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PubMed2002

Propagating hydrodynamic modes in confined fluids.

In molecular dynamics simulations in the microcanonical ensemble (MEMD) we calculate the intermediate scattering function F(k(||),t) for a "simple" fluid confined to nanoscopic slit pores with chemically homogeneous, planar substrate surfaces. Since system properties are translationally invariant in the x-y plane, we focus on the propagation of density modes parallel with the confining substrates by choosing a two-dimensional wave vector |k(||)|=k(||)=(k(x),k(y)) for our analysis. Within the framework of classical hydrodynamics, we develop conservation laws for z-averaged fluxes of heat and momentum. Using in-plane versions of the macroscopic stress tensor and internal-energy current as constitutive equations we derive an expression for F(k(||),t) in the hydrodynamic limit depending on the thermal diffusivity D(T), the sound attenuation coefficient Gamma, the in-plane adiabatic velocity of sound v(||), and the ratio of heat capacities at constant transverse stress and volume gamma. Through a fit of F(k(||),t) in the hydrodynamic limit and its associated memory function M(k(||),t) to MEMD data, reliable values for the set [D(T),Gamma,v(||),gamma] of material coefficients can be obtained. Variations in [D(T),Gamma,v(||),gamma] with s(z) may be correlated with variations in the solvation pressure -tau(zz)-P(b) with s(z) (tau(zz) is the stress exerted by the fluid along the surface normal and P(b) is the bulk pressure) and therefore linked to stratification of the confined fluid.

Journal Article↗
PubMed2003

Hydrodynamics of bacterial colonies: a model.

We propose a hydrodynamic model for the evolution of bacterial colonies growing on soft agar plates. This model consists of reaction-diffusion equations for the concentrations of nutrients, water, and bacteria, coupled to a single hydrodynamic equation for the velocity field of the bacteria-water mixture. It captures the dynamics inside the colony as well as on its boundary and allows us to identify a mechanism for collective motion towards fresh nutrients, which, in its modeling aspects, is similar to classical chemotaxis. As shown in numerical simulations, our model reproduces both usual colony shapes and typical hydrodynamic motions, such as the whirls and jets recently observed in wet colonies of Bacillus subtilis. The approach presented here could be extended to different experimental situations and provides a general framework for the use of advection-reaction-diffusion equations in modeling bacterial colonies.

Agar↗
PubMed2004

Generalized hydrodynamics and microflows.

In this paper, a mathematical model within the framework of generalized hydrodynamics is developed for the description of flows in microsystems where the Knudsen number is large and the aspect ratio [(width)/(length)] is not so small. The model is based on a set of empirical generalized hydrodynamic equations, which are fashioned from the steady-state generalized hydrodynamic equations derived from the Boltzmann equation in a manner consistent with the laws of thermodynamics. The constitutive equations used for the model are highly nonlinear, unlike the Newtonian law of viscosity and the Fourier law of heat conduction, but they are thermodynamically consistent. In the absence of heat conduction, the model yields exact solutions for the velocity components and a nonlinear differential equation for the pressure distribution in the rectangular microchannel. The Langmuir adsorption model for surface-gas interaction is used for boundary conditions for the velocity. The calculated flow rate exhibits a Knudsen minimum with respect to the Knudsen number. The longitudinal velocity profile is also non-Poiseuille. The differential equation for pressure distribution is also solved approximately in order to obtain an analytic formula for the flow rate, which exhibits a Knudsen minimum. The formula, although approximate, provides considerable insights into the Knudsen flow phenomena in microchannels.

Journal Article↗
PubMed2004

Hydrodynamics and electrokinetics of spherical liposomes with coatings of terminally anchored poly(ethylene glycol): numerically exact electrokinetics with self-consistent mean-field polymer.

