We measure hydrodynamic interactions between colloidal particles confined in a thin sheet of fluid. The reduced dimensionality, compared to a bulk fluid, increases dramatically the range of couplings. Using optical tweezers we force a two body system along the eigenmodes of the mobility tensor and find that eigen-mobilities change logarithmically with particle separation. At a hundred radii distance, the mobilities for correlated and anti-correlated motions differ by a factor of two, whereas in bulk fluids, they would be practically indistinguishable. We derive the two dimensional counterpart of the Oseen hydrodynamic tensor which quantitatively reproduces the observed behavior. These results highlight the importance of dimensionality for transport and interactions in colloidal systems and proteins in biological membranes.
Directed transport of self-propelled particles is numerically investigated in a three-dimensional asymmetric potential. Beside the steric repulsive forces, hydrodynamic interactions between particles have been taken into account in an approximate way. From numerical simulations, we find that hydrodynamic interactions can strongly affect the rectified transport of self-propelled particles. Hydrodynamic interactions enhance the performance of the rectified transport when particles can easily pass across the barrier of the potential, and reduce the rectified transport when particles are mainly tr…
Based on the Wilemski-Fixman approach (J. Chem. Phys. 60, 866 (1974)) we showed that for a flexible chain in theta solvent hydrodynamic interaction treated with an pre-averaging approximation makes ring closing faster if the chain is not very short. Only for a very short chain the ring closing is slower with hydrodynamic interaction on. We have also shown that the ring closing time for a chain with hydrodynamic interaction in theta solvent scales with the chain length (N) as N^(1.527), in good agreement with previous renormalization group calculation based prediction by Freidman et al. (Phys. …
We experimentally and theoretically investigate the collective behavior of three colloidal particles that are driven by a constant force along a toroidal trap. Due to hydrodynamic interactions, a characteristic limit cycle is observed. When we additionally apply a periodic sawtooth potential, we find a novel caterpillar-like motional sequence that is dominated by hydrodynamic interactions and promotes the surmounting of potential barriers by the particles.
The development of a coherent conceptual basis for the treatment of non-linear microscopic phenomena, such as, hydrodynamic interaction, finite extensibility, excluded volume and internal viscosity, in molecular theories of dilute polymer solutions, is discussed. In particular, recent advances in the treatment of hydrodynamic interaction are reviewed, and the successive refinements which have ultimately led to the prediction of universal viscometric functions in theta solvents are highlighted.
We study single-chain motion in semidilute solutions of polymers of length N = 1000 with excluded-volume and hydrodynamic interactions by a novel algorithm. The crossover length of the transition from Zimm (short lengths and times) to Rouse dynamics (larger scales) is proportional to the static screening length. The crossover time is the corresponding Zimm time. Our data indicate Zimm behavior at large lengths but short times. There is no hydrodynamic screening until the chains feel constraints, after which they resist the flow: "Incomplete screening" occurs in the time domain.
At the surfaces of autophoretic colloids, slip velocities arise from local chemical gradients that are many-body functions of particle configuration and activity. For rapid chemical diffusion, coupled with slip-induced hydrodynamic interactions, we deduce the chemohydrodynamic forces and torques between colloids. Near a no-slip wall, the forces can be expressed as gradients of a non-equilibrium potential which, by tuning the type of activity, can be varied from repulsive to attractive. When this potential has a barrier, we find arrested phase separation with a mean cluster size set by competin…
We investigate numerically the dynamical behaviour of a polymer chain collapsing in a dilute solution. The rate of collapse is measured with and without the presence of hydrodynamic interactions. We find that hydrodynamic interactions both accelerate polymer collapse and alter the folding pathway.
The effect of hydrodynamic interactions on the free-solution electrophoresis of polyelectrolytes is investigated with coarse-grained molecular dynamics simulations. By comparing the results to simulations with switched-off hydrodynamic interactions, we demonstrate their importance in modelling the experimentally observed behaviour. In order to quantify the hydrodynamic interactions between the polyelectrolyte and the solution, we present a novel way to estimate its effective charge. We obtain an effective friction that is different from the hydrodynamic friction obtained from diffusion measure…
A density functional theory for colloidal dynamics is presented which includes hydrodynamic interactions between the colloidal particles. The theory is applied to the dynamics of colloidal particles in an optical trap which switches periodically in time from a stable to unstable confining potential. In the absence of hydrodynamic interactions, the resulting density breathing mode, exhibits huge oscillations in the trap center which are almost completely damped by hydrodynamic interactions. The predicted dynamical density fields are in good agreement with Brownian dynamics computer simulations.
