New analysis of contact melting of phase change material around a hot sphere

The process of contact melting of the solid phase change material (PCM) around a hot sphere, which is driven by the temperature difference between the PCM and the sphere, is analyzed in this paper. Considering the difference of the normal angle between the sphere surface and the solid–liquid interface of the melting PCM, the fundamental equations of the melting process are derived with the film theory. The new film thickness and pressure distribution inside the liquid film and the variation law of the normal angle of the solid–liquid interface and the melting velocity of the sphere are also obtained. It is found that (1) while normal angle at sphere surface φ is within a certain value φ₀, which is related to Ste number and the outside force F, it has no obvious effect on the pressure distribution inside the liquid film and the numerical results by the present model are in accordance with the analytical results in the published literature, (2) the film thickness at φ = ±90° is constringent to a certain value and not the infinity, (3) the analytical results can be employed approximately to analyze the contact melting process except for the film thickness at φ = ±90°.     

Segmented gas–liquid flow characterization in rectangular microchannels

We used optical methods such as Laser Induced Fluorescence (LIF) and confocal Laser Scanning Microscopy (LSM) to characterize gas–liquid phase distribution in rectangular microchannels. Using a 2 m long microchannel with a hydraulic diameter of 200 μm enables the precise measurement of important parameters such as liquid slug length, bubble length, pressure drop and film thickness at the wall as well as in the corner of the microchannel for low Capillary numbers (Ca) ranging from 2 × 10⁻⁴ to 1 × 10⁻². This range of Ca was obtained by using different fluid pairs such as ethanol, water and different concentrated aqueous solutions of glycerol in combination with nitrogen.     

Optical measurement of liquid film thickness and wave velocity in liquid film flows

Two optical techniques are described for measurement of a liquid film's surface. Both techniques make use of the total internal reflection which occurs at a liquid-vapor interface due to the refractive index difference between a liquid and a vapor. The first technique is used for film thickness determination. A video camera records the distance between a light source and the rays which are reflected back from the liquid-vapor interface. This distance can be shown to be linearly proportional to film thickness. The second technique measures surface wave velocities. Two photo sensors, spaced a fixed distance apart, are used to record the time varying intensity of light reflected from the liquid-vapor interface. The velocity is then deduced from the time lag between the two signals.The authors appreciate the support of the Air Conditioning and Refrigeration Center at the University of Illinois at Urbana-Champaign under project 45.     

Dynamical deformation of a flat liquid–liquid interface

The passage of solid spheres through a liquid–liquid interface was experimentally investigated using a high-speed video and PIV (particle image velocimetry) system. Experiments were conducted in a square Plexiglas column of 0.1 m. The Newtonian Emkarox (HV45 50 and 65% wt) aqueous solutions were employed for the dense phase, while different silicone oils of different viscosity ranging from 10 to 100 mPa s were used as light phase. Experimental results quantitatively reveal the effect of the sphere’s size, interfacial tension and viscosity of both phases on the retaining time and the height of the liquid entrained behind the sphere. These data were combined with our previous results concerning the passage of a rising bubble through a liquid–liquid interface in order to propose a general relationship for the interface breakthrough for the wide range of Mo ₁/Mo ₂ ∈ [2 × 10⁻⁵–5 × 10⁴] and Re ₁/Re ₂ ∈ [2 × 10⁻³–5 × 10²].     

Solidification of nano-enhanced phase change material (NEPCM) in a wavy cavity

The effects of surface waviness (λ?=?0, 0.125, 0.25, 0.5) and nanoparticle dispersion (??=?0, 0.05, 0.1) on solidification of Cu-water nanofluid inside a vertical enclosure are investigated numerically for different Grashof number (Gr?=?10⁵, 10⁶, 10⁷). An enthalpy porosity technique is used to trace the solid and liquid interface. Comparisons with previously published works show the accuracy of the obtained results. A maximum of 25.9% relative variation of freezing time with surface waviness was observed for λ?=?0.5, while the relative variation of freezing time with nanoparticles in comparison with surface waviness was negative for high values of λ. It was observed that surface waviness can be used to control the solidification time based on enhancing different mechanism of solidification.     