A detailed theoretical model is presented to interpret electrokinetic experiments performed on colloids with uncharged polymer layers. The methodology removes many of the degrees of freedom that otherwise have to be accounted for by adopting multiple empirical fitting parameters. Furthermore, the level of detail provides a firm basis for future studies examining liposome surface chemistry and charge, surface-charge mobility, and the dynamics of adsorbed polymer on fluidlike membranes. The model predictions are compared with experimental measurements of the electrophoretic mobility of stealth liposomes with molecular weights of terminally anchored poly(ethylene glycol) (PEG) in the range 0.35-10 kg mol(-1) [J.A. Cohen and V.A. Khorosheva, Colloids Surf. A 195, 113 (2001)]. The experimental data are interpreted by drawing upon self-consistent mean-field calculations of the polymer segment density distributions and numerically exact solutions of the governing transport equations [R.J. Hill, D.A. Saville, and W.B. Russel, J. Colloid Interface Sci. 258, 56 (2003)]. The approach leads to excellent agreement between theory and experiment with one adjustable parameter--the hydrodynamic size (Stokes radius) a(s) approximately equal to 0.175 A of the statistical PEG segments with (Kuhn) length l=7.1 A . The remarkably small Stokes radius is demonstrated to be consistent with other applications of the well-known Debye-Brinkman model and, consequently, this work reveals important limitations of the mean-field hydrodynamic model. Despite such limitations, the "full" electrokinetic model is robust in its predictive capacity. The molecular weights of the terminally anchored PEG span the range where the coatings undergo a transition from mushroomlike to brushlike conformations, and the hydrodynamic size and electrophoretic mobility of the liposomes are demonstrated to be sensitive to the PEG chain length and the effects of double-layer polarization.

Coated Materials, Biocompatible↗
PubMed2004

Comparisons between molecular dynamics and hydrodynamics treatment of nonstationary thermal processes in a liquid.

Molecular dynamics (MD) and Navier-Stokes hydrodynamics have been performed to model thermal relaxation processes arising from an initially established nonequilibrium stationary state. A nanoscale two-layer Lennard-Jones (LJ) liquid system was constructed in which the two parts were initially at a different temperature, with a narrow transitional zone between the two layers that was spatially linear in temperature. The highest-temperature layer had widths of five or 20 LJ particle diameters. The hydrodynamics model used parametrized MD-derived transport coefficients and the LJ equation of state as input functions. The temporal and spatial temperature and density profiles produced by the two methods show good agreement, indicating that a hydrodynamics description is reliable even for nonstationary phenomena down to the scale of a few molecular diameters. We found that at certain locations the Navier-Stokes solution predicted that the pressure and temperature profiles relaxed in a damped oscillatory manner, which we could discern despite the fluctuations in the MD data.

Journal Article↗
PubMed2005

Hydrodynamic resistance of close-approached slip surfaces with a nanoasperity or an entrapped nanobubble.

We present a general solution of hydrodynamic resistance of close-approached slippery surfaces with a nanoasperity or a nanobubble as an idealized roughness effect. Based on Reynolds' lubrication theory and a simple slip boundary condition, the pressure distribution in the thin liquid film is predicted analytically and the total hydrodynamic resistance force at limiting cases are formulated in terms of correction functions to the Taylor's equation. Accessible parameters are included for the drainage experiment using atomic force microscope or surface force apparatus. We provide case studies to demonstrate the implication of roughness effect and the possible uncertainties involved in the dynamic force measurement. We found that in the lubrication regime, the hydrodynamic resistance is dominated by the local behavior near the asperity, thus the apparent slip length can not always represent the surface roughness.

Journal Article↗
PubMed2006

Dynamical behavior of hydrodynamic Lyapunov modes in coupled map lattices.

In our previous study of hydrodynamic Lyapunov modes (HLMs) in coupled map lattices, we found that there are two classes of systems with different lambda-k dispersion relations. For coupled circle maps we found the quadratic dispersion relations lambda approximately k2 and lambda approximately k for coupled standard maps. Here, we carry out further numerical experiments to investigate the dynamic Lyapunov vector (LV) structure factor which can provide additional information on the Lyapunov vector dynamics. The dynamic LV structure factor of coupled circle maps is found to have a single peak at omega=0 and can be well approximated by a single Lorentzian curve. This implies that the hydrodynamic Lyapunov modes in coupled circle maps are nonpropagating and show only diffusive motion. In contrast, the dynamic LV structure factor of coupled standard maps possesses two visible sharp peaks located symmetrically at +/- omega. The spectrum can be well approximated by the superposition of three Lorentzian curves centered at omega=0 and +/-omegau, respectively. In addition, the omega-k dispersion relation takes the form omegau=cuk for k --> 2pi/L. These facts suggest that the hydrodynamic Lyapunov modes in coupled standard maps are propagating. The HLMs in the two classes of systems are shown to have different dynamical behavior besides their difference in spatial structure. Moreover, our simulations demonstrate that adding damping to coupled standard maps turns the propagating modes into diffusive ones alongside a change of the lambda-k dispersion relation from lambda approximately k to lambda approximately k2. In cases of weak damping, there is a crossover in the dynamic LV structure factors; i.e., the spectra with smaller k are akin to those of coupled circle maps while the spectra with larger k are similar to those of coupled standard maps.