We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard-sphere particles in a dense monodisperse suspension. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from discontinuous molecular dynamics simulations. At distances exceeding 3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with prediction…
Nonequilibrium molecular dynamics simulations are used to investigate the influence of hydrodynamic interactions on vertical segregation (stratification) in drying mixtures of long and short polymer chains. In agreement with previous computer simulations and theoretical modeling, the short polymers stratify on top of the long polymers at the top of the drying film when hydrodynamic interactions between polymers are neglected. However, no stratification occurs at the same drying conditions when hydrodynamic interactions are incorporated through an explicit solvent model. Our analysis demonstrat…
It has been shown recently that the coefficient of collective diffusion in a colloidal monolayer is divergent due to the hydrodynamic interactions mediated by the ambient fluid in bulk. The analysis is extended to allow for time--dependent hydrodynamic interactions. Novel observational features specific to this time dependency are predicted. The possible experimental detection in the dynamics of the monolayer is discussed.
In this letter, we investigate several aspects related to the effect of hydrodynamics interactions on phase separation-induced gelation of colloidal particles. We explain physically the observation of Tanaka and Araki[Phys. Rev. Lett. {\bf 85}, 1338 (2000)] of hydrodynamic stabilization of cellular network structures in two dimensions. We demonstrate that hydrodynamic interactions have only a minor quantitative influence on the structure of transient gels in three dimensions. We discuss some experimental implications of our results.
Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions in a compressible fluid on the basis of …
We provide numerical evidence that hydrodynamic interactions are screened for charged polymers in salt solution on time scales below the Zimm time. At very short times, a crossover to hydrodynamic behavior is observed. Our conclusions are drawn from extensive coarse-grained computer simulations of polyelectrolytes in explicit solvent and explicit salt, and discussed in terms of analytical arguments based on the Debye-Hueckel approximation.
Hydrodynamic interactions are transmitted by viscous diffusion and sound propagation: the temporal evolution of hydrodynamic interactions by both mechanisms is studied by direct numerical simulation in this paper. The hydrodynamic interactions for a system of two particles in a fluid are estimated by the velocity correlation of the particles. In an incompressible fluid, hydrodynamic interactions propagate instantaneously at the infinite speed of sound, followed by the temporal evolution of viscous diffusion. On the other hand, in a compressible fluid, sound propagates at a finite speed, which …
We demonstrate that the attractive interaction measured between like-charged colloidal spheres near a wall can be accounted for by a nonequilibrium hydrodynamic effect. We present both analytical results and Brownian dynamics simulations which quantitatively capture the one-wall experiments of Larsen and Grier (Nature 385, p. 230, 1997).
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 …
Hydrodynamic interactions between fluid-dispersed particles are ubiquitous in soft matter and biological systems and they give rise to intriguing collective phenomena. While it was reported that these interactions can facilitate force-driven particle motion over energetic barriers, here we show the opposite effect in a flow-driven system, i.e. that hydrodynamic interactions hinder transport across barriers. We demonstrate this result by combining experiments and theory. In the experiments, we drive colloidal particles using rotating optical traps, thus creating a vortex flow in the corotating …
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.
Motivated by the implications of the complex and dynamic modular geometry of an enzyme on its motion, we investigate the effect of combining long-range internal and external hydrodynamic interactions due to thermal fluctuations with short-range surface interactions. An asymmetric dumbbell consisting of two unequal subunits, in a nonuniform suspension of a solute with which it interacts via hydrodynamic interactions as well as non-contact surface interactions, is shown to have two alignment mechanisms due to the two types of interactions. In addition to alignment, the chemical gradient results …
Dynamics of a Brownian particle in an asymmetric micro-channel that is subjected to an external oscillating force is numerically analyzed. In addition to the elastic collisions with the walls that are kind of short range interactions, the long range hydrodynamic influences of the walls have been considered. We demonstrate how the geometrical parameters of the channel change the rectified current of the particle. As a result of numerical calculations, we show that long range hydrodynamic interactions with walls, decrease the efficiency of the Brownian ratchet.