A focusing aid for the X-ray projection microscope

Summary Part of the electrons reflected by the target of an X-ray microscope pass the demagnifying lens in opposite direction and form a magnified image of the focus in the electron source. This secondary image can be caught on a fluorescent screen and observed. The position, shape and size of the image give information on alignment, focusing conditions and image errors. The brightness is a factor 10³ to 10⁴ higher than that of the X-ray fluorescent image under normal focusing conditions. If a magnetic objective is used, centering can be done very accurately (angle of tilt < 1/600 radians). In practice this method proves to be very satisfactory, even for voltages as low as 6 kV and less. At these voltages the depth of penetration of the electrons in gold is less than 500 Å, so that for a 0.1 resolution there is no need for a thin target.     

Numerical study on the effect of initial flow velocity on liquid film thickness of accelerated slug flow in a micro tube

Numerical simulation of air–water slug flows accelerated from steady states with different initial velocities in a micro tube is conducted. It is shown that the liquid film formed between the gas bubble and the wall in an accelerated flow is significantly thinner than that in a steady flow at the same instantaneous capillary number. Specifically, the liquid film thickness is kept almost unchanged just after the onset of acceleration, and then gradually increases and eventually converges to that of an accelerated flow from zero initial velocity. Due to the flow acceleration, the Stokes layer is generated from the wall, and the instant velocity profile can be given by superposition of the Stokes layer and the initial parabolic velocity profile of a steady flow. It is found that the velocity profile inside a liquid slug away from the bubble can be well predicted by the analytical solution of a single-phase flow with acceleration. The change of the velocity profile in an accelerated flow changes the balance between the inertia, surface tension and viscous forces around the meniscus region, and thus the resultant liquid film thickness. By introducing the displacement thickness, the existing correlation for liquid film thickness in a steady flow (Han and Shikazono, 2009) is extended so that it can be applied to a flow with acceleration from an arbitrary initial velocity. It is demonstrated that the proposed correlation can predict liquid film thickness at Re < 4600 within the range of ±10% accuracy.     

Experimental study on surface wave and film breakdown of falling liquid film flow

In order to evaluate characteristics of the liquid film flow and their influences on heat and mass transfer, measurements of the instantaneous film thickness using a capacitance method and observation of film breakdown are performed. Experimental results are reported in the paper. Experiments are carried out at Re = 250–10000, T _in = 20–50°C and three axial positions of vertically falling liquid films for film thickness measurements. Instantaneous surface waveshapes are given by the interpretation of the test data using the cubic spline method. The correlation of the mean film thickness versus the film Reynolds number is also given by fitting the test data. It is revealed that the surface wave has nonlinear behavior. Observation of film breakdown is performed at Re = 1.40 × 10³–1.75 × 10⁴ and T _in = 85–95°C. From experimental results, the correlation of the film breakdown criterion can be obtained as follows: Bd = 1.567 × 10⁻⁶ Re ^1.183     

Simultaneous entrainment of oil and water droplets in high Reynolds number gas turbulence in horizontal pipe flow

We develop a 1D cross sectional concentration profile model for oil and water droplets that coexist in the turbulent gas phase (of Re ∼ 10⁶) in near horizontal stratified pipe flows. Entrainment of the oil and water mixture from a liquid film near the bottom of the pipe into the gas is modeled based on earlier single-fluid entrainment correlations. A Gamma distribution for the droplet sizes based on the breakup of liquid filaments, is adopted. An explicit algebraic–exponential formula for the total concentration profile for either phase can then be derived.     

