Local Film Thickness Research Articles

Visualization of film wavelike characteristics and measurement of film thickness in spray cooling

An experimental investigation was performed to study the heat transfer in an eight-nozzle spray cooling system with de-ionized water as the working fluid. Visualization of the liquid-solid contact area and the flow near the heated surface was made using a microscopic lens system in conjunction with an advanced high-speed camera. The film thickness and film wavelike characteristics under liquid volume flow rates ranged from 2.78×10 -6 m 3 /s to 1.39×10 -5 m 3 /s and surface temperatures between 22℃ and 78.2℃ were examined respectively. The development process of the liquid film on the heated surface was observed. The local mean film thickness, the film wavelike characteristics and the behavior of the bubbles appeared in the liquid film were captured using an image processing technique. It is discovered that there exists a climax of local mean film thickness during the starting process of spray cooling. When the liquid film reaches the dynamic stable state, the dimensionless mean film thickness decreases with the increase of the liquid volume flow rate, and increases with the increase of surface temperature generally. Besides, the volume flow rate has a more significant impact on the wavelength and amplitude of the liquid film compared to the surface temperature.

Experimental investigation of 3-dimensional wavy liquid films under the coupled influence of thermo-capillary and electrostatic forces

Three-dimensional interfacial waves developing on the free surface of falling liquid films are known to intensify heat and mass transfer. In this context, the present paper studies the effect of electrostatic as well as of thermo-capillary forces on a falling film of a dielectric liquid. Therefore, measurements of the local film thickness using a confocal chromatic imaging method were performed under isothermal and heated conditions. The experimental results show that both forces destabilize the flow. It is found, that the application of an additional electric field under heating conditions enhances the generation of rivulets, thereby reducing the overall heat transfer coefficient.

EXPERIMENTAL INVESTIGATION OF DYNAMICS AND ATOMIZATION OF A LIQUID FILM FLOWING OVER A SPINNING DISK

One of the most commonly used methods of liquid atomization is the rotary atomization. In this process a radially spreading thin liquid film is created on a surface of a rotating disk, due to centrifugal forces. The liquid flows over the disk edge and disintegrates. The liquid film is mostly wavy. The radially propagating waves induce fluctuations resulting in an expansion of the drop size distribution after atomization. An experimental apparatus has been built to investigate the effect of the film dynamics on the atomization process. A water jet is impinging at the center of a rotating disk made of stainless steel. The local instantaneous film thickness is measured using a confocal chromatic sensoring technique. The drop sizes are determined using the shadowgraphy method. The film flow on the rotating disk has been investigated in a wide range of parameters. The strongly wavy structure of the film flow has been observed for all sets of parameters. The development of waves depends on the nozzle-to-disk distance. The radial distribution of the time-averaged film thickness over the disk surface agrees fairly well with the correlations found in the literature. First results of the drop size distribution show a bimodal distribution for low liquid mass flow rates.

Numerical analysis of thermodynamic behaviour of falling film outside a horizontal tube

Falling film evaporation and condensation on horizontal tubes have been widely employed in the field of chemical, petroleum refining and desalinization. A numerical investigation on the thermodynamic behaviour of falling film outside a horizontal tube is presented. Based on the analysis of falling film state around a horizontal tube, a mathematical model is proposed, which takes into account the effect of jet impingement at the tube top on falling film behaviour. The numerical local heat transfer coefficients agree well with the experimental, which proves the reliability of the developed model. The variation of the local heat transfer coefficients and film thickness with flow density and evaporation temperature is simulated and analysed.

