Wave regimes of ascending flow of a thin layer of a viscous liquid in contact with a gas

The flow of a liquid in thin layers is one of the hydrodynamic problems of chemistry and heat engineering. The large surface area of films and their small thickness make it possible to accelerate thermal, diffusive, and chemical processes at the gas-liquid boundary.Theoretical studies of liquid flow in a vertical descending thin layer are presented in [1–4]. In this paper we study ascending wave flows of a liquid in a thin vertical layer in contact with a gas, i.e., flows in the direction opposite the action of the force due to gravity, with account for the action of the gas on the liquid surface. Such motions are encountered when oil is extracted from strata that are saturated with gas. At some distance from the stratum the oil and gas separate: the gas travels at high velocity inside the pipe, occupying a considerable portion of the pipe, and the liquid is displaced toward the pipe walls, forming a thin film. In certain cases a wave-like interface develops between the oil and gas that travels with a velocity greater than that of the liquid but less than the average gas velocity. Similar phenomena are observed in high velocity mass exchangers.We examine the effect of the gas for both laminar and turbulent flow.Studies that neglect the effect of the gas flow on the liquid show that for waves on the film surface whose lengths are considerably longer than the average thickness of the layer, the liquid motion in the film is described by boundary layer equations in which account is taken of the mass force, i.e., the force due to gravity. With some approximation, we can assume that in accounting for the effect of the gas on the liquid the liquid flow is described by these same equations.     

Pure steam condensation model with laminar film in a vertical tube

A new physical model for calculating the liquid film thickness and condensation heat transfer coefficient in a vertical condenser tube is proposed by considering the effects of gravity, liquid viscosity, and vapor flow in the core region of the flow. To estimate the velocity profile in the liquid film, the liquid film was assumed to be in Couette flow forced by the interfacial velocity at the liquid–vapor interface. For simplifying the calculation procedures, the interfacial velocity was estimated by introducing an empirical power-law velocity profile. The resulting film thickness and heat transfer coefficient from the model were compared with the experimental data and the results obtained from the other condensation models. The results demonstrated that the proposed model described the liquid film thinning effect by the vapor shear flow and predicted the condensation heat transfer coefficient from experiments reasonably well.     

Nonlinear vibrations of a vapor film in the presence of intense heat fluxes

Waves propagating along the interface between a thin vapor film and a liquid layer in the presence of a heat flux are investigated. The boundary conditions on the vapor-liquid phase surface take into account the temperature dependence of the pressure and the possibilities of formation of the metastable state of the superheated liquid and mass flow. Variations in the saturation pressure as functions of the temperature and mass flux lead to generation of weakly damped periodic waves of low amplitude whose velocity can be much higher than the velocity of the gravity waves. The waves ensure stability of the vapor film beneath the liquid layer in the gravity field. The finite-amplitude waves on the surface of the vapor film differ from the Stokes surface waves on the free surface of isothermal fluid. Instability regimes related with superheating of the liquid ant its explosive boiling when the amplitude of an initially small wave increases to infinity in a finite time can develop in a certain working-parameter regime.     

Flow boiling behaviors in hydrophilic and hydrophobic microchannels

Surface wettability is a critical parameter in small scale phenomena, especially two-phase flow, since the surface force becomes dominant as size decreases. In present study, experiments of water flow boiling in hydrophilic and hydrophobic rectangular microchannels were conducted to investigate the wettability effect on flow boiling in rectangular microchannels. The rectangular microchannels were fabricated with a photosensitive glass to visualize flow pattern. The hydrophilic bare photosensitive glass microchannel was chemically treated to obtain a hydrophobic microchannel. And, visualization of flow patterns was carried out. And boiling heat transfer and two-phase pressure drop was analyzed with visualization results. The boiling heat transfer coefficient in the hydrophobic rectangular microchannel was higher than that in the hydrophilic rectangular microchannel, which was highly related with nucleation site density and liquid film motion. And the pressure drop in the hydrophobic rectangular microchannel was higher than that in the hydrophilic rectangular microchannel, which was highly related with unstable motions of bubble and liquid film. Finally, we find out the wettability is important parameter on the flow pattern, which were highly related with two-phase heat and mass transfer.     