Flow patterns and pressure drop of ionic liquid–water two-phase flows in microchannels

The two-phase flow of a hydrophobic ionic liquid and water was studied in capillaries made of three different materials (two types of Teflon, FEP and Tefzel, and glass) with sizes between 200 μm and 270 μm. The ionic liquid was 1-butyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}amide, with density and viscosity of 1420 kg m⁻³ and 0.041 kg m⁻¹ s⁻¹, respectively. Flow patterns and pressure drop were measured for two inlet configurations (T- and Y-junction), for total flow rates of 0.065–214.9 cm³ h⁻¹ and ionic liquid volume fractions from 0.05 to 0.8. The continuous phase in the glass capillary depended on the fluid that initially filled the channel. When water was introduced first, it became the continuous phase with the ionic liquid forming plugs or a mixture of plugs and drops within it. In the Teflon microchannels, the order that fluids were introduced did not affect the results and the ionic liquid was always the continuous phase. The main patterns observed were annular, plug, and drop flow. Pressure drop in the Teflon microchannels at a constant ionic liquid flow rate, was found to increase as the ionic liquid volume fraction decreased, and was always higher than the single phase ionic liquid value at the same flow rate as in the two-phase mixture. However, in the glass microchannel during plug flow with water as the continuous phase, pressure drop for a constant ionic liquid flow rate was always lower than the single phase ionic liquid value. A modified plug flow pressure drop model using a correlation for film thickness derived for the current fluids pair showed very good agreement with the experimental data.     

Measurement of liquid film thickness in micro square channel

In micro channels, slug flow becomes one of the main flow regimes due to strong surface tension. In micro channel slug flow, elongated bubble flows with the thin liquid film confined between the bubble and the channel wall. Liquid film thickness is an important parameter in many applications, e.g., micro heat exchanger, micro reactor, coating process etc. In the present study, liquid film thickness in micro square channels is measured locally and instantaneously with the confocal method. Square channels with hydraulic diameter of D_h = 0.3, 0.5 and 1.0 mm are used. In order to investigate the effect of inertial force on the liquid film thickness, three working fluids, ethanol, water and FC-40 are used. At small capillary numbers, liquid film at the channel center becomes very thin and the bubble interface is not axisymmetric. However, as capillary number increases, bubble interface becomes axisymmetric. Transition from non-axisymmetric to axisymmetric flow pattern starts from lower capillary number as Reynolds number increases. An empirical correlation for predicting axisymmetric bubble radius based on capillary number and Weber number is proposed from the present experimental data.     

Magnetic resonance imaging of velocity fields, the void fraction and gas dynamics in a cavitating liquid

In acoustic cavitation, the relationship between the bubble dynamics on the microscale and the flow properties on the macroscale is critical in determining sonochemical reaction kinetics. A new technique was developed to measure the void fraction and estimate water mobility in the vicinity of cavitating bubbles using phase-encoded magnetic resonance imaging with short characteristic measurement timescales (0.1–1 ms). The exponential behavior of the NMR signal decay indicated the fast diffusion regime, with the relationship between local mechanical dispersion D _mix and the average bubble radius R, D_mix >> \frac2R²10^-4s, D_{\rm mix}\gg \frac{2R^2}{10^{-4}\hbox{s}}, resulting in dispersion of orders of magnitude greater than diffusion in quiescent water. For two different samples (water and a surfactant solution), the independent measurements of three-dimensional void fraction and velocity fields permitted the calculation of compressibility, divergence and vorticity of the cavitating medium. The measured dynamics of the dissolved gas, compared with that of the surrounding liquid, reflected the difference in the bubble coalescence and lifetimes and correlated with the macroscopic flow parameters.     

