Marangoni convection in a rectangular container

If the free liquid-gas interface of a liquid in a rectangular Container is subjected to a temperature gra-dient the shear stress on the free liquid surface being temperature dependent transmits by viscous traction a thermo-capillary convection into the bulk of the liquid. For constant temperature T ₁ at one wall and T ₂ at the other a steady Marangoni convection takes place while for time-oscillatory temperatures of the walls a time-dependent thermo-capillary convection appears, which will create wave patterns on the free liquid surface. They shall, depending on the forcing frequency of the temperature, exhibit resonance peaks. The velocity distribution, the response magnitude inside the Container, the forced free surface displacement and the influence of the Prandtl number have been investigated.     

Combined thermo-capillary- and natural convection and g-jitter in a constant micro-gravity field

Since a temperature gradient at the free liquid surface of a z-independent liquid column induces a thermo-capillary convection and since the residual gravity in a space laboratory still renders a natural convection, the combined effect is of importance for space processings and is therefore investigated. Stream functions and velocity distributions have been derived analytically. Isothermal-and stream lines have been presented for various temperature distributions. From the various unsteady cases only theg-jitter case has been evaluated numerically. It was found that depending on the magnitude of the temperature and Bond number the convection may influence the materials processing considerably and may contribute to reduced quality of the products.     

The'thin-film' state of 4He on Cs and Rb

At temperatures less than the wetting temperature, T _w, ⁴ He exists in equilibrium, either as a thin film on the surface of Cs or Rb, or as a macroscopic drop with a finite contact angle. The thin-film state is at most around a few monolayers thick and can exist as a two-dimensional (2D) gas or a 2D liquid. We present evidence of a gas /liquid transition at T _gl 1.5K on Cs. For T < T _gl the gas density falls rapidly with decreasing temperature to 10 ^–6 monolayers at T = 0.1K. On Rb there can be a superfluid thin liquid film for T T _w but no 2D gas state has been seen. We discuss the free energy of the solid/vapour interface and its temperature dependence.     

Localization and Ordering of Carriers in a Quasi-One-Dimensional Electron System on Liquid Helium

Charge transport in a quasi-one-dimensional (Q1D) electron system on liquid helium surface is studied in a temperature range 0.1–1.3 K at linear electron densities 6×10³–10⁵ cm⁻¹ in confining electric fields up to 1000 V/cm. It is shown that the electron conductivity increases with decreasing temperature T and starts to decrease passing through a maximum at T≈0.8 K. The plasma frequency ω _p of the electrons in Q1D channels has been estimated; the value of ω _p is much larger than that for free electrons. We attribute this effect to localization of carriers and the formation of polarons (microdimples on the liquid helium surface). The mobility of polarons is smaller than that for free electrons. The decrease in the conductivity at T<0.8 K may be connected with spatial ordering of the polarons in Q1D channels.     

Two-Dimensional Numerical Simulation for Flow Pattern Transition of Thermal-Solutal Capillary Convection in an Annular Pool

In order to understand the transition characteristics of the thermal-solutal capillary convection in an annular pool, a series of two-dimensional numerical simulations were conducted. The bottom of the pool is adiabatic rigid wall and the top is adiabatic and non-deformable free surface. The inner and outer cylindrical walls maintain at constant temperature and solute concentration, respectively. The thermo-capillary force is supposed to equal to the solute-capillary force, but their directions are contrary. Results show that the thermal-solutal capillary convection is steady at a small Reylonds number. When the capillary Reynolds number exceeds a critical value, the steady flow transits into unstable thermal-solutal capillary convection. The transition from the steady to oscillatory flow undergoes a Hopf bifurcation. Furthermore, the effects of the liquid layer aspect ratio, the radius ratio, the Prandtl number and the Lewis number on the onset of flow pattern transition are discussed. The physical mechanism of the unstable thermal-solutal capillary convection is also analyzed.     

The surface pressure in a faceted nanocrystal

An expression for the surface pressure P _sf in a nanocrystal with a free surface is obtained. The nanocrystal is assumed to have the shape of a parallelepiped with a square base and the number of atoms N that can vary from eight to infinity. The surface pressure depends on the nanocrystal size (P _sf ∼ N ^{− 1/3}), and this dependence increases when the shape of the nanocrystal deviates from cubic. For any substance, there exists a certain inversion temperature T _i at which the P _sf(T) curves for nanocrystals of various dimensions intersect. The dispersion of nanocrystals leads to a growth of the surface pressure at T < T _i and to a decrease in this pressure at T > T _i . It is also established that, as the size of nanocrystals decreases, the surface pressure produces compression of the crystals below a certain temperature T _e0 and stretches the crystals at higher temperatures.     