Fundamentals of a liquid (soap) film tunnel

 The continuously running liquid film tunnel (LFT) is a novel device suitable for the study of two-dimensional flows. In this innovation, the films start from a reservoir, run over a horizontal or non-horizontal wire frame and get pulled/washed by a water sheet or by gravity of liquid film. How-ever, despite the simple design and widespread application of LFT, its working mechanisms are not well understood. In the present work, an experimental effort for explaining these mechanisms is reported. The results show that both film velocities and film flow rates increase with water sheet velocity up to a saturation level. This behavior is described via a force balance between the shear force produced by the water sheet and the opposing pulling force of reservoir and boundary layer frictions. The results also show that the average film thickness depends on the surfactant concentration. This is as predicted by a model based on Langmuir’s adsorption theory, in which the liquid film contains two external monolayers of surfactant and a slab of surfactant solution in between. When a film is drawn from the reservoir to the water sheet, the surfactant molecules start migrating from the former to the latter. To restore the thermodynamic equilibrium, the dragged film pulls more surfactant due to Marangoni elasticity, and thus a flow is established. The film flow soon reaches an equilibrium rate as required by the force balance mentioned above. Received: 15 August 1996/Accepted: 12 November 1996     

Flow behavior in microchannel made of different materials with wall slip velocity and electro-viscous effects

In a microfluidic system, flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in a microchannel. The flow-electricity interaction in a complex microfluidic system subjected to joint action of wall slip and electro-viscous effect is an important topic. This paper presents an analytic solution of pressuredriven liquid flow velocity and flow-induced electric field in a two-dimensional microchannel made of different materials with wall slip and electro-viscous effects. The Poisson- Boltzmann equation and the Navier-Stokes equation are solved for the analytic solutions. The analytic solutions agree well with the numerical solutions. It was found that the wall slip amplifies the fow-induced electric field and enhances the electro-viscous effect on flow. Thus the electro-viscous effect can be significant in a relatively wide microchannel with relatively large kh, the ratio of channel width to thickness of electric double layer, in comparison with the channel without wall slip.     

Two-fluid modeling in analyzing the interfacial stability of liquid film flows

The area-averaged two-fluid model formulation of a separated two-phase flow system is used to investigate interfacial stability of liquid film flows. The analysis takes into account the effects of phase change at the interface as well as the dynamic effects of the adjacent vapor flow on the interfacial stability. Wave formation and instability criteria are established in terms of the generalized fluid and flow parameters. The criteria are applied to investigate the stability of laminar liquid film flow with interfacial shear and phase change. The influence of various dimensionless parameters characterizing film thickness, gravity, phase change and interfacial shear are studied with respect to the neutral stability, temporal growth factor and the wave propagation velocity. The results of the present study indicate that the interfacial stability analysis developed within the frame of the two-fluid model formulation proves to be quite accurate as judged by comparing its results with the available experimental data and with the results of much longer and more complex analytical investigations which are valid only for the liquid film free of interfacial shear.     

Wave development on a thinning liquid film

Experimental results are presented for the growth of surface waves on a liquid film that thins as it flows under gravity over the surface of an upright circular cone. The characteristics of the mean film are calculated on the assumption of quasi-parallel flow, and the actual mean thickness found to relate very closely to that found on this basis. The development of the film was found to fall into three phases: the entry zone in which the velocity profile of the film becomes established where no waves are visible, a region of wave growth in which amplitude, wave speed, and wave length all grow, and a final region in which amplitude and wave speed decline as the film thins further although wave length continues to grow. An empirical relationship is presented which expresses the wave number at any point on the cone in terms of the flow rate and a parameter based on the local Reynolds and Weber numbers and cone angle. It was found that for a given flow rate the maximum wave amplitude was reached at a value of wave number of 0·048.     