Measurement of liquid film in microchannels using a laser focus displacement meter

This paper presents a new method for measuring the interfacial displacement of a liquid film in microchannels using a laser focus displacement meter (LFD). The purpose of the study is to clarify the effectiveness of the new method for obtaining detailed information concerning interfacial displacement, especially in the case of a thin liquid film, in microchannels and minichannels. To prevent the tube wall signal from disturbing that of the gas–liquid interface, a fluorocarbon tube with a water box was used; the refraction index of this device is the same as that for water. With this method, accurate instantaneous measurements of the interfacial displacement of the liquid film were achieved. The error caused by refraction of the laser beam passing through the acrylic water box and fluorocarbon tube was estimated analytically and experimentally. The formulated analytical equation can estimate the real interface displacement by using the measured displacement in a fluorocarbon tube of 25 m to 2.0 mm I.D. A preliminary test using fluorocarbon tubes of 1 mm and 2 mm I.D. showed that the corrected interface displacement calculated by the equation agreed with the real displacement to within a 1% margin of error. It was also confirmed that the LFD in the system could measure a liquid film of 0.25 m at the thinnest. We made simultaneous measurements of the interface in fluorocarbon tubes of 0.5 mm and 1 mm I.D. using the LFD and a high-speed video camera with a microscope. These showed that the LFD could measure the interface of a liquid film with high spatial and temporal resolution during annular, slug, and piston flow regimes. The data also clarified the existence of a thin liquid film of less than 1 m in thickness in the slug and annular flow regimes.     

A slit viscometer for the measurement of the viscosity of aqueous systems at high temperatures

A slit viscometer has been constructed to measure the viscosity of aqueous systems at temperatures up to 140 °C. Liquid is forced backwards and forwards through the slit by the use of varying air pressure. The flow rate is obtained from the time for the liquid to pass conductivity probes located in liquid reservoirs either side of the slit. The pressure difference between two points on the slit wall is determined using a differential pressure transducer. By varying the slit height measurements can be made on liquids with viscosities in the range 10 to 10^–3 Pa s. Shear rates from 10 to 10⁴ s^–1 can be achieved. A simple microcomputer control system enables the shear stress to be automatically increased and decreased stepwise. Representative data on polysaccharide solutions and strach suspensions are presented. The viscometer is particularly well-suited for following temperature-dependent biopolymer transitions and the thermal depolymerisation of water soluble polymers.     

A model for film-forming with Newtonian and shear-thinning fluids

The formation of a thin film by (i) the slow penetration of a gas bubble into a liquid filled tube, (ii) the withdrawal of a planar substrate from a liquid filled gap, is investigated theoretically for the cases of both Newtonian and shear-thinning liquids; the latter conforming to either a power–law or Ellis model. Formulated as a boundary value problem underpinned by lubrication theory, the analysis gives rise to a system of ordinary differential equations which are solved numerically subject to appropriate boundary conditions. For Newtonian liquids comparison of the predicted residual film thickness for a wide range of capillary number, Ca  (10⁻⁴, 10), is made with others obtained using existing expressions, including the classical one of Bretherton, in the region of parameter space over which they apply. In the case of (i), prediction of the behaviour of the residual fluid fraction and gap-to-film thickness ratio, for a Newtonian liquid and one that is shear-thinning and modelled via a power–law, is found to be in particularly good agreement with experimental data for Ca < 0.2. For (ii), both shear-thinning models are utilized and contour plots of residual film thickness generated as a function of Ca and the defining parameters characteristic of each model.     

Effect of Schmidt number on the structure and propagation of density currents

The results of a numerical study of two- and three-dimensional Boussinesq density currents are described. They are aimed at exploring the role of the Schmidt number on the structure and dynamics of density driven currents. Two complementary approaches are used, namely a spectral method and a finite-volume interface capturing method. They allow for the first time to describe density currents in the whole range of Schmidt number 1 ≤ Sc ≤ ∞ and Reynolds number 10² ≤ Re ≤ 10⁴. The present results confirm that the Schmidt number only weakly influences the structure and dynamics of density currents provided the Reynolds number of the flow is large, say of O(10⁴) or more. On the contrary low- to moderate-Re density currents are dependant on Sc as the structure of the mixing region and the front velocities are modified by diffusion effects. The scaling of the characteristic density thickness of the interface has been confirmed to behave as (ScRe)^−1/2. Three-dimensional simulations suggest that the patterns of lobes and clefts are independent of Sc. In contrast the Schmidt number is found to affect dramatically (1) the shape of the current head as a depression is observed at high-Sc, (2) the formation of vortex structures generated by Kelvin–Helmholtz instabilities. A criterion is proposed for the stability of the interface along the body of the current based on the estimate of a bulk Richardson number. This criterion, derived for currents of arbitrary density ratio, is in agreement with present computed results as well as available experimental and numerical data.      