Effects of wetted wall on laminar natural convection in vertical annular ducts

Abstract

A detailed numerical analysis is performed to investigate the effects of latent heat exchange, in connection with evaporation of the liquid film on the wall, on the natural convection heat transfer in vertical concentric annuli. Major governing parameters identified are Gr_T, Gr_M, Pr, Sc, and N. Results are specifically presented for an air‐water system under various heating conditions to illustrate the latent heat transport during the evaporation process. The effects of the channel length, ratio of radii N and wetted wall temperature on the momentum, heat and mass transfer are examined in detail. Tremendous enhancement in heat transfer due to the exchange of latent heat was clearly demonstrated.     

Equation of State for Molten Alkali Metals from Surface Tension. Part II

This work presents a new method for predicting the equation of state for molten alkali metals, based on statistical–mechanical perturbation theory from two scaling constants that are available from measurements at ordinary pressures and temperatures. The scaling constants are the surface tension and the liquid density at the boiling temperature (_b, _b). Also, a reference temperature, T _Ref, is presented at which the product (T _Ref T _b ^1/2 ) is an advantageous corresponding temperature for the second virial coefficient, B ₂(T). The virial coefficient of alkali metals cannot be expected to obey a law of corresponding states for normal fluids, because two singlet and triplet potentials are involved. The free parameter of the Ihm–Song–Mason equation of state compensates for the uncertainties in B ₂(T). The vapor pressure of molten alkali metals at low temperatures is very low and the experimental data for B ₂(T) of these metals are scarce. Therefore, an equation of state for alkali metals from the surface tension and liquid density at boiling temperature (_b, _b) is a suitable choice. The results, the density of Li through Cs from the melting point up to several hundred degrees above the boiling temperature, are within 5%.     

Non-Darcy regime mixed convection on vertical plates in saturated porous media with lateral mass flux

Summary A unified treatment is presented of mixed convection on vertical plates embedded in fluid saturated porous media with prescribed variable plate temperature or surface heat flux for the case of non-Darcy limiting regime. The plates are permeable with lateral mass flux. By suitable similarity transformations, it is shown that the two problems of prescribed temperature and prescribed heat flux lead to identical differential equations with two common boundary conditions and third boundary condition differing in the two cases. The effect of lateral mass flux and the free stream on the Nusselt number and the energy transport by the boundary layer is investigated. The unified approach to the mixed convection problem includes free convection problem as a special case. Exact analytical solutions are obtained for two cases of free convection problem.Notation b inertial coefficient - c specific heat - D _p pore diameter - E rate of upward energy transport - Ê dimensionless rate of energy transport - f dimensionless stream function - f _w mass flux parameter - g acceleration due to gravity - k thermal conductivity - K permeability of the porous medium - m exponent in the variation of heat flux - M mixed convection parameter - Nu _x Nusselt number - Pe _x Peclet number - q _w surface heat flux - Ra _x local Rayleigh number - Ra _x ^* modified local Rayleigh number - T temperature - T _e ambient temperature - T _w plate temperature - T _w temperature difference=T _w-T_e - u velocity in thex-direction - u _e free stream velocity - v velocity in they-direction - v _w lateral velocity at the plate - x coordinate along the plate in the upward direction - y coordinate normal to the plate - equivalent thermal diffusivity =k/c _e - coefficient of thermal expansion - porosity - dimensionless variable - dimensionless temperature - viscosity - fluid density - _e ambient density - exponent in the variation of plate temperature - stream function     

Texturing by cooling a metallic melt in a magnetic field

Abstract

Processing in a magnetic field leads to the texturing of materials along an easy-magnetization axis when a minimum anisotropy energy exists at the processing temperature; the magnetic field can be applied to a particle assembly embedded into a liquid, or to a solid at a high diffusion temperature close to the melting temperature or between the liquidus and the solidus temperatures in a region of partial melting. It has been shown in many experiments that texturing is easy to achieve in congruent and noncongruent compounds by applying the field above the melting temperature T_m or above the liquidus temperature of alloys. Texturing from a melt is successful when the overheating temperature is just a few degrees above T_m and fails when the processing time above T_m is too long or when the overheating temperature is too high; these observations indicate the presence of unmelted crystals above T_m with a size depending on these two variables that act as growth nuclei. A recent model that predicts the existence of unmelted crystals above the melting temperature is used to calculate their radius in a bismuth melt.     

