribution for a charged particle in an unbounded fluid. Contrary to recent reports in the experimental literature, we find neither experimental nor theoretical evidence of an anomalously large enhancement of electroviscous forces on a confined charged nanoparticle in solution.

Connecting Hindered Transport in Porous Media across Length Scales: From Single-Pore to Macroscopic

Hindered mass transport is widely observed in various porous media; however, there is no universal model capable of predicting transport in porous media due to the heterogeneity of porous structures and the complexity of the underlying microscopic mechanisms. Here, we used a highly ordered porous medium as a model system to directly explore the effects of geometric parameters (i.e., pore size, pore throat size, and tracer particle size) and microscopic interaction parameters (e.g., controlled by ionic strength) on nanoparticle transport in porous environments using single-particle tracking. We found a linear scaling relation between the macroscopic diffusion coefficient and microscopic diffusion behavior involving a combination of parameters associated with pore-scale features and phenomena, including both geometric effects and particle-wall interactions. The proportionality coefficient relating micro and macro behaviors was complex and related to the connectivity of the matrix and the pore-size variation, which could lead to tortuous diffusion pathways, hindering macroscopic transport.

Diffusive Escape of a Nanoparticle from a Porous Cavity

Narrow escape from confinement through a nanochannel is the critical step of complex transport processes including size-exclusion-based separations, oil and gas extraction from the microporous subsurface environment, and ribonucleic acid translocation through nuclear pore complex channels. While narrow escape has been studied using theoretical and computational methods, experimental quantification is rare because of the difficulty in confining a particle into a microscopic space through a nanoscale hole. Here, we studied narrow escape in the context of continuous nanoparticle diffusion within the liquid-filled void space of an ordered porous material. Specifically, we quantified the spatial dependence of nanoparticle motion and the sojourn times of individual particles in the interconnected confined cavities of a liquid-filled inverse opal film. We found that nanoparticle motion was inhibited near cavity walls and cavity escape was slower than predicted by existing theories and random-walk simulations. A combined computational-experimental analysis indicated that translocation through a nanochannel is barrier controlled rather than diffusion controlled.

Density-Dependent Speed-up of Particle Transport in Channels

Collective transport through channels shows surprising properties under one-dimensional confinement: particles in a single file exhibit subdiffusive behavior, while liquid confinement causes distance-independent correlations between the particles. Such interactions in channels are well studied for passive Brownian motion, but driven transport remains largely unexplored. Here, we demonstrate gating of transport due to a speed-up effect for actively driven particle transport through microfluidic channels. We prove that particle velocity increases with particle density in the channel due to hydrodynamic interactions under electrophoretic and gravitational forces. Numerical models demonstrate that the observed speed-up of transport originates from a hydrodynamic pistonlike effect. Our discovery is fundamentally important for understanding protein channels and transport through porous materials and for designing novel sensors and filters.

Machine learning wall effects of eccentric spheres for convenient computation

In confined systems, such as the inside of a biological cell, the outer boundary or wall can affect the dynamics of internal particles. In many cases of interest both the internal particle and outer wall are approximately spherical. Therefore, quantifying the wall effects from an outer spherical boundary on the motion of an internal eccentric sphere is very useful. However, when the two spheres are not concentric, the problem becomes nontrivial. In this paper we improve existing analytical methods to evaluate these wall effects and then train a feed-forward artificial neural network within a broader model. The final model generally performed with ∼0.001% error within the training domain and ∼0.05% when the outer spherical wall was extrapolated to an infinite plane. Through this model, the wall effects of an outer spherical boundary on the arbitrary motion of an internal sphere for all experimentally achievable configurations can now be conveniently and efficiently determined.

Experimental evidence of symmetry breaking of transition-path times

While thermal rates of state transitions in classical systems have been studied for almost a century, associated transition-path times have only recently received attention. Uphill and downhill transition paths between states at different free energies should be statistically indistinguishable. Here, we systematically investigate transition-path-time symmetry and report evidence of its breakdown on the molecular- and meso-scale out of equilibrium. In automated Brownian dynamics experiments, we establish first-passage-time symmetries of colloids driven by femtoNewton forces in holographically-created optical landscapes confined within microchannels. Conversely, we show that transitions which couple in a path-dependent manner to fluctuating forces exhibit asymmetry. We reproduce this asymmetry in folding transitions of DNA-hairpins driven out of equilibrium and suggest a topological mechanism of symmetry breakdown. Our results are relevant to measurements that capture a single coordinate in a multidimensional free energy landscape, as encountered in electrophysiology and single-molecule fluorescence experiments.