Measurement of locally heated liquid film thickness by a double-fiber optical probe

An experimental investigation of thermocapillary deformations in a film of 10% ethyl alcohol solution in water, flowing down a plate with a heater of length 6.7 mm and width 68 mm, is performed. Heating of the film results in the formation of a horizontal liquid bump at the top edge of the heater. On the heater the flow divides into vertical rivulets with a thin film between them. Film deformations in the bump and the thin film between the rivulets are investigated. Local film thickness is measured by means of a double-fiber optical probe. The method is based on the dependence of the intensity of reflected light on the distance between the probe and the reflecting surface. The measurement results are compared to those previously obtained using the schlieren method. The experiment is controlled by three parameters. They are, with their respective values, the plate inclination angle (4–90°), the Reynolds number (0.15–62) and the heat flux density (0–4.5 W/cm²).     

Liquid film characterization in horizontal,annular, two-phase,gas–liquid flow using time-resolved laser-induced fluorescence

A non-intrusive optical technique was developed to provide time-resolved longitudinal and cross-sectional images of the liquid film in horizontal annular pipe flow of air and water, revealing the interfacial wave behavior. Quantitative information on the liquid film dynamics was extracted from the time-resolved images. The planar laser-induced fluorescence technique was utilized to allow for optical separation of the light emitted by the film from that scattered by the air–water interface. The visualization test section was fabricated from a tube presenting nearly the same refractive index as water, which allowed the visualization of the liquid film at regions very close to the pipe wall. Longitudinal images of the liquid film were captured using a high-frame-rate digital video camera synchronized with a high-repetition-rate laser. An image processing algorithm was developed to automatically detect the position of the air–water interface in each image frame. The thickness of the liquid film was measured at two axial stations in each processed image frame, providing time history records of the film thickness at two different positions. Wave frequency information was obtained by analyzing the time-dependent signals of film thickness for each of the two axial positions recorded. Wave velocities were measured by cross-correlating the amplitude signals from the two axial positions. For the film cross-section observations, two high-speed digital video cameras were used in a stereoscopic arrangement. Comparisons with results from different techniques available in literature indicate that the technique developed presents equivalent accuracy in measuring the liquid film properties. Time-resolved images of longitudinal and cross-section views of the film were recorded, which constitute valuable information provided by the technique implemented.     

Determination of thermal conductivity and interfacial energy of solid Zn solution in the Zn-Al-Bi eutectic system

The equilibrated grain boundary groove shapes for solid Zn solution (Zn-3.0 at.% Al-0.3 at.% Bi) in equilibrium with the Zn-Al-Bi eutectic liquid (Zn-12.7 at.% Al-1.6 at.% Bi) have been observed from quenched sample with a radial heat flow apparatus. Gibbs-Thomson coefficient, solid-liquid interfacial energy and grain boundary energy for solid Zn solution in equilibrium with Al-Bi-Zn eutectic liquid have been determined to be (5.1 ± 0.4) × 10⁻⁸ K m, (80.1 ± 9.6) × 10⁻³ and (158.6 ± 20.6) × 10⁻³ J m⁻² from the observed grain boundary groove shapes, respectively. The thermal conductivity variation with temperature for solid Zn solution has been measure with radial heat flow apparatus and the value of thermal conductivity for solid Zn solution has been determined to be 135.68 W/km at the eutectic melting temperature. The thermal conductivity ratio of equilibrated eutectic liquid to solid Zn solution, R = K_L(Zn)/K_S(Zn) has also been measured to be 0.85 with Bridgman type solidification apparatus.