In the approach of biomolecules to a nanopore, it is essential to capture the effects of hydrodynamic anisotropy of the molecules and the near-wall hydrodynamic interactions which hinder their diffusion. We present a detailed theoretical analysis of the behaviour of a rod-like molecule attracted electrostatically by a charged nanopore. We first estimate the time scales corresponding to Brownian and electrostatic translations and reorientation. We find that Brownian motion becomes negligible at distances within the pore capture radius, and numerically determine the trajectories of the nano-rod in this region to explore the effects of anisotropic mobility. This allows us to determine the range of directions from the pore in which hydrodynamic interactions with the boundary shape the approach dynamics and need to be accounted for in detailed modelling.
We investigate the translocation of rods with different charge distributions using hybrid Langevin Dynamics and Lattice Boltzmann (LD-LB) simulations. Electrostatic interactions are added to the system using the $P^3M$ algorithm to model the electrohydrodynamic interactions (EHI). We first examine the free-solution electrophoretic properties of rods with various charge distributions. Our translocation simulation results suggest that the order parameter is asymmetric during the capture and escape processes despite the symmetric electric field lines, while the impacts of the charge distribution …
We present a neutron and X-rays scattering study of the phase transitions of 4-n-octyl-4'-cyanobiphenyl (8CB) confined in unidirectional nanopores of porous alumina and porous silicon (PSi) membranes with an average diameter of 30 nm. Spatial confinement reveals a rich polymorphism, with at least four different low temperature phases in addition to the smectic A phase. The structural study as a function of thermal treatments and conditions of spatial confinement allows us to get insights into the formation of these phases and their relative stability. It gives the first description of the comp…
Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. Results show the existence of concentration polarization layers on the surfaces of the membrane. The nonuniformity of the ionic distribution gives rise to an electric pressure that drives vortical motion in the fluid. There is also a net hydrodynamic flow through the nanopore due to an asymmetry induced by the membrane surface charge. The qualitative behavior is similar to that observed in a previous study using molecular dynamic simulations. The …
In fluid transport across nanopores, there is a fundamental dissipation that arises from the connection between the pore and the macroscopic reservoirs. This entrance effect can hinder the whole transport in certain situations, for short pores and/or highly slipping channels. In this paper, we explore the hydrodynamic permeability of hourglass shape nanopores using molecular dynamics (MD) simulations, with the central pore size ranging from several nanometers down to a few Angstr{ö}ms. Surprisingly, we find a very good agreement between MD results and continuum hydrodynamic predictions, even f…
Using nonequilibrium Langevin dynamics simulations of an electrolyte with explicit solvent particles, we investigate the effect of hydrodynamic interactions on the power spectrum of ionic nanopore currents. At low frequency, we find a power-law dependence of the power spectral density, with an exponent depending on the ion density. Surprisingly, however, the exponent is not affected by the presence of the neutral solvent particles. We conclude that hydrodynamic interactions do not affect the shape of the power spectrum in the frequency range studied.
We consider voltage-driving DNA translocation through a nanopore in the present study. By assuming the DNA is coaxial with the cylindrical nanopore, a hydrodynamic model for determining effective force on a single DNA molecule in a nanopore was presented, in which density functional theory (DFT) combined with the continuum Navier-Stokes (NS) equations is utilized to investigate electro-osmotic flow and the viscous drag force acting on the DNA inside a nanopore. Surface charge on the walls of the nanopore is also taken into account in our model. The consistence between our calculation and the p…
We present an X-ray diffraction study of the normale alkane nonadecane C_{19}H_{40} embedded in nanoporous Vycor glass. The confined molecular crystal accomplishes a close-packed structure by alignment of the rod-like molecules parallel to the pore axis while sacrificing one basic principle known from the bulk state, i.e. the lamellar ordering of the molecules. Despite this disorder, the phase transitions observed in the confined solid mimic the phase behavior of the 3D unconfined crystal, though enriched by the appearance of a true rotator phase known only from longer alkane chains.
In a previous paper [S. Ghosal, Phys. Rev. E 74, 041901 (2006)] a hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through an axially symmetric slowly varying nanopore was presented in the limit of a vanishingly small Debye length. Here the case of a finite Debye layer thickness is considered while restricting the pore geometry to that of a cylinder of length much larger than the diameter. Further, the possibility of a uniform surface charge on the walls of the nanopore is taken into account. It is thereby shown that the calculated transit times are consistent …
We investigate the voltage-driven translocation of an inhomogeneously charged polymer through a nanopore by utilizing discrete and continuous stochastic models. As a simplified illustration of the effect of charge distribution on translocation, we consider the translocation of a polymer with a single charged site in the presence and absence of interactions between the charge and the pore. We find that the position of the charge that minimizes the translocation time in the absence of pore--polymer interactions is determined by the entropic cost of translocation, with the optimum charge position…
Moving micron scale objects are strongly coupled to each other by hydrodynamic interactions. The strength of this coupling decays as the inverse particle separation when the two objects are sufficiently far apart. It has been recently demonstrated that the reduced dimensionality of thin fluid layer gives rise to longer ranged, logarithmic coupling. Using holographic tweezers we show that microrods display both behaviors interacting like point particle in 3D at large distance and like point particles in 2D for distances shorter then their length. We derive a simple analytical expression that fi…
We study the mobility of extended objects (rods) on a spherical liquid-liquid interface to show how this quantity is modified in a striking manner by both the curvature and the topology of the interface. We present theoretical calculations and experimental measurements of the interfacial fluid velocity field around a moving rod bound to the crowded interface of a water-in-oil droplet. By using different droplet sizes, membrane viscosities, and rod lengths, we show that the viscosity mismatch between the interior and exterior fluids leads to a suppression of the fluid flow on small droplets tha…