Brownian motion near an elastic cell membrane: A theoretical study

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this paper, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.

When does near-wall hindered diffusion influence mass transport towards targets?

The diffusion of a particle is slowed as it moves close to a surface. We identify the conditions under which this hindered diffusion is significant and show that is strongly dependant on the sizes of both the particle and the target. We focus particularly on the transport of nano-particles to a variety of targets including a planar surface, a sphere, a disc and a wire, and provide data which allows the frequency of impacts to be inferred for a variety of experimental conditions. Equations are given to estimate the particle fluxes and we explain literature observations reported on the detected frequency of impacts. Finally we observe a drastic effect on the calculation of the mean first passage time of a single particle impacting a sub-micron sized target, showing the importance of this effect in biological systems.

Colloid-colloid hydrodynamic interaction around a bend in a quasi-one-dimensional channel

We report a study of how a bend in a quasi-one-dimensional (q1D) channel containing a colloid suspension at equilibrium that exhibits single-file particle motion affects the hydrodynamic coupling between colloid particles. We observe both structural and dynamical responses as the bend angle becomes more acute. The structural response is an increasing depletion of particles in the vicinity of the bend and an increase in the nearest-neighbor separation in the pair correlation function for particles on opposite sides of the bend. The dynamical response monitored by the change in the self-diffusion [D_{11}(x)] and coupling [D_{12}(x)] terms of the pair diffusion tensor reveals that the pair separation dependence of D_{12} mimics that of the pair correlation function just as in a straight q1D channel. We show that the observed behavior is a consequence of the boundary conditions imposed on the q1D channel: both the single-file motion and the hydrodynamic flow must follow the channel around the bend.

Impact of complex surfaces on biomicrorheological measurements using optical tweezers

The characterisation of physical properties in biologically relevant processes and the development of novel microfluidic devices for this purpose are experiencing a great resurgence at present. In many of measurements of this type where a probe in a fluid is used, the strong influence of the boundaries of the volume used is a serious problem. In these geometries the proximity of a probe to a wall can severely influence the measurement. However, although much knowledge has been gained about flat walls, to date, the effect of non-planar surfaces at microscopic scale on rotational motion of micro-objects has not been studied. Here we present for the first time both experimental measurements and numerical computations which aim to study the drag torque on optically trapped rotating particles moving near 3D-printed conical and cylindrical walls on-chip. These results are essential for quantifying how curved walls can effect the torque on particles, and thus enable accurate hydrodynamic simulations at the micron-scale. This opens the potential for new sensing approaches under more complex conditions, allowing both dynamic and microrheological studies of biological systems and lab-on-chip devices.

Particle transport across a channel via an oscillating potential

Membrane protein transporters alternate their substrate-binding sites between the extracellular and cytosolic side of the membrane according to the alternating access mechanism. Inspired by this intriguing mechanism devised by nature, we study particle transport through a channel coupled with an energy well that oscillates its position between the two entrances of the channel. We optimize particle transport across the channel by adjusting the oscillation frequency. At the optimal oscillation frequency, the translocation rate through the channel is a hundred times higher with respect to free diffusion across the channel. Our findings reveal the effect of time-dependent potentials on particle transport across a channel and will be relevant for membrane transport and microfluidics application.

Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels

In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, such as ionic channels, zeolites, and nanopores. While extensive theoretical and numerical studies on this subject have produced many important predictions, experimental verifications of the predictions are rare. Here, we experimentally measure colloidal diffusion times in microchannels with periodically varying width and contrast results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predict the entropic effect of the varying channel width, they fail to account for hydrodynamic effects, which include both an overall decrease and a spatial variation of diffusivity in channels. Neglecting such hydrodynamic effects, the theory and simulation underestimate the mean and standard deviation of first passage times by 40% in channels with a neck width twice the particle diameter. We further show that the validity of the Fick-Jacobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus shows that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.

