arXiv subjects

Ryuichi Okamoto

Publications and source records attributed to Ryuichi Okamoto.

At least 19 recordsLinked to original sources

arXiv2022

Fluctuating hydrodynamics of dilute electrolyte solutions: systematic perturbation calculation of effective transport coefficients governing large-scale dynamics

We study the transport properties of dilute electrolyte solutions on the basis of the fluctuating hydrodynamic equation, which is a set of nonlinear Langevin equations for the ion densities and flow velocity. The nonlinearity of the Langevin equations generally leads to effective kinetic coefficients for the deterministic dynamics of the average ion densities and flow velocity; the effective coefficients generally differ from the counterparts in the Langevin equations and are frequency-dependent. Using the path-integral formalism involving auxiliary fields, we perform systematic perturbation calculations of the effective kinetic coefficients for ion diffusion, shear viscosity, and electrical conductivity, which govern the dynamics on the large length scales. As novel contributions, we study the frequency dependence of the viscosity and conductivity in the one-loop approximation. Regarding the conductivity at finite frequencies, we derive the so-called electrophoretic part in addition to the relaxation part, where the latter has been obtained by Debye and Falkenhagen; it is predicted that the combination of these two parts gives rise to the frequency $ω_{\rm max}$ proportional to the salt density, at which the real part of the conductivity exhibits a maximum. The zero-frequency limits of the conductivity and shear viscosity coincide with the classical limiting laws for dilute solutions, derived in different means by Debye, Falkenhagen, and Onsager. As for the effective kinetic coefficients for slow ion diffusions in large length scales, our straightforward calculation yields the cross kinetic coefficient between cations and anions. Further, we discuss the possibility of extending the present study to more concentrated solutions.

cond-mat.stat-mech↗

arXiv2020

Theory of electrolytes including steric, attractive, and hydration interactions

We present a continuum theory of electrolytes composed of a waterlike solvent and univalent ions. First, we start with a density functional $\cal F$ for the coarse-grained solvent, cation, and anion densities, including the Debye-Hückel free energy, the Coulombic interaction, and the direct interactions among these three components. These densities fluctuate obeying the distribution $\propto \exp(- {\cal F}/k_BT)$. Eliminating the solvent density deviation in $\cal F$, we obtain the effective non-Coulombic interactions among the ions, which consist of the direct ones and the solvent-mediated ones. %where the latter are written in terms of the ion volumes %and are inversely proportional to the solvent compressibility. We then derive general expressions for the ion correlation, the apparent partial volume, and the activity and osmotic coefficients up to linear order in the average salt density $n_{\rm s}$. Secondly, we perform numerical analysis using the Mansoori-Carnahan-Starling-Leland model $[$J. Chem. Phys. {\bf 54}, 1523 (1971)$]$ for three-component hardspheres. The effective interactions sensitively depend on the cation and anion sizes due to competition between the steric and hydration effects, which are repulsive between small-large ion pairs and attractive between symmetric pairs. These agree with previous experiments and Collins' rule $[$Biophys. J. {\bf 72}, 65 (1997)$]$. We also give simple approximate expressions for the ionic interaction coefficients valid for any ion sizes.

cond-mat.soft↗

arXiv2018

A three-sphere microswimmer in a structured fluid

We discuss the locomotion of a three-sphere microswimmer in a viscoelastic structured fluid characterized by typical length and time scales. We derive a general expression to link the average swimming velocity to the sphere mobilities. In this relationship, a viscous contribution exists when the time-reversal symmetry is broken, whereas an elastic contribution is present when the structural symmetry of the microswimmer is broken. As an example of a structured fluid, we consider a polymer gel, which is described by a "two-fluid" model. We demonstrate in detail that the competition between the swimmer size and the polymer mesh size gives rise to the rich dynamics of a three-sphere microswimmer.

cond-mat.soft↗

arXiv2018

Theory of nonionic hydrophobic solutes in mixture solvent: Solvent-mediated interaction and solute-induced phase separation

