Effective screening of hydrodynamic interactions in charged colloidal suspensions

We investigate the hydrodynamic interaction in suspensions of charged colloidal silica spheres. The volume fraction as well as the range of the electrostatic repulsion between the spheres is varied. Using a combination of dynamic x-ray scattering, cross-correlated dynamic light scattering, and small angle x-ray scattering, the hydrodynamic function H(q) is determined experimentally. The effective hydrodynamic interactions are found to be screened, if the range of the direct interaction is relatively long and the static density correlations are strong. This observation of effective hydrodynamic screening is in marked contrast to hard-sphere-like systems.     

Driven magnetic particles on a fluid surface: pattern assisted surface flows

Magnetic microparticles suspended on the liquid-air interface and subjected to an alternating magnetic field exhibit spontaneous formation of dynamic localized snake patterns. These patterns are accompanied by four large-scale hydrodynamic vortices located at the opposite ends of the snake patterns. We report detailed studies of these large-scale vortices and their relationship to the collective response of magnetic particles in the presence of an alternating magnetic field. We present a model based on the amplitude equation for surface waves coupled to the large-scale hydrodynamic mean flow equation. The model describes both the formation of the dynamic snake patterns and the induced structure of the experimentally observed hydrodynamic flows.     

Non-hydrodynamic collective modes in liquid metals and alloys

A short review of analytical and numerical results, obtained for collective dynamics in liquid metals and alloys within a theoretical approach of Generalized Collective Modes (GCM) is presented. The GCM approach permits to represent dynamic structure factors in wide ranges of wave numbers and frequencies as a sum of contributions from hydrodynamic and non-hydrodynamic processes. The origin of collective modes that make important contributions to dynamic structure factors beyond the hydrodynamic regime in liquid metals and alloys is discussed.     

Hydrodynamic Stress Tensor in Inhomogeneous Colloidal Suspensions: an Irving-Kirkwood Extension *

Based on statistical mechanics for classical fluids, general expressions for hydrodynamic stress in inhomogeneous colloidal suspension are derived on a molecular level. The result is exactly an extension of the Iving-Kirkwood stress for atom fluids to colloidal suspensions where dynamic correlation emerges. It is found that besides the inter-particle distance, the obtained hydrodynamic stress depends closely on the velocity of the colloidal particles in the suspension, which is responsible for the appearance of the solvent-mediated hydrodynamic force. Compared to Brady's stresslets for the bulk stress, our results are applicable to inhomogeneous suspension, where the inhomogeneity and anisotropy of the dynamic correlation should be taken into account. In the near-field regime where the packing fraction of colloidal particles is high, our results can reduce to those of Brady. Therefore, our results are applicable to the suspensions with low, moderate, or even high packing fraction of colloidal particles.     

Flow waves of hierarchical pattern formation induced by chemical waves: The birth, growth and death of hydrodynamic structures

We introduce a short review of chemically driven convection together with a series of our experiments on hydrodynamic instabilities induced by chemical waves excited in the batch reactor of a Belousov-Zhabotinsky reaction. Several unresolved phenomena are picked out and possible mechanisms are discussed extensively. Interesting features of these phenomena can be summarized as being caused by the ‘global and dynamic hydrodynamic pattern induced by chemical waves’. These chemically induced global pattern of hydrodynamic phenomena may not be simply explained by the reaction-diffusion-convection model based on Marangoni instability (surface tension-driven convection), which produces only a localized structure of the convection pattern. Observed flow waves show global and dynamic patterns of convection that generate a functional structure associated with hierarchical patterns appearing in the reaction-diffusion-convection system. In particular, we clarify the existence of a continuous stream of hydrodynamic flow with growing amplitude and its rotating direction. We find that the flow does not stabilize to a motionless state until the system has self-collapsed. This new picture of the flow waves requires a revision of the reaction-diffusion-convection model. The established flow structure can be regarded as a mixing and/or transport process to supply the substrate from the peripheral region to the centre of the chemical waves to sustain the reaction. This characteristic may be a function of the hierarchical structure. A new mechanism for the viscous-elastic feature of the gas-liquid interface is discussed in order to understand these curious phenomena of interest.     

Coupling of velocity gradients to orientation densities

Velocity gradients and orientation densities are coupled in liquids composed of anisometric molecules, as is evidenced by flow birefringence and by the Rytov dip observed in VH depolarized light scattering. The coupling strength can be related to a dimensionless parameter R which can be expressed in terms of correlations over molecular quantities or, when evaluated by a hydrodynamic model, in terms of geometric factors. Both cases are discussed. Although R depends on the temporal behaviour of molecular quantities, i.e. it is a dynamic factor, it is actually a ratio of dynamic factors and can be approximated by static or equilibrium quantities. In the hydrodynamic limit, i.e. for brownian particles, this approximation is rigorously valid.     

Transient and Stationary Simulations for a Quantum Hydrodynamic Model

The transient and stationary characteristics of a one-dimensional quantum hydrodynamic model are comparatively studied for semiconductor charge transport in a resonant tunnelling diode. When the bias is not small, our numerical results show a deviation of the asymptotic transient solutions from the stationary ones. A dynamic instability accounts for such deviation. The stationary quantum hydrodynamic model is therefore unsuitable in general for simulating quantum devices.     