Single file dynamics in soft materials

The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.

Hydrodynamic interaction between particles near elastic interfaces

We present an analytical calculation of the hydrodynamic interaction between two spherical particles near an elastic interface such as a cell membrane. The theory predicts the frequency dependent self- and pair-mobilities accounting for the finite particle size up to the 5th order in the ratio between particle diameter and wall distance as well as between diameter and interparticle distance. We find that particle motion towards a membrane with pure bending resistance always leads to mutual repulsion similar as in the well-known case of a hard-wall. In the vicinity of a membrane with shearing resistance, however, we observe an attractive interaction in a certain parameter range which is in contrast to the behavior near a hard wall. This attraction might facilitate surface chemical reactions. Furthermore, we show that there exists a frequency range in which the pair-mobility for perpendicular motion exceeds its bulk value, leading to short-lived superdiffusive behavior. Using the analytical particle mobilities we compute collective and relative diffusion coefficients. The appropriateness of the approximations in our analytical results is demonstrated by corresponding boundary integral simulations which are in excellent agreement with the theoretical predictions.

Hydrodynamic mobility of a solid particle near a spherical elastic membrane: Axisymmetric motion

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements, which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a nonvanishing resistance toward shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.

General Model of Hindered Diffusion

The diffusion of a particle from bulk solution is slowed as it moves close to an adsorbing surface. A general model is reported that is easily applied by theoreticians and experimentalists. Specifically, it is shown here that in general and regardless of the space size, the magnitude of the effect of hindered diffusion on the flux is a property of the diffusion layer thickness. We explain and approximate the effect. Predictions of concentration profiles show that a "hindered diffusion layer" is formed near the adsorbing surface within the diffusion layer, observed even when the particle radius is just a 0.1% of the diffusion layer thickness. In particular, we focus on modern electrochemistry processes involving with impact of particles with either ultrasmall electrodes or particles in convective systems. The concept of the "hindered diffusion layer" is generally important for example in recent biophysical models of particles diffusion to small targets.

Rotational friction of dipolar colloids measured by driven torsional oscillations

Despite its prominent role in the dynamics of soft materials, rotational friction remains a quantity that is difficult to determine for many micron-sized objects. Here, we demonstrate how the Stokes coefficient of rotational friction can be obtained from the driven torsional oscillations of single particles in a highly viscous environment. The idea is that the oscillation amplitude of a dipolar particle under combined static and oscillating fields provides a measure for the Stokes friction. From numerical studies we derive a semi-empirical analytic expression for the amplitude of the oscillation, which cannot be calculated analytically from the equation of motion. We additionally demonstrate that this expression can be used to experimentally determine the rotational friction coefficient of single particles. Here, we record the amplitudes of a field-driven dipolar Janus microsphere with optical microscopy. The presented method distinguishes itself in its experimental and conceptual simplicity. The magnetic torque leaves the local environment unchanged, which contrasts with other approaches where, for example, additional mechanical (frictional) or thermal contributions have to be regarded.

Spatially dependent diffusion coefficient as a model for pH sensitive microgel particles in microchannels

Solute transport and intermixing in microfluidic devices is strongly dependent on diffusional processes. Brownian Dynamics simulations of pressure-driven flow of model microgel particles in microchannels have been carried out to explore these processes and the factors that influence them. The effects of a pH-field that induces a spatial dependence of particle size and consequently the self-diffusion coefficient and system thermodynamic state were focused on. Simulations were carried out in 1D to represent some of the cross flow dependencies, and in 2D and 3D to include the effects of flow and particle concentration, with typical stripe-like diffusion coefficient spatial variations. In 1D, the mean square displacement and particle displacement probability distribution function agreed well with an analytically solvable model consisting of infinitely repulsive walls and a discontinuous pH-profile in the middle of the channel. Skew category Brownian motion and non-Gaussian dynamics were observed, which follows from correlations of step lengths in the system, and can be considered to be an example of so-called "diffusing diffusivity." In Poiseuille flow simulations, the particles accumulated in regions of larger diffusivity and the largest particle concentration throughput was found when this region was in the middle of the channel. The trends in the calculated cross-channel diffusional behavior were found to be very similar in 2D and 3D.