Using a fluid-particle dynamics approach, we numerically study the effects of hydrodynamic interactions on the collective dynamics of active suspensions within a simple model for bacterial motility: each microorganism is modeled as a stroke-averaged dumbbell swimmer with prescribed dipolar force pairs. Using both simulations and qualitative arguments, we show that, when the separation between swimmers is comparable to their size, the swimmers' motions are strongly affected by activity-induced hydrodynamic forces. To further understand these effects, we investigate semidilute suspensions of swi…
We study the role of hydrodynamic interactions in the collective behaviour of collections of microscopic active particles suspended in a fluid. We introduce a novel calculational framework that allows us to separate the different contributions to their collective dynamics from hydrodynamic interactions on different length scales. Hence we are able to systematically show that lubrication forces when the particles are very close to each other play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that motility-induced phase separation i…
We consider a simple model for steady-state luminescence of single polymer chains in a dilute solution in the case when excitation quenching is due to energy transfer between a donor and an acceptor attached to the ends of the chain. We present numerical results for Rouse chains without or with hydrodynamic interactions, which are taken into account in a perturbative manner. We consider the situations of a quiescent solvent as well as the chain in a shear flow and discuss the dependence of the steady-state luminescence intensity on the strength of hydrodynamic interaction and on the shear rate…
In dense colloids it is commonly assumed that hydrodynamic interactions do not play a role. However, a found theoretical quantification is often missing. We present computer simulations that are motivated by experiments where a large colloidal particle is dragged through a colloidal crystal. To qualify the influence of long-ranged hydrodynamics, we model the setup by conventional Langevin dynamics simulations and by an improved scheme with limited hydrodynamic interactions. This scheme significantly improves our results and allows to show that hydrodynamics strongly impacts on the development …
The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic int…
This article gives an overview of recent theoretical and experimental findings concerning the hydrodynamic interaction between liquid-embedded particles in various confined geometries. A simple unifying description emerges, which accounts for the various findings based on the effect of confinement on conserved fields of the embedding liquid. It shows, in particular, that the hydrodynamic interaction under confinement remains long-ranged, decaying algebraically with inter-particle distance, except for the case of confinement in a rigid linear channel.
Confinement between two parallel surfaces is found, theoretically and experimentally, to drastically affect the hydrodynamic interaction between colloid particles, changing the sign of the coupling, its decay with distance and its concentration dependence. In particular, we show that three-body effects do not modify the coupling at large distances as would be expected from hydrodynamic screening.
Self-organization of moving objects in hydrodynamic environments has recently attracted considerable attention in connection to natural phenomena and living systems. However, the underlying physical mechanism is much less clear due to the intrinsically nonequilibrium nature, compared with self-organization of thermal systems. Hydrodynamic interactions are believed to play a crucial role in such phenomena. To elucidate the fundamental physical nature of many-body hydrodynamic interactions at a finite Reynolds number, here we study a system of co-rotating hard disks in a two-dimensional viscous …
Some types of bacteria use rotating helical flagella to swim. The motion of such organisms takes place in the regime of low Reynolds numbers where viscous effects dominate and where the dynamics is governed by hydrodynamic interactions. Typically, rotating flagella form bundles, which means that their rotation is synchronized. The aim of this study is to investigate whether hydrodynamic interactions can be at the origin of such a bundling and synchronization. We consider two stiff helices that are modelled by rigidly connected beads, neglecting any elastic deformations. They are driven by cons…
Microswimmers often exhibit surprising patterns due to the nonequilibrium nature of their dynamics. Collectively, suspensions of microswimmers appear as a liquid whose properties set it apart from its passive counterpart. To understand the impact of hydrodynamic interactions on the basic statistical features of a microswimmer's liquid, we investigate its structure by means of the pair distribution function. We perform particle-based simulations of microswimmers that include steric effects, shape anisotropy, and hydrodynamic interactions. We find that hydrodynamic interactions considerably alte…
We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the non-equilibrium properties of the system. We derive a general dynamical density functional theory (DDFT) which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing DDFTs and a Navier-Stokes-like equation with additional non-local terms.