CIRCUMFERENTIAL NONUNIFORMITY OF WAVES ON LIQUID FILM IN ANNULAR FLOW WITHOUT LIQUID ENTRAINMENT

The wavy structure of liquid film in downward annular flow without liquid entrainment is studied. Temporal evolution of instantaneous distributions of local film thickness over longitudinal and circumferential coordinates is studied using high-speed laser-induced fluorescence technique. Wavy structure in such flow consists of fast long-living primary waves and slow short-living secondary waves that are generated at the back slopes of primary waves. An automatic algorithm of identification of characteristic lines of primary waves is applied to data obtained in a number of circumferential positions. Contours of waves in each time frame are identified to obtain temporal evolution of the shape of each wave in longitudinal and circumferential coordinates. Circumferential size of primary waves is estimated based on frequency of different kinds of waves. It is shown that variation of primary waves’ height along circumferential coordinate is most likely caused by absorption and generation of secondary waves.

Analysis and modeling of the optical endpoint signal for precision etching

Endpoint detection is an essential methodology for process control in dry etching for modern semiconductor manufacturing technology. In this paper, an analysis has been performed on the factors, such as the local etch rate, the local film thickness differences, and the open area and the global uniformities of the etch rate and film thickness, affecting the change in the optical emission endpoint signals on a patterned device wafer. Also, a model of the endpoint signal evolution, which includes an effective open ratio, the ratio of the relative open area after considering the local difference in the etch rate and the film thickness to the total open area at the very beginning of the etch process, has been established. Compared to the conventional open ratio, which is the ratio derived from the reticle used for lithography, the effective open ratio is better in explaining and predicting the endpoint signal change. The effective open ratio can be used to design dummy patterns that are used to improve endpoint detection in critical dry etch processes such as gate cuts in logic gate formation, etc.

Liquid film circumferential asymmetry prediction in horizontal annular two-phase flow

This study considers the prediction of the degree of asymmetry in the circumferential distribution of the liquid film in the tube cross section of horizontal annular gas–liquid two-phase flow, endemic of the lower region of this flow regime near the stratified-wavy flow transition boundary. Focusing on disturbance waves as the predominant mechanism for transporting the liquid in the annular film from the bottom to the top of the tube to counterbalance the draining effect of gravity, a new prediction method for the degree of asymmetry in the annular liquid film is proposed that outperforms existing correlations. Flow pattern maps for horizontal gas–liquid two-phase flow of frequent use in the design of evaporators and condensers can thus be explicitly updated to account for both symmetric and asymmetric annular flows. The underlying experimental database contains 184 measured liquid film circumferential profiles, corresponding to 1276 local liquid film thickness measurements collected from 15 different literature studies for tube diameters from 8.15mm to 95.3mm.

Prediction of wind turbine gear micropitting under variable load and speed conditions using ISO/TR 15144-1: 2010

Wind turbine gearbox operates under a wide array of highly fluctuating and dynamic load conditions caused by the stochastic nature of wind and operational wind turbine controls. Micropitting damage is one of failure modes commonly observed in wind turbine gearboxes. This article investigates gear micropitting of high-speed stage gears of a wind turbine gearbox operating under nominal and varying load and speed conditions. Based on the ISO standard of gear micropitting (ISO/TR 15144-1:2010) and considering the operating load and speed conditions, a theoretical study is carried out to assess the risk of gear micropitting by determining the contact stress, sliding parameter, local contact temperature and lubricant film thickness along the line of action of gear tooth contact. The non-uniform distributions of temperature and lubricant film thickness over the tooth flank are observed due to the conditions of torque and rotational speed variations and sliding contact along the gear tooth flanks. The lubricant film thickness varies along the tooth flank and is at the lowest when the tip of the driving gear engages with the root of the driven gear. The lubricant film thickness increases with the increase of rotational speed and decreases as torque and sliding increase. It can be concluded that micropitting is most likely to initiate at the addendum of driving gear and the dedendum of driven gear. The lowest film thickness occurs when the torque is high and the rotational speed is at the lowest which may cause direct tooth surface contact. At the low-torque condition, the varying rotational speed condition may cause a considerable variation of lubricant film thickness thus interrupting the lubrication which may result in micropitting.