Single-File Escape of Colloidal Particles from Microfluidic Channels

Single-file diffusion is a ubiquitous physical process exploited by living and synthetic systems to exchange molecules with their environment. It is paramount to quantify the escape time needed for single files of particles to exit from constraining synthetic channels and biological pores. This quantity depends on complex cooperative effects, whose predominance can only be established through a strict comparison between theory and experiments. By using colloidal particles, optical manipulation, microfluidics, digital microscopy, and theoretical analysis we uncover the self-similar character of the escape process and provide closed-formula evaluations of the escape time. We find that the escape time scales inversely with the diffusion coefficient of the last particle to leave the channel. Importantly, we find that at the investigated microscale, bias forces as tiny as 10^{-15}  N determine the magnitude of the escape time by drastically reducing interparticle collisions. Our findings provide crucial guidelines to optimize the design of micro- and nanodevices for a variety of applications including drug delivery, particle filtering, and transport in geometrical constrictions.

Self-Optimized Biological Channels in Facilitating the Transmembrane Movement of Charged Molecules

We consider an anisotropically two-dimensional diffusion of a charged molecule (particle) through a large biological channel under an external voltage. The channel is modeled as a cylinder of three structure parameters: radius, length, and surface density of negative charges located at the channel interior-lining. These charges induce inside the channel a potential that plays a key role in controlling the particle current through the channel. It was shown that to facilitate the transmembrane particle movement the channel should be reasonably self-optimized so that its potential coincides with the resonant one, resulting in a large particle current across the channel. Observed facilitation appears to be an intrinsic property of biological channels, regardless of the external voltage or the particle concentration gradient. This facilitation is very selective in the sense that a channel of definite structure parameters can facilitate the transmembrane movement of only particles of proper valence at corresponding temperatures. Calculations also show that the modeled channel is nonohmic with the ion conductance which exhibits a resonance at the same channel potential as that identified in the current.

Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles

The physical approach of a small particle (virus, medical drug) to the cell membrane represents the crucial first step before active internalization and is governed by thermal diffusion. Using a fully analytical theory we show that the stretching and bending of the elastic membrane by the approaching particle induces a memory in the system, which leads to anomalous diffusion, even though the particle is immersed in a purely Newtonian liquid. For typical cell membranes the transient subdiffusive regime extends beyond 10 ms and can enhance residence times and possibly binding rates up to 50%. Our analytical predictions are validated by numerical simulations.

The Raspberry model for hydrodynamic interactions revisited. II. The effect of confinement

The so-called "raspberry" model refers to the hybrid lattice-Boltzmann (LB) and Langevin molecular dynamics schemes for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. In this paper, we present a follow up to our study of the effectiveness of the raspberry model in reproducing hydrodynamic interactions in the Stokes regime for spheres arranged in a simple-cubic crystal [Fischer et al., J. Chem. Phys. 143, 084107 (2015)]. Here, we consider the accuracy with which the raspberry model is able to reproduce such interactions for particles confined between two parallel plates. To this end, we compare our LB simulation results to established theoretical expressions and finite-element calculations. We show that there is a discrepancy between the translational and rotational mobilities when only surface coupling points are used, as also found in Part I of our joint publication. We demonstrate that adding internal coupling points to the raspberry can be used to correct said discrepancy in confining geometries as well. Finally, we show that the raspberry model accurately reproduces hydrodynamic interactions between a spherical colloid and planar walls up to roughly one LB lattice spacing.

Diffusive dynamics of nanoparticles in ultra-confined media

Differential dynamic microscopy (DDM) was used to investigate the diffusive dynamics of nanoparticles of diameter 200-400 nm that were strongly confined in a periodic square array of cylindrical nanoposts. The minimum distance between posts was 1.3-5 times the diameter of the nanoparticles. The image structure functions obtained from the DDM analysis were isotropic and could be fit by a stretched exponential function. The relaxation time scaled diffusively across the range of wave vectors studied, and the corresponding scalar diffusivities decreased monotonically with increased confinement. The decrease in diffusivity could be described by models for hindered diffusion that accounted for steric restrictions and hydrodynamic interactions. The stretching exponent decreased linearly as the nanoparticles were increasingly confined by the posts. Together, these results are consistent with a picture in which strongly confined nanoparticles experience a heterogeneous spatial environment arising from hydrodynamics and volume exclusion on time scales comparable to cage escape, leading to multiple relaxation processes and Fickian but non-Gaussian diffusive dynamics.