We study the kinetics of assembly of two plates of varying hydrophobicity, including cases where drying occurs and water strongly solvates the plate surfaces. The potential of mean force and molecular-scale hydrodynamics are computed from molecular dynamics simulations in explicit solvent as a function of particle separation. In agreement with our recent work on nanospheres [J. Phys. Chem. B 116, 378 (2012)] regions of high friction are found to be engendered by large and slow solvent fluctuations. These slow fluctuations can be due to either drying or confinement. The mean first passage times…
Under partial confinement, the motion of colloidal particles is restricted to a plane but their dynamics is influenced by hydrodynamic interactions mediated by the unconfined, three--dimensional flow of the embedding fluid. We demonstrate that this dimensionality mismatch induces a characteristic divergence in the two--dimensional collective diffusion coefficient of the colloidal monolayer. This result, independent from the specific interparticle forces in the monolayer, is solely due to the kinematical constraint on the colloidal particles, and it is different from the known divergence of tra…
In this article we develop a theoretical framework to study the hydrodynamic interactions in the presence of a non-flat and no-slip boundary. We calculate the influence of a small amplitude and sinusoidal deformations of a boundary wall in the self mobility and the two body hydrodynamic interactions for spherical particles. We show that the surface roughness enhances the self mobility of a sphere in a way that, for motion in front of a local hump of the surface, the mobility strength decreases while it increases for the motion above a local deep of the rough surface. The influence of the surfa…
It is intuitive that the diffusivity of an isolated particle differs from those in a monodisperse suspension, in which hydrodynamic interactions between the particles are operative. Batchelor (1976,1983) calculated how hydrodynamic interactions influenced the diffusivity of a dilute suspension of spherical particles and Russel et al.(1991), and Brady (1994) treated non-dilute (higher particle volume fraction) suspensions. Although most particles lack perfect sphericity, little is known about the effects of hydrodynamic interactions on the diffusivity of spheroidal particles, which are the simp…
Exact expressions are derived for the pair and three-body hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds number hydrodynamics. The results follow by a combination of the solutions for flow about a sphere with no-slip boundary condition derived by Stokes and Kirchhoff, and the result derived by Oseen for the Green tensor of Stokes' equations in the presence of a fixed sphere.
Multiparticle collision dynamics (MPCD) is a flexible and robust mesoscale computational technique for simulating solvent-mediated hydrodynamic interactions in soft materials. Here, we provide a critical overview of the MPCD method and summarize its current strengths and limitations. The capabilities of the method are highlighted by reviewing its recent applications to simulate diverse phenomena, ranging from the flow of complex fluids and thermo-osmotic transport to bacterial swimming and active particle self-assembly. We also discuss outstanding challenges and emerging methodological develop…
We present experiments on RBCs that flow through microcapillaries under physiological conditions. We show that the RBC clusters form as a subtle imbrication between hydrodynamics interaction and adhesion forces because of plasma proteins. Clusters form along the capillaries and macromolecule-induced adhesion contribute to their stability. However, at high yet physiological flow velocities, shear stresses overcome part of the adhesion forces, and cluster stabilization due to hydrodynamics becomes stronger. For the case of pure hydrodynamic interaction, cell-to-cell distances have a pronounced b…
Using a simple model of self-propelled particle, the effective shear viscosity of a dilute, spatially homogeneous suspension of active particles is studied. We use formulation of non-linear Fokker-Planck equation to drive a kinetic description, including the effect of external flow field, rotary diffusion, and particle-particle hydrodynamic interactions in two dimensions. Analytical expressions are obtained for the stress tensor at small Peclet numbers, in a simple shear flow, up to second order of volume fraction of the swimmers, which shows the explicit dependence of shear viscosity on the d…
Separation of magnetically tagged cells is performed by attaching markers to a subset of cells in suspension and applying fields to pull from them in a variety of ways. The magnetic force is proportional to the field gradient, and the hydrodynamic interactions play only a passive, adverse role. Here we propose using a homogeneous rotating magnetic field only to make tagged particles rotate, and then performing the actual separation by means of hydrodynamic interactions, which thus play an active role. The method, which we explore here theoretically and by means of numerical simulations, lends …