Thin film evaporation in microchannels with slope- and curvature-dependent disjoining pressure

Physics of thin film evaporation plays a critical role in designing highly efficient micro-scale thermal management systems. In such systems, envelope of the evaporating thin film is an extended meniscus beyond the apparent contact line at a liquid/solid interface, which experiences strong intermolecular forces because of micro-scale interactions. Traditionally, such forces are represented by disjoining pressures that are postulated solely on the basis of the local film thickness, disregarding the local slope and curvature of the interfacial profile. In the present study, an improved model for evaporation in thin liquid films in microfluidic channels is developed, which explicitly takes into account the slope and curvature dependence of the disjoining pressure, under the assumption of a steady meniscus in existence with its own vapor. Such an improved formalism essentially prevents the contact line movement without slip, and allows an asymptotic merging of the evaporating interfacial profile to an infinitesimally thin non-evaporating adsorbed film. Implications of this rigorous disjoining pressure model on the thermo-physics of thin film evaporation in a kinetically controlled limit are investigated in details, and contrasting confluences as compared to the traditional descriptions of the disjoining pressure are emphatically pinpointed.

Experimental investigation into three-dimensional wavy liquid films under the influence of electrostatic forces

Three-dimensional interfacial waves that develop on the free surface of falling liquid films are known to intensify heat and mass transfer. In this context, the present paper studies the effect of electrostatic forces applied to a falling film of dielectric liquid on its three-dimensional nonlinear wave dynamics. Therefore, measurements of the local film thickness using a confocal chromatic imaging method were taken, and the complex wave topology was characterized through photography. The experiments show a complex interaction between the electric field and the hydrodynamics of the falling film, whereby electrostatic forces were found to both increase and decrease wave peak height in different regions of the wave. Additionally, an electrically induced breakup of the three-dimensional wave fronts, which leads to a locally doubled frequency in streamwise direction, is found. The ability to influence the wave topology demonstrated here opens the possibility to optimize heat transfer processes in falling liquid films.

Effect of neighboring perturbations on drop coalescence at an interface

Coalescence at a quiescent silicone oil/water glycerine interface was investigated for water/glycerine drops with Bond number ∼7 and Ohnesorge number = 0.01 using high-speed imaging and time-resolved tomographic particle image velocimetry. In addition to a single drop case, three perturbation cases were considered corresponding with a second drop, a solid particle wetted in oil, and a solid particle wetted in water/glycerine placed adjacent to the coalescing drop. Each perturbing object caused an initial tilting of the drop, influencing its rupture location and eventual collapse behavior. Once tilted, drops typically ruptured near their lowest vertical position which was located either toward or away from the perturbing object depending on the case. The initial retraction speed of the ruptured film was higher for drops initially tilted at significant angles, and the local variations in retraction speed correlated well with the expected variations in local film thickness. The drop fluid always collapsed away from the drop axis in the direction of the rupture location in all unperturbed or perturbed cases. In the case of a drop next to a particle wetted in water/glycerine, the collapsing fluid travelled away from the particle, and the downward propagating vortex ring which developed was similar to that resulting from an unperturbed drop rupture. By contrast, the drop fluid collapsed toward either a second drop or a particle wetted in oil. The resulting vortex rings were more asymmetric, and viscous interaction between the particle and collapsing fluid hindered the downward motion of the associated ring.

A mathematical approach to predict dryout in a rod bundle

In this paper, we present the development of a mathematical model to predict dry-out in a rod bundle using film thickness model and subchannel analysis. In two-phase annular flow regime, liquid phase is assumed to divide into liquid film attached to the rod surface and droplets entrained into the gas (vapor) phase existing in the subchannels. Conservation equations in two-phase annular flow regime for each subchannel consist of two mixture equations for the continuity and the momentum, gas phase continuity, liquid film continuity and liquid phase energy. Also, at the interface of adjacent subchannels, radial diversion cross flow equation is considered. It is assumed that dryout occurs when the local film thickness in the annular flow approaches zero. The transfer of mass, momentum and energy between adjacent subchannels are split into diversion cross-flow, turbulent mixing and void drift components. Rod-centered approach which is compatible with the annular flow regime is used for subchannel analysis. It was observed that turbulent mixing and void drift phenomena have significant effect on the prediction of dryout power. The model is verified against several available experimental data and proved viable for prediction of dryout heat flux in rod bundle geometry especially for mass flux greater than 400kg/m2s.