Journal Article↗
PubMed2006

Hydrodynamics of polar liquid crystals.

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local C infinity v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D infinity h) in that it contains terms violating the n --> -n symmetry. First we show that these Z2-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.

Journal Article↗
PubMed2006

Nearly incompressible fluids: hydrodynamics and large scale inhomogeneity.

A system of hydrodynamic equations in the presence of large-scale inhomogeneities for a high plasma beta solar wind is derived. The theory is derived under the assumption of low turbulent Mach number and is developed for the flows where the usual incompressible description is not satisfactory and a full compressible treatment is too complex for any analytical studies. When the effects of compressibility are incorporated only weakly, a new description, referred to as "nearly incompressible hydrodynamics," is obtained. The nearly incompressible theory, was originally applied to homogeneous flows. However, large-scale gradients in density, pressure, temperature, etc., are typical in the solar wind and it was unclear how inhomogeneities would affect the usual incompressible and nearly incompressible descriptions. In the homogeneous case, the lowest order expansion of the fully compressible equations leads to the usual incompressible equations, followed at higher orders by the nearly incompressible equations, as introduced by Zank and Matthaeus. With this work we show that the inclusion of large-scale inhomogeneities (in this case time-independent and radially symmetric background solar wind) modifies the leading-order incompressible description of solar wind flow. We find, for example, that the divergence of velocity fluctuations is nonsolenoidal and that density fluctuations can be described to leading order as a passive scalar. Locally (for small lengthscales), this system of equations converges to the usual incompressible equations and we therefore use the term "locally incompressible" to describe the equations. This term should be distinguished from the term "nearly incompressible," which is reserved for higher-order corrections. Furthermore, we find that density fluctuations scale with Mach number linearly, in contrast to the original homogeneous nearly incompressible theory, in which density fluctuations scale with the square of Mach number. Inhomogeneous nearly incompressible equations for higher order fluctuation components are derived and it is shown that they converge to the usual homogeneous nearly incompressible equations in the limit of no large-scale background. We use a time and length scale separation procedure to obtain wave equations for the acoustic pressure and velocity perturbations propagating on fast-time-short-wavelength scales. On these scales, the pseudosound relation, used to relate density and pressure fluctuations, is also obtained. In both cases, the speed of propagation (sound speed) depends on background variables and therefore varies spatially. For slow-time scales, a simple pseudosound relation cannot be obtained and density and pressure fluctuations are implicitly related through a relation which can be solved only numerically. Subject to some simplifications, a generalized inhomogeneous pseudosound relation is derived. With this paper, we extend the theory of nearly incompressible hydrodynamics to flows, including the solar wind, which include large-scale inhomogeneities (in this case radially symmetric and in equilibrium).

Journal Article↗
PubMed2006

Hydrodynamic interactions and Brownian forces in colloidal suspensions: coarse-graining over time and length scales.

We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons-keeping in mind that there is no such thing as a free lunch-that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.

Journal Article↗
PubMed2000

Hydrodynamics of nuclear matter in the chiral limit

Using the Poisson bracket method, we construct the hydrodynamics of nuclear matter in the chiral limit, which describes the dynamics of all low-energy degrees of freedom, including the fluid-dynamical and pionic ones. The hydrodynamic equations contain, beside five Euler equations of relativistic fluid dynamics, N(2)(f)-1 second order equations describing propagating pions and N(2)(f)-1 first order equations describing the advection of the vector isospin charges. We present hydrodynamic arguments showing that the pion velocity vanishes at the second order phase transition at N(f) = 2.

Journal Article↗
PubMed2001

Hydrodynamic interactions in quasi-two-dimensional colloidal suspensions.