Contact Angle of Liquid 4He on Cs: Evidence for Ripplons at the He-Cs Interface

Two independent methods to measure the contact angle, , of isotopically pure ⁴ He on Cs are described, and applied to the same Cs sample. The two methods agree well. The contact angle as a function of temperature is measured and clearly shows a first order surface phase transition with a wetting temperature T _w = 2 K. From (T) the difference in surface free energy of the Cs-vapour interface and the Cs-liquid interface is calculated. Its large temperature dependence suggests the existence of ripplons at the liquid He-Cs interface. This surprising possibility is discussed.     

Hydromagnetic convection at a continuous moving surface

Summary Exact solution for hydromagnetic convection at a continous moving surface with uniform suction is obtained. Flow of this type represents a new class of boundary-layer problems, with solutions substantially different from those for boundary-layer flow at a surface of finite length. Moreover, this is an exact solution of the complete Navier-Stokes equations (including, buoyancy force-term). The solutions for the velocity and skin friction are evaluated numerically for several sets of values of the parameters;G, the Grashof number,P, the Prandtl number, andM, the Hartmann number. It is observed that there is a reverse flow in the boundary-layer due to heating of the fluid (close to the moving surface). That is, whenT _w>T , the fluid in the boundary-layer will be heated up and thus the free convection currents will set in. Also, it is observed that, there is an increase in the skin friction (absolute) with increasingG, P andM.With 7 Figures     

Nucleate boiling

The study deals with the effect of the surface conditions on the nucleate boiling curve. A relation is proposed which describes the complete nucleate boiling curve.Notation q thermal flux - q* thermal flux at which the liquid boils after one-phase convection - q_c thermal flux during one-phase convection - q_cr1, q_cr2 first and the second critical thermal flux - T saturation temperature - T superheat of the heating surface relative to the saturation temperature - T* superheat prior to boiling of the liquid after one-phase convection - T_cr1 superheat during the first boiling crisis - T_cr3min minimum superheat at which the third boiling crisis can occur - P pressure - P_cr critical pressure - heat transfer coefficient during nucleate boiling - R_cr radius of a critical vapor forming nucleus - coefficient of surface tension - r latent heat of evaporation - thermal conductivity of the liquid - kinematic viscosity of the liquid - , densities of the liquid and the vapor - g gravitational constant - k Boltzmann constant - N Avogadro number - h Planck's constant Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 394–401, March, 1981.     

Surface glass transition temperatures of monodisperse polystyrene films by scanning force microscopy

Surface molecular motion of monodisperse polystyrene (PS) films was examined by scanning viscoelasticity microscopy (SVM) in conjunction with lateral force microscopy (LFM). The dynamic storage modulus, ?, and loss tangent, tan d , at a PS film surface with a smaller number-average molecular weight, M_n, than 40k were found to be smaller and larger than those for the bulk sample even at room temperature, meaning that the PS surface is in a glass–rubber transition state or a fully rubbery one at this temperature if the M_n, is small. In order to elucidate quantitatively how vigorous the molecular motion at the PS surface is, SVM and LFM measurements were made at various temperatures. The glass transition temperature, T_g, at the surface wasdiscerned to be markedly lower than its bulk T_g, and the discrepancy of T_g between surface and bulk becomes larger with the decreasing M_n. Such an intensive activation of thermal molecular motion at the PS surfaces can be explained in terms of an excess free volume in the vicinit of the film surfaceinduced by the preferential segregation of chain end groups.     

Alkali halide surfaces near melting: Wetting and nanofriction properties

Alkali halide (1 0 0) crystal surfaces are poorly wetted by their own melt at the triple point. We carried out simulations for NaCl(1 0 0) within the well tested BMHFT model potential. Calculations of the solid–vapor, solid–liquid and liquid–vapor free energies showed that solid NaCl(1 0 0) is a non-melting surface, and explain its bad wetting in detail. The extreme stability of NaCl(1 0 0) is ideal for a study of the nanofriction in the high temperature regime, close to and even above the bulk melting temperature (T_M). Our simulations reveal in this regime two distinct and opposite phenomena for plowing and for grazing friction. We found a frictional drop close to T_M for deep ploughing and wear, but on the contrary a frictional rise for grazing, wearless sliding. For both phenomena we obtain a fresh microscopic understanding, relating the former to “skating” through a local liquid cloud, the latter to softening of the free substrate surface. It is argued that both phenomena, to be pursued experimentally, should be much more general than the specific NaCl surface case. Most metals in particular possessing one or more close packed non-melting surface, such as Pb, Al or Au(1 1 1), should behave quite similarly.     