Phoretic particles self-propel using self-generated physico-chemical gradients at their surface. Within a suspension, they interact hydrodynamically by setting the fluid around them into motion, and chemically by modifying the chemical background seen by their neighbours. While most phoretic systems evolve in confined environments due to buoyancy effects, most models focus on their interactions in unbounded flows. Here, we propose a first model for the interaction of phoretic particles in Hele-Shaw confinement and show that in this limit, hydrodynamic and phoretic interactions share not only t…
Active fluids comprise a variety of systems composed of elements immersed in a fluid environment which can convert some form of energy into directed motion; as such they are intrinsically out-of-equilibrium in the absence of any external forcing. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of the autonomous propulsion and agent-agent interactions determine the collective dynamics of the system. We study numerically suspensions of self-propelled diffusiophoretic colloids, in (quasi)-2d configurations, accounting for both dynamicall…
We study the role of hydrodynamic interactions for the relaxation of segments' orientations in dendrimers. The dynamics is considered in the Zimm framework. It is shown that inclusion of correlations between segments' orientations plays a major role for the segments' mobility, that reveals itself in the NMR relaxation functions. The enhancement of the reorientation dynamics of segments due to the hydrodynamic interactions is more significant for the inner segments. This effect is clearly pronounced in the reduced spectral density $ωJ(ω)$, whose maximum shifts to higher frequencies when the hyd…
Cellular biology abound with filaments interacting through fluids, from intracellular microtubules, to rotating flagella and beating cilia. While previous work has demonstrated the complexity of capturing nonlocal hydrodynamic interactions between moving filaments, the problem remains difficult theoretically. We show here that when filaments are closer to each other than their relevant length scale, the integration of hydrodynamic interactions can be approximately carried out analytically. This leads to a set of simplified local equations, illustrated on a simple model of two interacting filam…
The effect of fluctuating internal viscosity and hydrodynamic interactions on a range of rheological properties of dilute polymer solutions is examined using a finitely extensible dumbbell model for a polymer. Brownian dynamics simulations are used to compute both transient and steady state viscometric functions in shear flow. The results enable a careful differentiation of the influence, on rheological properties, of solvent-mediated friction from that of a dissipative mechanism that is independent of solvent viscosity. In particular, hydrodynamic interactions have a significant influence on …
We study experimentally and theoretically the hydrodynamic coupling between Brownian colloidal particles diffusing along a linear channel. The quasi-one-dimensional confinement, unlike other constrained geometries, leads to a sharply screened interaction. Consequently, particles move in concert only when their mutual distance is smaller than the channel width, and two-body interactions remain dominant up to high particle densities. The coupling in a cylindrical channel is predicted to reverse sign at a certain distance, yet this unusual effect is too small to be currently detectable.
We use lattice Boltzmann simulations, in conjunction with Ewald summation methods, to investigate the role of hydrodynamic interactions in colloidal suspensions of dipolar particles, such as ferrofluids. Our work addresses volume fractions $ϕ$ of up to 0.20 and dimensionless dipolar interaction parameters $λ$ of up to 8. We compare quantitatively with Brownian dynamics simulations, in which many-body hydrodynamic interactions are absent. Monte Carlo data are also used to check the accuracy of static properties measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic interact…
We investigate the hydrodynamic interaction between two elastic swimmers which are composed of three spheres and two harmonic springs. In this model, the natural length of each spring is assumed to undergo a prescribed cyclic change, representing internal states of the swimmer [K. Yasuda et al., J. Phys. Soc. Jpn. 86, 093801 (2017)]. We obtain the average velocities of two identical elastic swimmers as a function of the distance between them both for structurally asymmetric and symmetric swimmers. We show that the mean velocity of the two swimmers is always smaller than that of a single elasti…
Understanding the influence of hydrodynamic stresses and colloidal interactions between droplets and membranes will inform better engineered membrane surfaces and process conditions. Using a long-wave hydrodynamic description that incorporates wettability and electrostatic repulsion, we numerically investigate the influence of droplet shapes and membrane characteristics on the overall repulsion-attraction towards the membrane surface. A stability phase diagram classifies stable-unstable drop shapes and investigate whether there is reversible deposition of droplets onto the membrane.
Particle-particle interactions are of paramount importance in every multi-body system as they determine the collective behaviour and coupling strength. Many well-known interactions like electro-static, van der Waals or screened Coulomb, 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, mi…