Hydrodynamic symmetries for the Whitham equations for the sine-Gordon equation

The effective structure of the hydrodynamic symmetries for the Whitham equations, derived for simplest one-phase solutions of the sine-Gordon equation, is presented. This structure is analogous to the one, that was obtained for the Whitham equations for the KdV equation and the nonlinear Schrödinger equation (NSE). The hydrodynamic symmetries for the gas dynamic equations are described.     

Importance of hydrodynamic shielding for the dynamic behavior of short polyelectrolyte chains

The dynamic behavior of polyelectrolyte chains in the oligomer range is investigated with coarse-grained molecular dynamics simulation and compared to data obtained by two different experimental methods, namely, capillary electrophoresis and electrophoresis NMR. We find excellent agreement of experiments and simulations when hydrodynamic interactions are accounted for in the simulations. We show that the electrophoretic mobility exhibits a maximum in the oligomer range and for the first time illustrate that this maximum is due to the hydrodynamical shielding between the chain monomers. Our findings demonstrate convincingly that it is possible to model dynamic behavior of polyelectrolytes using coarse-grained models for both the polyelectrolyte chains and the solvent induced hydrodynamic interactions.     

Hydrodynamic boundary conditions: An emergent behavior of fluid–solid interactions

By using the Onsager principle of minimum energy dissipation, the hydrodynamic boundary conditions at the fluid–solid interface are shown to be the natural emergent behavior of microscopic interactions that lead to the interfacial tension and the tangential friction at the fluid–solid interface [T. Qian, C. Qiu, P. Sheng, J. Fluid Mech. 611 (2008) 333]. This is satisfying because the equations of motion, e.g., the Stokes equation, and the hydrodynamic boundary conditions can now be derived from a unified framework. The resulting continuum hydrodynamic formulation yields predictions for immiscible two-phase flows that are in quantitative agreement with molecular dynamic simulations. In particular, the classical problem of the moving contact line is resolved. We also show results on the moving contact line over chemically patterned surfaces which exhibit striking nanoscale characteristics as well as sub-quadratic dependence of the moving contact line dissipation on its average velocity.     

A New Method for Analysis of the Fluid Interaction with a Deformable Membrane

The lattice Boltzmann cellular automaton method has been successfully extended for analysis of fluid interactions with a deformable membrane or web. The hydrodynamic forces on the solid web are obtained through computation of the fluid flow stress at the moving boundary using the lattice Boltzmann method. Analysis of solid boundary deformation or vibration due to hydrodynamic force is based on Newtonian dynamics and a molecular dynamic type approach.     

Hydroelastic dynamic characteristics of a slender axis-symmetric body

The slender axis-symmetric submarine body moving in the vertical plane is the object of our investigation.A coupling model is developed where displacements of a solid body as a Euler beam(consisting of rigid motions and elastic deformations) and fluid pressures are employed as basic independent variables,including the interaction between hydrodynamic forces and structure dynamic forces.Firstly the hydrodynamic forces,depending on and conversely influencing body motions,are taken into account as the governing equations.The expressions of fluid pressure are derived based on the potential theory.The characteristics of fluid pressure,including its components,distribution and effect on structure dynamics,are analyzed.Then the coupling model is solved numerically by means of a finite element method(FEM).This avoids the complicacy,combining CFD(fluid) and FEM(structure),of direct numerical simulation,and allows the body with a non-strict ideal shape so as to be more suitable for practical engineering.An illustrative example is given in which the hydroelastic dynamic characteristics,natural frequencies and modes of a submarine body are analyzed and compared with experimental results.Satisfactory agreement is observed and the model presented in this paper is shown to be valid.     

Magnetic response functions I: Conserving systems

The magnetic dynamic response function is studied in detail for systems in which the magnetization is conserved and is carried by the spin of one type of particle. Hydrodynamic equations for the magnetization in magnetic systems in the paramagnetic and ferromagnetic regimes in the absence of an external field are derived and are shown to be inapplicable when there is an external field present. The hydrodynamic forms of the response function are used to motivate general analytic expressions for the full dynamic response function. Some consideration is given to feasibility of observing the hydrodynamic regime in real systems.     

Dissipation and large thermodynamic fluctuations

The results of recent work of Kipnis, Olla, and Varadhan on the dynamic large deviations from a hydrodynamic limit for some interacting particle models are formally extended to a general hydrodynamic situation, including non-equilibrium steady states, as a fluctuation-dissipation hypothesis. The basic conjecture is that the exponent of decay in the probability of a large thermodynamic fluctuation is given by the dissipation of the force required to produce the fluctuation. It is shown that this hypothesis leads to a nonlinear version of Onsager-Machlup fluctuation theory that had previously been proposed by Graham. A direct consequence of the theory is a dynamic variational principle for the most probable thermodynamic history subject to imposed constraints (Onsager's principle of least dissipation). Following Graham, the theory leads also to a generalized potential, analogous to an equilibrium free energy, for the nonequilibrium steady state and an associated static variational principle. Finally, a formulation of nonlinear fluctuating hydrodynamics is proposed in which the noise enters multiplicatively so as to reproduce the conjectured large-deviations theory on a formal analogy with the results of Freidlin and Wentzell for finite-dimensional systems.     

Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings

The major purpose of this study is to predict the dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings in the presence of rigid support movements, the target application being turbochargers of vehicles or rotating machines subject to seismic excitation. The proposed on-board rotor model is based on Timoshenko beam finite elements. The dynamic modeling takes into account the geometric asymmetry of shaft and/or rigid disk as well as the six deterministic translations and rotations of the rotor rigid support. Depending on the type of analysis used for the bearing, the fluid film forces computed with the Reynolds equation are linear/nonlinear. Thus the application of Lagrange's equations yields the linear/nonlinear equations of motion of the rotating rotor in bending with respect to the moving rigid support which represents a non-inertial frame of reference. These equations are solved using the implicit Newmark time-step integration scheme. Due to the geometric asymmetry of the rotor and to the rotational motions of the support, the equations of motion include time-varying parametric terms which can lead to lateral dynamic instability. The influence of sinusoidal rotational or translational motions of the support, the accuracy of the linear 8-coefficient bearing model and the interest of the nonlinear model for a hydrodynamic journal bearing are examined and discussed by means of stability charts, orbits of the rotor, time history responses, fast Fourier transforms, bifurcation diagrams as well as Poincaré maps.     

On the hydrodynamic theory of a magnetic liquid I. General description

Using Zubarev's method of nonequilibrium statistical operator, the generalized hydrodynamic equations are obtained for a model of magnetic liquid in an inhomogeneous external field. In this model the “liquid” subsystem is treated as a classical one and the “magnetic” subsystem is described by quantum mechanical methods. The properties of the transport equations are analysed in the case of a weak nonequilibrium. The equations for time correlation functions and collective mode spectrum are also found in the same manner. It is shown that the generalized hydrodynamic equations reduce to the well-known results in the limiting cases when the dynamic variables of one subsystem are formally neglected. As an illustration, a simple model of spin relaxation is considered, and the frequency matrix and the matrix of memory functions are calculated. A comparison with previous works is made.     

Nonstationary motion of electrons in a double plasma layer subjected to the self-consistent electric field of the space charge

Nonstationary 1D equations describing the motion of electrons in a double plasma layer subjected to the self-consistent electric field of the space charge are investigated with allowance for friction force. Analytical solutions to a set of nonlinear hydrodynamic equations for plasma electrons are derived. The variation of the electric field strength, as well as of the electron velocity and concentration, in space and time is found. Electron plasma motions of different types of symmetry are characterized in terms of dynamic parameters.     

NVH and reliability analyses of the engine with different interaction models between the crankshaft and bearing

The precision of the interaction model is very important to predict NVH and the reliability of an internal combustion engine. The interaction model between the crankshaft and the bearing is hard to be established precisely due to its complex interaction relationship and dynamic characteristic. In this paper, the elasto-hydrodynamic lubrication model with cavitation theory is built to couple with multi-body dynamic theory to analyze the noise and reliability of the engine, the results were compared with nonlinear spring model and hydrodynamic lubrication model based on a typical in-line six cylinder engines, such as load carrying capacity of the bearing, velocity level of the engine surface, noise level of engine surface and stress of the crankshaft. The results showed that the vibration, noise and stress prediction difference is due to the exciting of the oil film pressure distribution, rigid and flexible body that is used to build the dynamic model will lead the load capacity of the bearing to be great different. Nonlinear spring model and hydrodynamic lubrication model are precise enough to predict the vibration or noise. The All the analysis will provide the guidance for the engine NVH optimization and structural reliability design.     

Electrokinetic and hydrodynamic properties of charged-particles systems

Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective diffusion coefficients, sedimentation coefficients, and electrophoretic mobilities and conductivities of ionic particle species in an external electric field. Advances by our group are also discussed, including a novel mode-coupling-theory method for conduction-diffusion and viscoelastic properties of strong electrolyte solutions. Furthermore, results are presented for dispersions of solvent-permeable particles, and particles with non-zero hydrodynamic surface slip. The concentration-dependent swelling of ionic microgels is discussed, as well as a far-reaching dynamic scaling behavior relating colloidal long- to short-time dynamics.     

Hydrodynamic interactions of dilute polymer solutions in elongational flow

Dumbbell models are only crude representations of actual polymer molecules, but their simplicity allows for explicit calculations which in many instances have shed light on the connection between molecular properties and rheological behavior. On the other hand, hydrodynamic interactions are known to strongly influence the dynamic response of polymer solutions and this makes the representation of the hydrodynamic drag an important aspect in the calculations. In the present work, the effects of the state of flow are incorporated explicitly in the frictional properties of the FENE model of a dilute polymer solution. Results for the steady elongational viscosity and the mean square end-to-end distance arc presented.