We study how adsorption of a near-critical binary mixture in a nanopore is modified by flow inside the pore. We identify three types of steady states upon variation of the pore Péclet number (${\rm Pe}_p$), which can be reversibly accessed by the application of an external pressure. Interestingly, for small ${\rm Pe}_p$ the pore acts as a weakly selective membrane which separates the mixture. For intermediate ${\rm Pe}_p$, the flow effectively shifts the adsorption in the pore thereby opening possibilities for enhanced and tunable solute transport through the pore. For large ${\rm Pe}_p$, the …
Accurate modeling of diffusive transport of nanoparticles across nanopores is a particularly challenging problem. The reason is that for such narrow pores the large surface-to-volume ratio amplifies the relevance of the nanoscopic details and of the effective interactions at the interface with pore walls. Close to the pore wall, there is no clear separation between the length scales associated with molecular interactions, layering of the solvent at the interface with the pore and the particle size. Therefore, the standard hydrodynamic arguments may not apply and alternative solutions to determ…
In their search for metabolic resources microbes swim through viscous environments that present physical anisotropies, including steric obstacles across a wide range of sizes. Hydrodynamic forces are known to significantly alter swimmer trajectories near flat and low-curvature surfaces. In this work, we imaged hundreds-of-thousands of high-curvature scattering interactions between swimming bacteria and micro-fabricated pillars with radii from ~1 to ~10 cell lengths. As a function of impact parameter, cell-pillar interactions produced distinct chiral distributions for scattering angle -- includ…
Liquid transport through nanopore is central into many applications, from water purification to biosensing or energy harvesting. Ultimately thin nanopores are of major interest in these applications to increase driving potential and reduce as much as possible dissipation sources. We investigate here the efficiency of the electrical power generation through an ultrathin nanoporous membrane by means of streaming current (electrical current induced by ionic flow in the vicinity of the liquid/solid interface) or electroosmosis (flow rate induced by an electrical potential). Upscaling from one uniq…
Recent theoretical works exploring the hydrodynamics of soft material in non-equilibrium situations are reviewed. We discuss the role of hydrodynamic interactions for three different systems: i) the deformation and orientation of sedimenting semiflexible polymers, ii) the propulsion and force-rectification with a nano-machine realized by a rotating elastic rod, and iii) the deformation of a brush made of grafted semiflexible polymers in shear flows. In all these examples deformable polymers are subject to various hydrodynamic flows and hydrodynamic interactions. Perfect stiff nano-cylinders ar…
Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore the generic diagram of emerging states over a large range of rod densities and aspect ratios. The dynamics is studied using a simple numerical scheme for the overdamped noiseless frictional dynamics of a many-body system in which steric forces are dominant over hydrodynamic ones. The different emergent states are identified by various characteristic correlatio…
A new computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous interface by assuming a smoothed profile. This enabled us to calculate hydrodynamic interactions both efficiently and accurately, without neglecting many-body interactions. The validity of the method was tested by calculating the drag force acting on a single cylindrical rod moving in an incompressible Newtonian fluid. This method was then applied in order …
Self-propelled colloids (swimmers) in confining geometries follow trajectories determined by hydrodynamic interactions with the bounding surfaces. However, typically these interactions are ignored or truncated to lowest order. We demonstrate that higher-order hydrodynamic moments cause rod-like swimmers to follow oscillatory trajectories in quiescent fluid between two parallel plates, using a combination of lattice-Boltzmann simulations and far-field calculations. This behavior occurs even far from the confining walls and does not require lubrication results. We show that a swimmer's hydrodyna…
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 effec…
Linear Viscoelasticity of Semiflexible Polymers with Hydrodynamic Interactions
IITB-Monash Research Academy, Indian Institute of Technology Bombay（印度理工学院孟买分校 IITB-莫纳什研究院）；Department of Chemical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校化学工程系）；Department of Chemical and Biological Engineering, Monash University（莫纳什大学化学与生物工程系）
Self-propelled particles can exhibit surprising non-equilibrium behaviors, and how they interact with obstacles or boundaries remains an important open problem. Here we show that chemically propelled micro-rods can be captured, with little change in their speed, into close orbits around solid spheres resting on or near a horizontal plane. We show that this interaction between sphere and particle is short-range, occurring even for spheres smaller than the particle length, and for a variety of sphere materials. We consider a simple model, based on lubrication theory, of a force- and torque-free …
We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that the use of periodic boundary conditions in the directions along the surfaces results in dramatic finite-size effects, in addition to that of the physically relevant confining length. As in the simulation of bulk fluids, these effects arise from spurious hydrodynamic interactions between periodic images and from the constraint of total momentum conservation.…
A simple model for simulating flows of active suspensions is investigated. The approach is based on dissipative particle dynamics. While the model is potentially applicable to a wide range of self-propelled particle systems, the specific class of self-motile bacterial suspensions is considered as a modeling scenario. To mimic the rod-like geometry of a bacterium, two dissipative particle dynamics particles are connected by a stiff harmonic spring to form an aggregate dissipative particle dynamics molecule. Bacterial motility is modeled through a constant self-propulsion force applied along the…
In the last 50 years, equilibrium density functional theory (DFT) has been proven to be a powerful, versatile and predictive approach for the statics and structure of classical particles. This theory can be extended to the nonequilibrium dynamics of completely overdamped Brownian colloidal particles towards so-called dynamical density functional theory (DDFT). The success of DDFT makes it a promising candidate for a first-principle description of active matter. In this lecture, we shall first recapitulate classical DDFT for passive colloidal particles typically described by Smoluchowski equati…
