Hydrodynamic Region Research Articles

Longitudinal collective modes in simple liquid binary alloys: A computer simulation study

The dynamic collective properties of the liquid Li0.7-Mg0.3 alloy are studied by molecular-dynamics simulation. The dynamic structure factors and longitudinal current correlations at wave vectors between the hydrodynamic and kinetic regime (0.2,k, 4A 21 ) are analyzed. In order to discuss the influence of the mass difference between particles on the longitudinal modes, the same alloy, except that the mass of the heavy atoms was increased by a factor of 10, was simulated. The resulting properties are compared with those of the ordinary Li0.7-Mg0.3 alloy. It is shown that at wave vectors prior to the hydrodynamic region both fast and slow longitudinal modes of kinetic character propagate through light and heavy particles, respectively. In the hydrodynamic limit fast and slow modes merge into a single acoustic mode. It is corroborated that fast propagating modes in disparate mass liquid mixtures have a kinetic character. The number-number and concentration-concentration time correlation functions were also determined. The former shows a behavior analogous to that of the corresponding function in one-component liquids. The second reflects the existence of propagating concentration modes.

Double critical behavior and micellar size effect in the multicomponent surfactant solution

Multicomponent surfactant system, sodium dodecyl sulfate and butanol in an aqueous NaCl solution, which exhibits a closed-loop type reentrant phase separation, was investigated by light scattering experiments focusing on the double critical behaviors and the finite micellar size effect on the dynamic critical behavior. The loop size decreased with the decrease of NaCl concentration, and the double critical point appeared. Approaching the double critical point, the critical exponents ν for the long-range correlation length ξ and γ for the isothermal osmotic compressibility χT determined by use of the spinodal divergency theory showed a crossover behavior from Fisher’s renormalized Ising model values to the doubling of them. ξ and χT formed master curves as a function of εUL=|(TU−T)(TL−T)|/TUTL, and had the effective critical exponents ν=0.73 and γ=1.41 ascertaining the validity of Fisher’s renormalized Ising model. Here, TU and TL are the upper and lower critical solution temperatures, respectively. Dynamic critical behaviors were well explained in a unified manner over the hydrodynamic and critical regions by the modified dynamical droplet model taking the finite micellar size into account, which assumes that the local fluctuations activated thermally behave as the physical clusters with a fractal dimension of df=2.49 and a polydispersity exponent of τ=2.21. The evaluated monomer unit sizes are in good agreement with the micellar sizes obtained independently.

Generalized hydrodynamics of binary liquids: transverse collective modes

The parameter-free generalized collective modes approach in eight-variable approximation is applied for investigation of transverse dynamics of Lennard-Jones liquid Kr-Ar beyond the hydrodynamic region. We find four branches of propagating eigenmodes in the spectrum of transverse collective excitations. Different basis sets of dynamical variables are applied to estimate the origin of different branches in the spectrum. It is shown that for large wave numbers the general feature of transverse collective excitations is their "partial" character, while in hydrodynamic limit they are formed by collective behavior of liquid. A detailed analysis of the separated contributions from different collective modes into time correlation functions and spectral functions is performed. The condition of existence of high-frequency mass-concentration waves is derived. It is shown that high-frequency collective excitations, caused by the mass-concentration fluctuations, reflect some properties of optic phonon modes in solids.

Light scattering studies on aggregation behavior of polyvinyl chloride/dioxane solutions

In this work, the aggregation behavior of polyvinyl chloride/dioxane (PVC/DOA) solution was discussed through light scattering and viscometric measurements. From the static light scattering results, PVC/DOA solution has a negative value of the second virial coefficient, A 2 value (ca. −3.65×10 −4 cm 3 mol g −2) at 30°C, implying that a repulsive force appeared between PVC chains and DOA. The dynamic light scattering results indicate that the dynamic behavior of PVC solution could be classified into three regions by increasing the concentration of PVC. In the infinite dilution region, [ η] C<1, the single relaxation mode is considered related to the translational diffusion of the individual PVC coil. In the hydrodynamic screen region, 1<[ η] C<4, the relaxation time distribution was divided into two major relaxation modes; i.e. the fast mode resembled that of the individual PVC coil in the dilute solution, and the slow mode is considered related to the cluster formed from the aggregation of several individual coils. At higher concentrations, [ η] C>4, the polymer coils start to overlap and entangle further, then the third relaxation mode due to the transient gel network originated from the aggregation of the clusters in the concentrated solution was observed. On the other hand, the relative amplitudes of middle and slow modes for semi-dilute solutions decrease with increasing temperature. At a temperature of about 50°C, only a broad relaxation mode was observed indicating that intermolecular aggregation is disintegrated with increasing temperature, but the intramolecular aggregation of an isolated chain still exists due to the poor affinity of DOA to PVC chains in this temperature region. The poor solubility of the solvent used should be more favorable to the intramolecular aggregation of PVC chains, resulting in comparatively complex dynamic behaviors in semi-dilute solutions.