We present a theory of nonionic solutes in a mixture solvent composed of water-like and alcohol-like species. First, we show relationship among the solvation chemical potential, the partial volumes $v_i$, the Kirkwood-Buff integrals, the second osmotic virial coefficient, and the Gibbs transfer free energy. We examine how the solute density $n_3$ is coupled to the solvent densities $n_1$ and $n_2$ in thermodynamics. In the limit of small compressibility, we show that the space-filling condition $\sum_i v_i n_i=1$ nearly holds for inhomogeneous densities $n_i$, where the concentration fluctuations of the solvent can give rise to a large solute-solute attractive interaction. We also derive a solute spinodal density $n_3^{\rm spi}$ for solute-induced instability. Next, we examine gas-liquid and liquid-liquid phase transitions induced by a small amount of a solute using the Mansoori, Carnahan, Starling, and Leland model for hard-sphere mixtures $[${ J. Chem. Phys.} {\bf 54}, 1523 (1971)$]$. Here, we assume that the solvent is close to its gas-liquid coexistence and the solute interacts repulsively with the water-like species but attractively with the alcohol-like one. We calculate the binodal and spinodal curves in the phase diagrams and examine nucleation for these two phase transitions.

cond-mat.soft↗

arXiv2018

Dynamics of a bilayer membrane with membrane-solvent partial slip boundary conditions

We discuss the dynamics of a bilayer membrane with partial slip boundary conditions between the monolayers and the bulk fluid. Using Onsager's variational principle to account for the associated dissipations, we derive the coupled dynamic equations for the membrane height and the excess lipid density. The newly introduced friction coefficients appear in the renormalized fluid viscosities. For ordinary lipid bilayer membranes, we find that it is generally justified to ignore the effects of permeation and parallel slip at the membrane surface.

cond-mat.soft↗

arXiv2018

Thermal and active fluctuations of a compressible bilayer vesicle

We discuss thermal and active fluctuations of a compressible bilayer vesicle by using the results of hydrodynamic theory for vesicles. Coupled Langevin equations for the membrane deformation and the density fields are employed to calculate the power spectral density matrix of membrane fluctuations. Thermal contribution is obtained by means of the fluctuation dissipation theorem, whereas active contribution is calculated from exponentially decaying time correlation functions of active random forces. We obtain the total power spectral density as a sum of thermal and active contributions. An apparent response function is further calculated in order to compare with the recent microrheology experiment on red blood cells. An enhanced response is predicted in the low-frequency regime for non-thermal active fluctuations.

cond-mat.soft↗

arXiv2017

Thermally Driven Elastic Micromachines

We discuss the directional motion of an elastic three-sphere micromachine in which the spheres are in equilibrium with independent heat baths having different temperatures. Even in the absence of prescribed motion of springs, such a micromachine can gain net motion purely because of thermal fluctuations. A relation connecting the average velocity and the temperatures of the spheres is analytically obtained. This velocity can also be expressed in terms of the average heat flows in the steady state. Our model suggests a new mechanism for the locomotion of micromachines in nonequilibrium biological systems.

cond-mat.soft↗

arXiv2017

Coexistences of lamellar phases in ternary surfactant solutions

We theoretically investigate the coexistences of lamellar phases both in binary and ternary surfactant solutions. The previous free energy of a lamellar stack is extended to take into account the translational entropy of membrane segments. The obtained phase diagram for binary surfactant solutions (surfactant/water mixtures) shows a phase separation between two lamellar phases and also exhibits a critical point. For lamellar phases in ternary surfactant solutions (surfactant/surfactant/water mixtures), we explore possible phase behaviors and show that the phase diagrams exhibit various three-phase regions as well as two-phase regions in which different lamellar phases coexist. We also find that finite surface tension suppresses undulation fluctuations of membranes and leads to a wider three-phase and two-phase coexistence regions.

cond-mat.soft↗

arXiv2017

Dynamics of a Bilayer Membrane Coupled to a Two-dimensional Cytoskeleton: Scale Transfers of Membrane Deformations