Ethanol–CO2 two-phase flow in diverging and converging microchannels

The present study investigates experimentally two-phase flow patterns and pressure drop of ethanol and CO₂ in a converging or diverging rectangular microchannel. The two-phase flow pattern visualization is made possible using a high speed video camera. The increased superficial gas velocity due to the acceleration effect and the large pressure drop in a converging channel may result in the elongation of bubbles in slug flow, while the decreased superficial velocity owing to the deceleration effect and the possible pressure rise in the diverging channel may cause shortening of bubbles in slug flow significantly. For both types of channel, the collision and merger of two consecutive bubbles may take place and result in necking of bubbles. Two-phase flow pressure drop in the converging microchannel increases approximately linearly with the increasing liquid or gas flow rate with the frictional pressure drop being the major contributor to the channel pressure drop. In the diverging microchannel, the deceleration effect results in the pressure rise and counteracts the frictional pressure drop. Consequently, for low liquid flow rates the channel pressure drop increases only slightly with the gas flow rate while it is low and a reversed trend appears while it is high. For high liquid flow rates the effect of increasing gas flow rate on channel pressure drop is much more significant; a more significant reverse trend of the effect of gas flow rate is present in the region of high gas flow rates. The two-phase frictional multiplier in the converging or diverging microchannel is quite insensitive to the liquid flow rate and can be fitted very well within ±15% based on the Lockhart–Martinelli equation with a modified Chisholm parameter for the diverging microchannel and together with a modified coefficient for the X⁻² term for the converging microchannel.     

Microbubble lensing-induced photobleaching (μ-BLIP) with application to microflow visualization

The curvature of gas–liquid interfaces and the step change in properties across these interfaces in microchannels are shown here to create a powerful lens/mirror effect. In a hydrophilic system, light incident on the bubble is focused into the surrounding liquid, resulting in a locally increased total light exposure. The optical phenomena leading to this are discussed, and the effect is demonstrated experimentally by imaging the increased photobleaching rate of fluorophores in the near-bubble region. Numerical simulations of the system are performed to investigate the electrical potential and flow fields resulting from the application of an axial electric field. Microbubble lensing-induced photobleaching (-BLIP) is then applied as a method to inject a negative scalar flow marker for flow visualization in microchannels. Once formed, the electrokinetic transport of this marker is analyzed to determine the cross-channel velocity profile of the liquid phase and the liquid velocity in the film. Experimental data is verified by comparison with numerical predictions and previous experimental studies. This contribution represents both a new application of microscale gas–liquid interfacial phenomena, and a new technique for microfluidic flow visualization, particularly applicable (though not limited) to the study of multiphase microchannel flows.     

Simulation and measurement of 3D shear-driven thin liquid film flow in a duct

Three-dimensional flow behavior of thin liquid film that is shear-driven by turbulent air flow in a duct is measured and simulated. Its film thickness and width are reported as a function of air velocity, liquid flow rate, surface tension coefficient, and wall contact angle. The numerical component of this study is aimed at exploring and assessing the suitability of utilizing the FLUENT-CFD code and its existing components, i.e. Volume of Fluid model (VOF) along with selected turbulence model, for simulating the behavior of 3D shear-driven liquid film flow, through a comparison with measured results. The thickness and width of the shear-driven liquid film are measured using an interferometric technique that makes use of the phase shift between the reflections of incident light from the top and bottom surfaces of the thin liquid film. Such measurements are quite challenging due to the dynamic interfacial instabilities that develop in this flow. The results reveal that higher air flow velocity decreases the liquid film thickness but increases its width, while higher liquid flow rate increases both its thickness and width. Simulated results provide good estimates of the measured values, and reveal the need for considering a dynamic rather than a static wall contact angle in the model for improving the comparison with measured values.     