Friction in cold rolling of a low carbon steel with lubricants

Six commercial lubricants are tested during cold rolling of low carbon steel strips. The objectives are to test the ability of the oils to lower the loads on the mill; to determine the dependence of the coefficient of friction on the model used in inverse calculations and to establish the lubrication regimes during the rolling process. The roll separating forces, roll torques and the forward slip are monitored. The reduction and the speed of rolling are taken to be the independent variables. While the viscosities of the oils vary over a fairly large range, their effects on the roll forces, torques and the forward slip are not very pronounced. The oil, which caused the largest reduction of the loads on the mill is a synthetic one with no additives. The coefficients of friction are determined by two mathematical models. While both models show that the coefficients decrease with increasing speeds and reductions, their magnitudes are strongly dependent on the models. It is recommended that when the inverse technique is used to establish the friction coefficients, all three measured parameters: the force, torque and the forward slip be matched by the predicted ones. In all instances boundary or mixed lubrication regimes are in existence. The hydrodynamic region is approached but not reached.

Two-Fluid Hydrodynamics in Trapped Bose Gases and in Superfluid Helium

A review is given of recent theoretical work on the superfluid dynamics of trapped Bose gases at finite temperatures, where there is a significant fraction of non-condensate atoms. One can now reach large enough densities and collision cross-sections needed to probe the collective modes in the collision-dominated hydrodynamic region where the gas exhibits characteristic superfluid behavior involving the relative motions of the condensate and non-condensate components. The precise analogue of the Landau-Khalatnikov two-fluid hydrodynamic equations was recently derived from trapped Bose gases, starting from a generalized Gross-Pitaevskii equation for the condensate macroscopic wavefunction and a kinetic equation for the non-condensate atoms.

Electrorheological suspensions of two polarizable particles

Bi-disperse Electrorheological (ER) suspensions of two polarizable particles of the same size are investigated to understand the ER behavior of poly-disperse suspensions composed of various polarizable particles. The electrostatic polarization model is employed to describe ER suspensions, and solutions to the equation of motion are obtained by dynamic simulation. Even with the applied electric field, metastable structures and sheared configurations at a shear rate of 0.01 and 10 s-1 show no inhomogeneous higher polarizable particle distributions (no higher polarizable particle cluster formation) regardless of the ratio of the two types of particles. The shear stress increases with the increase of the higher polarizable particle concentration both in the electrostatic force and hydrodynamic force dominant regions.

Nanofiltration Mass Transfer at the Entrance Region of a Slit Laminar Flow

A numerical model to predict laminar flows hydrodynamics and concentration polarization of salt aqueous solutions in a slit is proposed and experimentally validated. Physical modeling for the flow and for the mass transfer process is incorporated, in association with the osmotic pressure constitutive equation and a variation law for the membrane intrinsic rejection coefficient. The finite volume formulation is used with the SIMPLE algorithm to solve the discretized equations derived from the partial nonlinear differential equations of the mathematical model. The convection terms of the transport equations are discretized by the second-order hybrid central differences/upwind scheme. The experimental cell is a slit 200 mm × 30 mm × 2 mm that simulates the two-dimensional hydrodynamic flow conditions of the open feed channel of a spiral wound module. The predicted values at the hydrodynamic entrance region for different permeation velocities and rejection coefficients for sodium sulfate solutions, and for a single Schmidt number of 850, are compared against the corresponding experimental values and exhibit an excellent agreement. A new mass transfer correlation Stp = 1 + 3.68 × 10-4(x/h)-1.11Re0.95Rep-1.79 is proposed.

Critical behavior of the three-dimensional Heisenberg antiferromagnetRbMnF3

The magnetic critical scattering of the near-ideal three-dimensional Heisenberg antiferromagnet (AF) ${\mathrm{RbMnF}}_{3}$ has been remeasured using neutron scattering. The critical dynamics has been studied in detail in the temperature range ${0.77T}_{N}&lt;T&lt;{1.11T}_{N},$ where ${T}_{N}$ is the N\'eel temperature. In agreement with previous measurements, at ${T}_{N}$ and for wave vectors away from the AF zone center, the scattering has a quasielastic component in addition to the inelastic response predicted by renormalization-group and mode-coupling theories. Both components scale with the dynamic exponent $z=1.43\ifmmode\pm\else\textpm\fi{}0.04$, in agreement with dynamic scaling. On cooling below ${T}_{N}$ the inelastic peaks transform into the transverse spin waves and a crossover has been observed in the dispersion from a power-law relation ${\ensuremath{\omega}}_{q}{=Aq}^{z}$ at ${T}_{N}$ to a linear behavior ${\ensuremath{\omega}}_{q}=cq$ in the hydrodynamic region below ${T}_{N}.$ The quasielastic component evolves below ${T}_{N}$ into the longitudinal susceptibility identified in an earlier polarized neutron experiment. The intensity and energy width of the longitudinal scattering decrease on cooling below ${T}_{N}.$ Down to the lowest temperatures where the longitudinal susceptibility could be measured the leading term in the scaling behavior of the energy width was ${\ensuremath{\gamma}}_{q}\ensuremath{\approx}{q}^{1.58\ifmmode\pm\else\textpm\fi{}0.03}$ (hydrodynamic theory predicts a ${q}^{2}$ law). Possible explanations for the observed behavior of the longitudinal susceptibility are discussed.