We theoretically investigate the dynamics of a floating lipid bilayer membrane coupled with a two-dimensional cytoskeleton network, taking into explicitly account the intermonolayer friction, the discrete lattice structure of the cytoskeleton, and its prestress. The lattice structure breaks lateral continuous translational symmetry and couples Fourier modes with different wavevectors. It is shown that within a short time interval a long-wavelength deformation excites a collection of modes with wavelengths shorter than the lattice spacing. These modes relax slowly with a common renormalized rate originating from the long-wavelength mode. As a result, and because of the prestress, the slowest relaxation is governed by the intermonolayer friction. Reversely, and most interestingly, forces applied at the scale of the cytoskeleton for a sufficiently long time can cooperatively excite large-scale modes.

cond-mat.soft↗

arXiv2017

Elastic three-sphere microswimmer in a viscous fluid

We discuss the dynamics of a generalized three-sphere microswimmer in which the spheres are connected by two elastic springs. The natural length of each spring is assumed to undergo a prescribed cyclic change. We analytically obtain the average swimming velocity as a function of the frequency of the cyclic change in the natural length. In the low-frequency region, the swimming velocity increases with the frequency and its expression reduces to that of the original three-sphere model by Najafi and Golestanian. In the high-frequency region, conversely, the average velocity decreases with increasing the frequency. Such a behavior originates from the intrinsic spring relaxation dynamics of an elastic swimmer moving in a viscous fluid.

cond-mat.soft↗

arXiv2017

Lateral diffusion induced by active proteins in a biomembrane

We discuss the hydrodynamic collective effects due to active protein molecules that are immersed in lipid bilayer membranes and modeled as stochastic force dipoles. We specifically take into account the presence of the bulk solvent which surrounds the two-dimensional fluid membrane. Two membrane geometries are considered: the free membrane case and the confined membrane case. Using the generalized membrane mobility tensors, we estimate the active diffusion coefficient and the drift velocity as a function of the size of a diffusing object. The hydrodynamic screening lengths distinguish the two asymptotic regimes of these quantities. Furthermore, the competition between the thermal and non-thermal contributions in the total diffusion coefficient is characterized by two length scales corresponding to the two membrane geometries. These characteristic lengths describe the crossover between different asymptotic behaviors when they are larger than the hydrodynamic screening lengths.

cond-mat.soft↗

arXiv2017

Anomalous diffusion in viscoelastic media with active force dipoles

With the use of the "two-fluid model", we discuss anomalous diffusion induced by active force dipoles in viscoelastic media. Active force dipoles, such as proteins and bacteria, generate non-thermal fluctuating flows that lead to a substantial increment of the diffusion. Using the partial Green's function of the two-fluid model, we first obtain passive (thermal) two-point correlation functions such as the displacement cross-correlation function between the two point particles separated by a finite distance. We then calculate active (non-thermal) one-point and two-point correlation functions due to active force dipoles. The time correlation of a force dipole is assumed to decay exponentially with a characteristic time scale. We show that the active component of the displacement cross-correlation function exhibits various crossovers from super-diffusive to sub-diffusive behaviors depending on the characteristic time scales and the particle separation. Our theoretical results are intimately related to the microrheology technique to detect fluctuations in non-equilibrium environment.

cond-mat.soft↗

arXiv2017

Swimmer-microrheology

We discuss a locomotion of a three-sphere microswimmer in a viscoelastic medium and propose a new type of active microrheology. We derive a relation which connects average swimming velocity and frequency-dependent viscosity of the surrounding medium. In this relation, the viscous contribution can exist only when the time-reversal symmetry is broken, whereas the elastic contribution is present only when the structural symmetry of the swimmer is broken. The Purcell's scallop theorem breaks down for a three-sphere swimmer in a viscoelastic medium.

cond-mat.soft↗

arXiv2017

Localization and diffusion of tracer particles in viscoelastic media with active force dipoles