Nondecaying Hydrodynamic Interactions along Narrow Channels

Particle-particle interactions are of paramount importance in every multibody system as they determine the collective behavior and coupling strength. Many well-known interactions such as electrostatic, van der Waals, or screened Coulomb interactions, decay exponentially or with negative powers of the particle spacing r. Similarly, hydrodynamic interactions between particles undergoing Brownian motion decay as 1/r in bulk, and are assumed to decay in small channels. Such interactions are ubiquitous in biological and technological systems. Here we confine two particles undergoing Brownian motion in narrow, microfluidic channels and study their coupling through hydrodynamic interactions. Our experiments show that the hydrodynamic particle-particle interactions are distance independent in these channels. This finding is of fundamental importance for the interpretation of experiments where dense mixtures of particles or molecules diffuse through finite length, water-filled channels or pore networks.

Measuring advection and diffusion of colloids in shear flow

An analysis of the dynamics of colloids in shear flow can be challenging because of the superposition of diffusion and advection. We present a method that separates the two motions, starting from the time-dependent particle coordinates. The restriction of the tracking to flow lanes and the subtraction of estimated advective displacements are combined in an iterative scheme that eventually makes the spatial segmentation redundant. Tracking errors due to the neglect of lateral diffusion are avoided, while drifts parallel and perpendicular to the flow are eliminated. After explaining the principles of our method, we validate it against both computer simulations and experiments. A critical overall test is provided by the mean square displacement function at high Peclet numbers (up to 50). We demonstrate via simulations how the measurement accuracy depends on diffusion coefficients and flow rates, expressed in units of camera pixels and frames. Also, sample-specific issues are addressed: inaccuracies in the velocity profile for dilute suspensions (volume fraction ≤0.03) and tracking errors for concentrated ones (VF ≥ 0.3). An analysis of experiments with colloidal spheres flowing through microchannels corroborates these findings and indicates perspectives for studies on transport, mixing, or rheology in microfluidic environments.

Front propagation in channels with spatially modulated cross section

Propagation of traveling fronts in a three-dimensional channel with spatially varying cross section is reduced to an equivalent one-dimensional reaction-diffusion-advection equation with boundary-induced advection term. Treating the advection term as a weak perturbation, an equation of motion for the front position is derived. We analyze channels whose cross sections vary periodically with L along the propagation direction of the front. Taking the Schlögl model as a representative example, we calculate analytically the nonlinear dependence of the front velocity on the ratio L/l where l denotes the intrinsic front width. In agreement with finite-element simulations of the three-dimensional reaction-diffusion dynamics, our theoretical results predicts boundary-induced propagation failure for a finite range of L/l values. In particular, the existence of the upper bound of L/l can be completely understood based on the linear eikonal equation. Last, we demonstrate that the front velocity is determined by the suppressed diffusivity of the reactants for L≪l.

Channel-facilitated diffusion boosted by particle binding at the channel entrance

We investigate single-file diffusion of Brownian particles in arrays of closely confining microchannels permeated by a variety of attractive optical potentials and connecting two baths with equal particle concentration. We simultaneously test free diffusion in the channel, diffusion in optical traps coupled in the center of the channel, and diffusion in traps extending into the baths. We found that both classes of attractive optical potentials enhance the translocation rate through the channel with respect to free diffusion. Surprisingly, for the latter class of potentials we measure a 40-fold enhancement in the translocation rate with respect to free diffusion and find a sublinear power law dependence of the translocation rate on the average number of particles in the channel. Our results reveal the function of particle binding at the channel entrances for diffusive transport and open the way to a better understanding of membrane transport and design of synthetic membranes with enhanced diffusion rate.