A correlation for overall mass transfer coefficients in rotating disc contactors

In this present work, a new correlation for the prediction of overall mass transfer coefficients, in terms of fundamental operating variables (viz., phase flow rates, rotor speed, column geometry, physical properties of the contacting phases), in the two hydrodynamic regions of operation, have been proposed.

SIMULTANEOUSLY DEVELOPING LAMINAR FLOW AND HEAT TRANSFER IN THE ENTRANCE REGION OF A CIRCULAR TUBE WITH CONSTANT WALL TEMPERATURE

The developing flow and heat transfer in the entry region of a heated circular tube is analyzed for the case of constant wall temperature. An integral or boundary-layer solution is presented which has a number of advantages over earlier Karman-Pohlhausen integral analyses. Thus, in the present analysis, the velocity and temperature distributions, the local and mean drag coefficients, and the local and mean Nusselt numbers approach their fully-developed values asymptotically. The new analysis is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Asthana (1978) to flow through a circular tube. This concept is extended to the combined entry-length problem by introducing a thermal transition region, herein called the thermally-filled region, between the thermal inlet boundary-layer region and the thermally fully-developed region. A thermal shape factor is also introduced which ensures smooth transition of all pertinent thermal quantities from the entrance region to the fully-developed region. Results for the variation of the local and mean Nusselt numbers with axial distance along the tube for Pr = 0.1,0.5,0.7,1,5, and 10 are presented. These results agree well with the numerical solutions of Hombeck (1965), Manohar (1969), and Hwang and Sheu (1974) and also with the correlations of Churchill and Ozoe (1973).

On the hydrodynamic theory of a magnetic liquid II. Hydrodynamic modes in the Heisenberg fluid

On the basis of our previous results (Physica A 220 (1995) 325) the collective mode spectrum of the Heisenberg ferrofluid model is studied in the hydrodynamic region. We start from the rigorous microscopic approach taking into account all conserved quantities and calculate the explicit expressions for the dispersion and damping coefficient of sound modes. It is shown that the sound velocity of Heisenberg ferrofluid at constant external magnetic field is isotropic and can be expressed by the adiabatic compressibility at constant magnetization m. We also calculate the heat and spin modes which are purely diffusive. Explicit expressions for the viscosity, thermal conductivity, spin diffusion and thermomagnetic diffusion coefficients containing time correlation functions are derived. Our results are compared with previous ones obtained mainly within phenomenological theories.

Critical ultrasonic behavior near phase transitions in BCCD crystals

Abstract The ultrasonic velocity and attenuation of longitudinal waves have been measured along the a, b and c directions as a function of frequency (10 – 70 MHz) and temperature (110 – 300 K) in single - crystal betaine calcium chloride dihydrate. The ultrasonic anomalies were observed at incomplete devil's staircase transition temperatures. The largest anomaly appeared at the normal - incommensurate phase transition at Ti ≈ 164 K Landau theory has been used to explain the experimental data below Ti. From attenuation data, the relaxation time of the amplitudon in the incommensurate phase has been estimated to be τ = (1.3 · 10−13) f 1, where t = (Ti-T)/Ti . In addition, the critical ultrasonic velocity behavior in the hydrodynamic region (ωτ≪ 1) was analyzed in terms of a scaling model. The critical - exponent value was found to be μ ≈ 0.3.

Tenside in der Textilveredlung

This paper reports on investigations of the thermal phase behaviour of microemulsions of the water-oil-amphiphile type near their plait points. Upon approaching the plait point the correlation length in the hydrodynamic region is characterized by a critical exponent v = 0.58-0.63, although the renormalized exponent of the three dimensional Ising model, v = 0.71, has been anticipated for such systems.