ESTIMATION OF LOCAL LIQUID FILM THICKNESS IN TWO-PHASE ANNULAR FLOW

In many semi-empirical analyses of flow boiling heat transfer, an annular flow is often assumed as a model flow and the local liquid film thickness is a key parameter in the analysis. This work considers a simple electrical conductance technique to estimate the local liquid film thickness in two-phase annular flows. In this approach, many electrodes are mounted flush with the inner wall of the pipe. Voltage differences between two neighboring electrodes for concentric annular flows with various liquid film thicknesses are obtained before the main experiments and logged in a look-up table. For an actual application in the annual flow, voltage differences of neighboring electrodes are measured and then corresponding local film thicknesses are determined by the interpolation of the look-up table. Even though the proposed technique is quite simple and straightforward, the numerical and static phantom experiments support its usefulness.

Film flow for power-law fluids: Modeling and linear stability

The paper deals with modeling of a power-law fluid film flowing down an inclined plane for small to moderate Reynolds numbers. A model, accurate up to second order [first order] for dilatant [pseudoplastic] fluids is proposed to describe the nonlinear behavior of the flow. The modeling procedure consists of a combination of the lubrication theory and the weighted residual approach using an appropriate projection basis. A suitable choice of weighting functions allows a significant reduction of the dimension of the problem. The resulting model is naturally unique, i.e., independent of the particular form of the trial functions. Reduced models are proposed for the evolution of the local film thickness and flow rate; their linear spectra are compared to that obtained from the full Orr–Sommerfeld numerical solution. To obtain the latter, a new formulation of the eigenvalue problem is proposed to overcome the classical divergence of the apparent viscosity at the free surface. The full model and its reduced forms all have the advantage of the Benney like model close to criticality. Far from the instability threshold the full model continues to follow the Orr–Sommerfeld solution up to sufficiently large Reynolds numbers and gives better predictions than the depth averaging model. An incomplete regularization procedure is performed to cure the rapid divergence of the reduced two-equation model. Due to its relative simplicity the latter might be preferred in practice to the full model, at least at the initial stage of the nonlinear regime. It is also shown that the convective nature of the instability is not affected by the variation of the power law index.

Direct and Transmission Milling of Suspended Silicon Nitride Membranes With a Focused Helium Ion Beam

Helium ion milling of suspended silicon nitride thin films is explored. Milled squares patterned by scanning helium ion microscope are subsequently investigated by atomic force microscopy and the relation between ion dose and milling depth is measured for both the direct (side of ion incidence) and transmission (side opposite to ion incidence) regimes. We find that direct-milling depth varies linearly with beam dose while transmission-milling depth varies with the square of the beam dose, resulting in a straightforward method of controlling local film thickness.

Prediction of dryout and post-dryout wall temperatures using film thickness model

In this paper, a model for calculating dryout and post-dryout wall temperature for two phase flow in a vertical tube using film thickness model is presented. The model is based on the mass and energy balance equations for vapor core, liquid film and corresponding closure laws for interface transfer processes. It is assumed that the dryout is reached when the local film thickness in the annular flow approaches zero. Thermal-hydraulic processes along the whole length of the boiling channel are simulated, from sub-cooled liquid flow at channel inlet, up to the liquid film dryout, gas entrained droplets, mist flow and post dryout region at tube exit. In the post dryout region, thermal non-equilibrium was assumed between vapor and entrained droplets and wall temperature was obtained iteratively by using a wall heat flux partitioning model. Also, the model is verified against several available experimental data and proved viable for prediction of the wall temperature and the dryout location.