Simulation studies of the hydrodynamics in high-temperature solutions for crystal growth. VI. Temperature fluctuations at the crystal/liquid interface

The temperature fluctuations at the crystal/liquid interface have been studied using model liquids. The character of the fluctuations varied depending on whether in the liquid there was only free convection or both free and forced convections were simultaneously present. It has been established that in the second case the amplitude of fluctuations is determined mainly by the rate of the resultant convection flow and the liquid viscosity. A maximum amplitude of fluctuations is observed at a resultant flow rate w_fl = O when the free and forced convections proceed in opposite directions, and at w_fl = min when both convection flows have the same direction. Larger amplitudes of temperature fluctuations are registered in low-viscosity liquids. The conditions under which a flat crystal/liquid interface showing no temperature fluctuations should be formed have been determined for crystal diameters of 10, 15 and 20 mm, respectively.     

Thermocapillary convection in a spherical drop partly attached to a spherical wall

For a liquid globule, partly captured in spherical caps of different meridian angles the thermo-capillary flow has been determined due to the change of temperature on the liquid surface. The variation of the applied temperature on the liquid surface causes a variation of the surface tension and therefore a tangential force moving from warm to cold. The streamlines are presented for linear and quadratic temperature distribution on the liquid surface. As the cap angle α increases the center of the ring vortex moves down and towards the free liquid surface. In addition the flow exhibits with increasing magnitude of cap coverage a reduced velocity distribution. For a quadratic temperature distribution the existence of two opposite vortex rings are shown for α<π/2. The upper vortex ring disappears as α becomes larger than π/2. In addition we notice the shift of the vortex core towards the free surface and bottom of the drop.     

Escape rate of two-dimensional electrons on a liquid helium surface around 1 K

Electron escape from a two-dimensional surface state on liquid helium to three-dimensional free space is studied. A thermal-activation-type temperature dependence of the escape rate is observed at 1.1>T>0.9 K for the first time. The mechanism of electron escape is discussed.     

Time-dependent thermal convection in dilute solutions of 3He in superfluid 4He

Time-dependent thermal convection can occur in a unity-aspect-ratio Rayleigh-Beard convection cell containing a dilute solution of ³He in superfluid ⁴He when the fluid is heated from above. Results are presented primarily for a 0.24 mole % He solution at 0.925 K. Means is provided for introducing heat at the top and separately for a central plug and an outer ring such that both are at a constant temperature gDT above the bottom. A critical temperature difference T _cfor convection can be defined above which both steady and time-dependent convection occur. The time-dependent effects include a region of T. near T _cand characterized only by excessive noise, a region of somewhat higher T where there are intermittent major changes in the plug heating rate with a time distribution like that for random events, and a region at still higher T where periodic but nonsinusoidal variation of the heat flow is observed. When a long enough time, several months, has elapsed after cooling down the apparatus, time-dependent states no longer occur, and the heat flow above T _cis limited to steady convection. Briefly raising the temperature of the apparatus to 77 K is sufficient to restore the possibility of time-dependent states.     

Thermodynamic behaviour of undercooled melts

The Gibbs free energy difference (ΔG) between the undercooled liquid and the equilibrium solid phases has been studied for the various kinds of glass forming melts such as metallic, molecular and oxides melts using the hole theory of liquids and an excellent agreement is found between calculated and experimental values of ΔG. The study is made for non-glass forming melts also. The temperature dependence of enthalpy difference (ΔH) and entropy difference (ΔS) between the two phases, liquid and solid, has also been studied. The Kauzmann temperature (T ₀) has been estimated using the expression for ΔS and a linear relation is found between the reduced glass transition temperature (T _g/T _m) and (T ₀)/T _m). The residual entropy (ΔS _R) has been estimated for glass forming melts and an attempt is made to correlate ΔS _R,T _g,T ₀, andT _m which play a very important role in the study of glass forming melts.