Influence of thermal boundary condition on laminar heat transfer in the hydrodynamic entrance region of circular ducts

Der laminare Warmeubergang bei hydrodynamischer Einlaufstromung in einem Kreisrohr wurde fur verschiedene thermische Randbedingungen durch numerische Losung der Kontinuitats-, der Bewegungs- und der Energiegleichung mit Hilfe der Finite-Differenzen-Methode berechnet. Ergebnisse werden fur linearen, sinusformigen und exponentiellen Verlauf der Warmestromdichte an der Wand in axialer Richtung dargestellt. Ein Vergleich zeigt, das der Einflu\ der thermischen Randbedingung auf den Warmeubergang mit zunehmender Ausbildung der Geschwindigkeits- und Temperaturprofile groser wird. Auserdem wurde eine verbesserte Naherungsgleichung fur den Fall konstanter Warmestromdichte bei hydrodynamischer Einlaufstromung entwickelt.

Drainage of a Partially Wetting Film: Dodecane on Silicon

Drainage of the partially wetting film dodecane on a vertical silicon substrate was investigated using image scanning ellipsometry (ISE). The ability of ISE to map every point on the surface simultaneously was demonstrated for the much more complicated case of the partially wetting fluid. Depending on the relative magnitude of the intermolecular, gravitational, and capillary forces, four flow regions were identified: the interfacial, transition, hydrodynamic, and meniscus regions. The partially wetting fluid began draining according to hydrodynamic theory, but after a short period the monotonically increasing film thickness profile became unstable and a mound or incipient drop began to form ∼1 mm from the leading edge of the fluid. Although the mound grew over time, differential drainage was never strong enough to nucleate a dry patch, and so the film drained to an adsorbed layer. Two-dimensional profiles show the thickness profile first becoming unstable in the flow direction and then evolving a seconda...

Piston ring friction loss behaviour for motored and fired reciprocating engines

AbstractA previously developed piston ring lubrication model has been further extended so that the piston ring frictional losses can be predicted in both hydrodynamic lubrication and metal‐to‐metal contact regions for various engine operating conditions. Ring friction results for two engine types are presented for both hot motoring and engine firing conditions. The hot motoring predictions were found to be in good agreement with tests. Results show that when the engine is motored, piston ring friction losses in the hydrodynamic lubrication region predominate. If the engine is fired, the losses in the metal‐to‐metal contact region become dominant due to high gas pressure and temperature effects. Ring friction loss can be significantly reduced by using low tension rings with a correct ring sliding face profile.

Dynamic structure factor in a random diffusion model

Let {Xt:≥0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew−1(Xt), where {w(x):x∈ℤd} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering functionF(q,t)=E0\(e^{iqX_l } \) (q∈ℝd) is completely monotonic int (E0 denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factorS(q, w)=2∫0∞ cos(ωt)F(q, t) exists for ω≠0 and is strictly positive. Ind=1, 2 it diverges as 1/|ω|1/2, resp. −ln(|ω|), in the limit ω→0; ind≥3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small ω such that |ω|≫D |q|2, whereD is the diffusion constant.

VISUALIZATION OF CONVECTIVE INSTABILITY PHENOMENA IN THE ENTRANCE REGION OF A HORIZONTAL RECTANGULAR CHANNEL HEATED FROM BELOW AND/OR COOLED FROM ABOVE

The developing secondary flow patterns caused by buoyancy forces in the simultaneous hydrodynamic and thermal entrance region of a horizontal rectangular channel (aspect ratio, a/b = 2) with isothermally heated lower wall and/or isothermally cooled upper wall are studied using the smoke injection method. The entrance air is at room temperature (around 23°C), and the temperature ranges for the lower and upper walls are 23-51°C and 15-23°C, respectively. The mean air velocities are 0.1, 0.2, 0.3, and 0.4 m/s. The Reynolds number varies from Re = 2.10 × 102 to 1.05 × 103 and the Grashof number ranges from Gr = 1.56 × 105 to 5.04 × 105. Photographic results reveal mixed convection, convective instability, and chaotic phenomena. Many new secondary flow patterns are revealed by this flow visualization study, and the photographic results should be useful for future theoretical study and measurements. The experiments were designed to understand flow physics.

Image scanning ellipsometry for measuring the transient, film thickness profiles of draining liquids

Image Scanning Ellipsometry, a technique to measure the two-dimensional thickness profile of a nonuniform, thin, liquid film, from several nanometers up to tens of microns, in the steady and transient states, was developed and tested. The ability of this full-field imaging technique to map every point on the surface simultaneously was demonstrated by measuring the thickness profiles of very thin, draining, liquid films in the interfacial, transition, hydrodynamic, and capillary regions. Depending on the relative size of the intermolecular, gravitational, and capillary forces, four flow regions were identified. Using a simple model for the transient film thickness profiles of a completely wetting, draining film of FC-70, the experimental results were successfully analyzed in the interfacial, transition, and hydrodynamic regions. A diffusion coefficient for the junction line between the interfacial and transition regions was theoretically and experimentally evaluated.