Fluorescence Excitation and Imaging of Single Molecules Near Coated Surfaces: A Theoretical Study

Microscopic fluorescent samples of interest to cell and molecular biology are almost always in aqueous medium near a solid surface. Frequently, that surface is coated with a thin film such as: a lipid monolayer, bilayer, or multilayer; a collagen or agarose layer deposited before cell plating or deposited by the cells themselves; acrylamide gel to immobilize beads or single molecules (such as in commercial preparations for nucleic acid sequencing); or a cell wall interposed between the substrate and cellular organelle. Both excitation and emission of fluorescent single molecules near film-coated surfaces are strongly affected by the proximity of the coated surface, the film thickness, its refractive index, and the fluorophore's orientation. For TIR excitation, multiple reflections in the film lead to unique resonance peaks in the evanescent intensity vs. incidence angle curve. For emission, multiple reflections coupled to the fluorophore's near field emission create a distinct intensity pattern in the back focal plane (BFP) of a high aperture objective. In principle, these features should allow retrieval of information about local film thickness and refractive index, and about fluorophore axial position and 3D molecular orientation. This entirely theoretical analysis with computer-generated images explores these possibilities. Supported by NIH grants 2R56NS038129-11 and 1R21NS073686-01 to DA and Ronald V. Holz.

Phenomenological Model for Pyroelectric Effects of Nano Graded Ferroelectric Films

In order to improve the pyroelectric properties of nanograded ferroelectric films (NGFF), and provide a theoretical reference for practical applications, the generalized Ginzburg-Landau-Denvonshire (GLD) theory is adopted to investigate the pyroelectric properties of the NGFF. A function is introduced to characterize the local structure in nanograded films. Influence of the local structure, film thickness and external electric field on the polarization distribution and pyroelectric properties are mainly discussed. The numerical results show that parameterand film thickness are two very important factors that influence the film properties, larger values lead to smaller spontaneous polarization and lower pyroelectric peak. Different directions of the external electric field can lead to greatly different effects on pyroelectric behaviors, whose effects is to expand the working temperature region, or else, change the order of phase transition.

Surface temperature reconstruction based on the thermocapillary effect

A thin liquid film subject to a temperature gradient is known to deform under the action of thermocapillary stresses which induce convective cells. The free surface deformation can be thought of as the signature of the imposed temperature gradient, and this study investigates the inverse problem of trying to reconstruct the temperature field from known free surface variations. The present work builds on the analysis of Tan et al. [“Steady thermocapillary flows of thin liquid layers I. Theory”, Phys. Fluids A 2 (1990) 313–321, doi:10.1063/1.857781] which provides a long-wave evolution equation for the fluid film thickness variation on nonuniformly heated substrates and proposes a solution strategy for the planar flow version of this inverse problem. The present analysis reveals a particular case for which there exists an explicit, closed-form solution expressing the local substrate temperature in terms of the local film thickness and its spatial derivatives. With some simplifications, this analysis also shows that this solution applies to three-dimensional flows. The temperature reconstruction strategies are successfully tested against “artificial” experimental data (obtained by solving the direct problem for known temperature profiles) and actual experimental data. doi:10.1017/S1446181111000654

The effect of an electrostatic field on the rupture of a thin viscous static film by van der Waals attractions

This research examines rupture phenomena of a horizontal static thin viscous layer on a solid plate under an electrostatic field generating from a charged foil above the film. The dynamics of the electrified liquid film is formulated to derive a long-wave evolution equation of local film thickness. It determines two-dimensional nonlinear behavior of the film subject to surface tension, viscous, electrically induced forces, and van der Waals attractions. Linear stability analysis is used to obtain the maximum growth rate of a periodic disturbance and its corresponding wavenumber. To see the development of film rupture the strongly nonlinear partial differential equation is numerically solved for the unlimited or limited foil length as part of an initial-value problem with spatially periodic boundary conditions. The stronger electric forces make the thin layer more unstable and speed up its rupture.