Optical tracking in vivo experiments reveal that diffusion of particles in biological cells is strongly enhanced in the presence of ATP and the experimental data for animal cells could previously be reproduced within a phenomenological model of a gel with myosin motors acting within it [EPL 110, 48005 (2015)]. Here, the two-fluid model of a gel is considered where active macromolecules, described as force dipoles, cyclically operate both in the elastic and the fluid components. Through coarse-graining, effective equations of motions for tracer particles displaying local deformations and local fluid flows are derived. The equation for deformation tracers coincides with the earlier phenomenological model and thus confirms it. For flow tracers, diffusion enhancement caused by active force dipoles in the fluid component, and thus due to metabolic activity, is found. The latter effect may explain why ATP-dependent diffusion enhancement could also be observed in bacteria that lack molecular motors in their skeleton or when the activity of myosin motors was chemically inhibited.

cond-mat.soft↗

arXiv2016

Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid

We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the cross-over mode between the bending and the slipping to a larger value. As the vesicle parameters approach toward the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.

cond-mat.soft↗

arXiv2016

Ionization at a solid-water interface in an applied electric field: Charge regulation

We investigate ionization at a solid-water interface in applied electric field. We attach an electrode to a dielectric film bearing silanol or carboxyl groups with an areal density $Γ_0$, where the degree of dissociation $α$ is determined by the proton density in water close to the film. We show how $α$ depends on the density $n_0$ of NaOH in water and the surface charge density $σ_m$ on the electrode. For $σ_m>0$, the protons are expelled away from the film, leading to an increase in $α$. In particular, in the range $0<σ_m<eΓ_0$, self-regulation occurs to realize $α\cong σ_m/eΓ_0 $ for $n_0\ll n_c$, where $n_c$ is $0.01$ mol$/$L for silica surfaces and is $2\times 10^{-5}$ mol$/$L for carboxyl-bearing surfaces. We also examine the charge regulation with decreasing the cell thickness $H$ below the Debye length $κ^{-1}$, where a crossover occurs at the Gouy-Chapman length. In particular, when $σ_m \sim eΓ_0$ and $H\ll κ^{-1}$, the surface charges remain only partially screened by ions, leading to an electric field in the interior.

cond-mat.soft↗

arXiv2016

Dynamics of a membrane interacting with an active wall

Active motions of a biological membrane can be induced by non-thermal fluctuations that occur in the outer environment of the membrane. We discuss the dynamics of a membrane interacting hydrodynamically with an active wall that exerts random velocities on the ambient fluid. Solving the hydrodynamic equations of a bound membrane, we first derive a dynamic equation for the membrane fluctuation amplitude in the presence of different types of walls. Membrane two-point correlation functions are calculated for three different cases; (i) a static wall, (ii) an active wall, and (iii) an active wall with an intrinsic time scale. We focus on the mean squared displacement (MSD) of a tagged membrane describing the Brownian motion of a membrane segment. For the static wall case, there are two asymptotic regimes of MSD ($\sim t^{2/3}$ and $\sim t^{1/3}$) when the hydrodynamic decay rate changes monotonically. In the case of an active wall, the MSD grows linearly in time ($\sim t$) in the early stage, which is unusual for a membrane segment. This linear-growth region of the MSD is further extended when the active wall has a finite intrinsic time scale.

cond-mat.soft↗

arXiv2016

Structure Formation due to Antagonistic Salts

Antagonistic salts are composed of hydrophilic and hydrophobic ions. In a mixture solvent (water-oil) such ion pairs are preferentially attracted to water or oil, giving rise to a coupling between the charge density and the composition. First, they form a large electric double layer at a water-oil interface, reducing the surface tension and producing mesophases. Here, the cations and anions are loosely bound by the Coulomb attraction across the interface on the scale of the Debye screening length. Second, on solid surfaces, hydrophilic (hydrophobic) ions are trapped in a water-rich (oil-rich) adsorption layer, while those of the other species are expelled from the layer. This yields a solvation mechanism of local charge separation near a solid. In particular, near the solvent criticality, disturbances around solid surfaces can become oscillatory in space. In mesophases, we calculate periodic structures, which resemble those in experiments.

cond-mat.soft↗