Proper orthogonal decomposition of oscillatory Marangoni flow in half-zone liquid bridges of low-Pr fluids

Proper orthogonal decomposition (POD) using method of snapshots was performed on three different types of oscillatory Marangoni flows in half-zone liquid bridges of low-Pr fluid (Pr = 0.01). For each oscillation type, a series of characteristic modes (eigenfunctions) have been extracted from the velocity and temperature disturbances, and the POD provided spatial structures of the eigenfunctions, their oscillation frequencies, amplitudes, and phase shifts between them. The present analyses revealed the common features of the characteristic modes for different oscillation modes: four major velocity eigenfunctions captured more than 99% of the velocity fluctuation energy form two pairs, one of which is the most energetic. Different from the velocity disturbance, one of the major temperature eigenfunctions makes the dominant contribution to the temperature fluctuation energy. On the other hand, within the most energetic velocity eigenfuction pair, the two eigenfunctions have similar spatial structures and were tightly coupled to oscillate with the same frequency, and it was determined that the spatial structures and phase shifts of the eigenfunctions produced the different oscillatory disturbances. The interaction of other major modes only enriches the secondary spatio-temporal structures of the oscillatory disturbances. Moreover, the present analyses imply that the oscillatory disturbance, which is hydrodynamic in nature, primarily originates from the interior of the liquid bridge. (C) 2007 Elsevier B.V. All rights reserved.

Growth of liquid bridge in AFM

Capillary forces are dominant in adhesive forces measured with an atomic force microscope (AFM) in ambient air, which are thought to be dependent on water film thickness, relative humidity and the free energy of the water film. In this paper, besides these factors, we study the nature of the 'pull-off' force on a variety of atmospheres as a function of the contact time. It is found that capillary forces strongly depend on the contact time. In lower relative humidity atmosphere, the adhesion force is almost independent of the contact time. However, in higher relative humidity, the adhesion force increases with the contact time. Based on the experiment and a model that we present in this paper, the growth of the liquid bridge can be seen as undergoing two processes: one is water vapour condensation; the other is the motion of the thin liquid film that is absorbed on the substrate. The experiment and the growth model presented in this paper have direct relevance to the working mechanism of AFM in ambient air.

Study on flow characteristics of solid/liquid system in lysozyme crystal growth

During the process of lysozyme protein crystallization with batch method, the macroscopic flow field of solid/liquid system was observed by particle image velocimetry (PIV). Furthermore, a normal growth rate of (110) face and local flow field around a single protein crystal were obtained by a long work distance microscope. The experimental results showed that the average velocity, the maximal velocity of macroscopic solid/liquid system and the velocity of local flow field around single protein crystal were fluctuant. The effective boundary layer thickness delta(eff), the concentration at the interface Q and the characteristic velocity V were calculated using a convection-diffusion model. The results showed that the growth of lysozyme crystal in this experiment was dominated by interfacial kinetics rather than bulk transport, and the function of buoyancy-driven flow in bulk transport was small, however, the effect of bulk transport in crystal growth had a tendency to increase with the increase of lysozyme concentration. The calculated results, also showed that the order of magnitude of shear force was about 10(-21) N, which was much less than the bond force between the lysozyme molecules. Therefore the shear force induced by buoyancy-driven flows cannot remove the protein molecules from the interface of crystal.

Studies on the phase behavior of lyotropic liquid crystal in DAD/C4OH/n-C8H18/D2O system

The lytropic liquid crystals in dodecanic acid diethanolamine (DAD)/n-butanol (C4OH)/octane (n-C8H18)/deuteron (D2O) system were studied to determine the phase regions and were investigated by H-2-NMR spectroscopy,optical polarizing microscope and small-angle X-ray diffraction (SAXD) methods. The results indicate that the lamellar, hexagonal and cubic liquid crystals all exist in the above system. Keeping the weight ratio of DAD and C4OH constant,the microphase structure, H-2 quadruple splitting and the interlayer spacing are all changed with the addition of deuteron.

Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude

Free surface waves in a cylinder of liquid under vertical excitation with slowly modulated amplitude are investigated in the current paper. It is shown by both theoretical analysis and numerical simulation that chaos may occur even for a single mode with modulation which can be used to explain Gollub and Meyer's experiment. The implied resonant mechanism accounting for this phenomenon is further elucidated.

Experimental study of thermocapillary convection on a liquid bridge consisting of fluid with low Prandtl number in a floating half-zone

A device of mercury liquid bridge of floating half-zone is designed to experimentally explore thermocapillary convection and its instability of a low Prandtl number liquid. Noncontacted diagnostic techniques were developed to monitor surface flow and surface deformation. The surface flow and the influence of a growing surface film (or skin) on the flow were observed. It is shown that the film is a key factor in changing the behavior associated with the thermocapillary convection. The experiment indicates that the critical Marangoni number should be much higher than that expected by the numerical simulation. The condition and process of surface film growth are discussed. The surface oscillation of the mercury bridge wrapped with ''dirt-film'' was observed, and the characteristics and the frequency associated with this oscillation are given.