The effects of the hydrodynamic interactions on the short-time dynamics of colloidal, hard-sphere-like particles confined between two parallel walls are measured by digital videomicroscopy. We find that such effects can be described in terms of an effective two-dimensional hydrodynamic function H(k), defined as a straightforward adaptation to two dimensions of the corresponding object describing collective dynamics for the three-dimensional (3D) suspensions. Interestingly, the behavior of H(k) is qualitatively similar to the hydrodynamic function of 3D suspensions of hard spheres. We also found that for values of k where the static structure factor is 1, the dynamics is determined only by self-diffusion.

Journal Article↗
PubMed2002

Hydrodynamic force measurements: boundary slip of water on hydrophilic surfaces and electrokinetic effects.

The hydrodynamic drainage force of aqueous medium between smooth hydrophilic surfaces was measured with the colloidal probe technique up to shear rates of typically 10(4) s(-1). Measured force curves were compared to simulations. To reach agreement between experimental and simulated force curves, the hydrodynamic force had to be fitted with a model allowing for boundary slippage. Boundary slip was characterized by a slip length of 8-9 nm. Force measurements with charged surfaces could be simulated taking only hydrodynamic and electrostatic double-layer forces into account.

Journal Article↗
PubMed2002

Calculation of hydrodynamic mass for atomic impurities in helium.

We present a simple numerical procedure for calculating the irrotational hydrodynamic flow around a spherical solute in superfluid helium. The results for alkali cations are compared to recent many-body variational Monte Carlo (VMC) calculations. The helium contribution to the effective masses calculated by the VMC and hydrodynamic methods are 12.9(4.6) versus 9.4 u for Li+, 48.2(5.6) versus 52.1 u for Na+, 69.6(4.8) versus 70.1 u for K+, and 6.4(8.8) versus 6.8 for Cs+. In all cases, the agreement of the two results are in within the error estimate of the VMC calculation, demonstrating the accuracy of hydrodynamic treatment of helium motion even on the atomic length scale.

Journal Article↗
PubMed2002

Relativistic hydrodynamic scaling from the dynamics of quantum field theory.

Relativistic hydrodynamic scaling or boost invariance is a particularly important hydrodynamic regime, describing collective flows of relativistic many body systems and is used in the interpretation of experiments from high-energy cosmic rays to relativistic heavy-ion collisions. We show evidence for the emergence of hydrodynamic scaling from the dynamics of relativistic quantum field theory. We consider a scalar lambdaphi(4) model in 1+1 dimensions in the Hartree approximation and study the relativistic collisions of two kinks and the decay of a localized high-energy density region. We find that thermodynamic scalar isosurfaces show approximate boost invariance at high-energy densities.

Journal Article↗
PubMed2004

Hydrodynamic and brownian fluctuations in sedimenting suspensions.

We use a mesoscopic computer simulation method to study the interplay between hydrodynamic and Brownian fluctuations during steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.1-15. Even when the hydrodynamic interactions are an order of magnitude weaker than Brownian forces, they still induce backflow effects that dominate the reduction of the average sedimentation velocity with increasing particle packing fraction. Velocity fluctuations, on the other hand, begin to show nonequilibrium hydrodynamic character for Pe>1.

Journal Article↗
PubMed2006

Breakdown of hydrodynamics in a simple one-dimensional fluid.

We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches; e.g., the hydrodynamic profiles relax algebraically toward their equilibrium values. Deviations from local thermodynamic equilibrium are persistent, decaying as a power law of the distance to the shock layer. Nonequipartition is observed infinitely far from the shock wave, and the velocity-distribution moments exhibit multiscaling. These results question the validity of simple hydrodynamic theories to understand collective behavior in 1D fluids.

Journal Article↗
PubMed2006

Hydrodynamic flow patterns and synchronization of beating cilia.

We calculate the hydrodynamic flow field generated far from a cilium which is attached to a surface and beats periodically. In the case of two beating cilia, hydrodynamic interactions can lead to synchronization of the cilia, which are nonlinear oscillators. We present a state diagram where synchronized states occur as a function of the distance of cilia and the relative orientation of their beat. Synchronized states occur with different relative phases. In addition, asynchronous solutions exist. Our work could be relevant for the synchronized motion of cilia generating hydrodynamic flows on the surface of cells.

Animals↗