Numerical simulation of coherent structure in two-dimensional compressible mixing layers

The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schemes. The process of development of flow structure is presented: loss of stability, development of Kelvin-Helmholtz instability, rolling up and pairing. The time and space development of the plane mixing layer and influence of the compressibility are investigated.

Experiment on the thermocapillary convection of a mercury liquid bridge in a floating half zone

A liquid bridge of a floating half zone consisting of liquid mercury sealed in a glass tube with nitrogen atmosphere was used for the experiment of thermocapillary convection with a low Prandtl number liquid. A non-contacted diagnostic method was developed to monitor the surface flow and the surface oscillation. A growing surface film (or skin) is a crucial source to suppress thermocapillary convection, and is discussed in this paper. For the case of a mercury Liquid bridge, the critical Marangoni number was obtained as 900, and the oscillatory frequency was around 5 Hz.

Tensile and compressive deformation of a short-glass-fiber-reinforced liquid-crystalline polymer

Results of tensile and compression tests on a short-glass-fiber-reinforced thermotropic liquid crystalline polymer are presented. The effect of strain rate on the compression stress-strain characteristics has been investigated over a wide range of strain rates epsilon between 10(-4) and 350 s-1. The low-strain-rate tests were conducted using a screw-driven universal tensile tester, while the high-strain-rate tests were carried out using the split Hopkinson pressure bar technique. The compression modulus was shown to vary with log10 (epsilon) in a bilinear manner. The compression modulus is insensitive to strain rate in the low-strain-rate regime (epsilon = 10(-4) - 10(-2) s-1), but it increases more rapidly with epsilon at higher epsilon. The compression strength changes linearly with log10 (epsilon) over the entire strain-rate range. The fracture surfaces were examined by scanning electron microscopy.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection .1. Experiments

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was experimentally studied, and discussions were concentrated on the influence of liquid bridge volume on the onset of oscillation. Distributions of critical applied temperature difference and frequency depending on the volume of the liquid bridge were obtained, and there was a gap range of liquid volume which separated the curve of marginal stability into two parts for fixed rod diameter and aspect ratio. The results imply that the volume of the liquid bridge is a sensitive critical parameter for the onset of oscillation. The implication on the instability is also discussed in the present paper.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection .2. Numerical-simulation

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was studied numerically for an unsteady and two-dimensional model, and studies were concentrated on the influence of liquid bridge volume on the onset of oscillation in comparison with the experimental results in the Paper I. The numerical results agree with the experimental ones presented in the previous paper, in which the distributions of critical applied temperature difference depending on the volume of liquid bridge and a gap range of liquid volume in marginal stability curve were obtained.

Experimental-study of free-surface oscillations of a liquid bridge by optical diagnostics

A non-contact optical method, consisting of a projecting grating technique for the relative measurement of a surface, and a technique of absolute measurement at a fixed point on the surface, are applied to measure the free surface vibration in a liquid bridge of half floating zone with small typical scale of a few of mm for emphasizing the thermocapillary effect in comparison with the effect of buoyancy. The radii variations in both longitudinal and azimuthal directions are obtained, and, then, the feature of surface wave could be analyzed in detail. The results show that there are values of principal oscillatory frequencies at different positions of free surface. The amplitudes of surface waves in longitudinal and azimuthal directions are several mum and several tenths of mum in order of magnitude. The phase of two-dimensional surface waves is different at different height for fixed cross section or at different azimuthal angle for fixed height. The wave features are discussed for the cases of typical parameter ranges.

The motion of solid particles in a liquid with vertical temperature-gradient

A ground-experiment study on the motions of solid particles in liquid media with vertical temperature gradient is performed in this paper. The movement of solid spheres toward the heating end of a close cell is observed. The behavior and features of the motions examined are quite similar to thermocapillary migration of bubbles and drops in a liquid. The motion velocities of particles measured are about 10(-3) to 10(-4) mm\s. The velocity is compared with the velocity of particles floated in two liquid media. The physical mechanism of motion is explored.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

The kinetic-theory for dilute solid liquid 2-phase flow

On the basis of a brief review of the continuum theory for macroscopic descriptions and the kinetic theory for microscopic descriptions in solid/liquid two-phase flows, some suggestions are presented, i.e. the solid phase may be described by the Boltzmann equation and the liquid phase still be described by conservation laws in the continuum theory. Among them the action force on the particles by the liquid fluid is a coupling factor which connects the phases. For dilute steady solid/liquid two-phase flows, the particle velocity distribution function can be derived by analogy with the procedures in the kinetic theory of gas molecules for the equilibrium state instead of being assumed, as previous investigators did. This done, more detailed information, such as the velocity probability density distribution, mean velocity distribution and fluctuating intensity etc. can be obtained directly from the particle velocity distribution function or from its integration. Experiments have been performed for dilute solid/liquid two-phase flow in a 4 x 6 cm2 sized circulating square pipe system by means of laser Doppler anemometry so that the theories can be examined. The comparisons show that the theories agree very well with all the measured data.