Stability of a vertical liquid film with consideration of the marangoni effect and heat exchange with the environment

The stability of a free vertical liquid film under the combined action of gravity and thermocapillary forces has been studied. An exact solution of the Navier-Stokes and thermal conductivity equations is obtained for the case of plane steady flow with constant film thickness. It is shown that if the free surfaces of the film are perfectly heat insulated, the liquid flow rate through the cross section of the layer is zero. It is found that to close the model with consideration of the heat exchange with the environment, it is necessary to specify the liquid flow rate and the derivative of the temperature with respect to the longitudinal coordinate or the flow rate and the film thickness. The stability of the solution with constant film thickness at small wave numbers is studied. A solution of the spectral problem for perturbations in the form of damped oscillations is obtained.     

Nonlinearwaves in a liquid film-gas flow system

The instability and regular nonlinear waves in the film of a heavy viscous liquid flowing along the wall of a round tube and interacting with a gas flow are investigated. The solutions for the wave film flows are numerically obtained in the regimes from free flow-down in a counter-current gas stream to cocurrent upward flow of the film and the gas at fairly large gas velocities. Continuous transition from the counter-current to the cocurrent flow via the state with a maximum amplitude of nonlinear waves and zero values of the liquid flow rate and the phase velocity is investigated. The Kapitsa-Shkadov method is used to reduce a boundary value problem to a system of evolutionary equations for the local values of the layer thickness and the liquid flow rate.     

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.     

Numerical simulation of convective heat transfer to a radial free surface jet impinging on a hot solid

The convective heat transfer between a circular free surface impinging jet and a solid surface has been studied numerically. The thin liquid film formed on the surface has been assumed to be in non-turbulent free surface flow. The effects of surface tension, viscosity, gravity and heat transfer between the film flow and the solid surface have been taken into account. The flow structure on a non-heated surface has been investigated first. Next, the steady-state flow structure in the liquid film as well as the heat transfer has been examined. The predicted results have been compared with experimental data for the purpose of validating the analysis. The hydrodynamics of the liquid film and the heat transfer processes have been investigated numerically to understand the physics of the phenomena. Received on 5 October 1998     

Turbulence modification in vertical upward annular flow passing through a throat section

Experimental studies on the turbulence modification in annular two-phase flow passing through a throat section were carried out. The turbulence modification in multi-phase flow due to the interactions between two-phases is one of the most interesting scientific issues and has attracted research attention. In this study, the gas-phase turbulence modification in annular flow due to the gas–liquid phase interaction is experimentally investigated. The annular flow passing through a throat section is under the transient state due to the changing cross sectional area of the channel and resultantly the superficial velocities of both phases are changed compared with a fully developed flow in a straight pipe. The measurements for the gas-phase turbulence were precisely performed by using a constant temperature hot-wire anemometer, and made clear the turbulence structure such as velocity profiles, fluctuation velocity profiles. The behavior of the interfacial waves in the liquid film flow such as the ripple or disturbance waves was also observed. The measurements for the liquid film thickness by the electrode needle method were also performed to measure the base film thickness, mean film thickness, maximum film thickness and wave height of the ripple or the disturbance waves.     

Model of a wavy flow in a falling film of a viscous liquid

A new model is developed for describing long-wave perturbations in a falling film of a viscous liquid. The model is based on an integral approach and an expansion of the velocity profile into a series in linearly independent basis functions of a boundary-value problem. A linear analysis of film flow stability is performed, and dispersion dependences are obtained. Results predicted by the new model are demonstrated to be in good agreement with available experimental data on the film flow over a gently sloping surface.     

Noncontact manipulation of microflow by photothermal control of viscous force

In this paper, we investigate a potential of local control of the viscous force in a microfluidic device for a noncontact microflow manipulation method. Photothermal effect and temperature dependence of the liquid viscosity play a key role to induce an inhomogeneous viscosity distribution in the flow field in a microchannel. Absorption of focused laser beam generates the local change in the viscosity of liquid corresponding to the temperature change. The velocity and temperature fields are measured by the micron-resolution particle image velocimetry and laser-induced fluorescence, respectively. Measurement results indicate that the local reduction of the fluid viscosity due to the temperature rise can cause the change of the flow structure in the microchannel. At the focused area of heating laser beam, namely high temperature area, the flow velocity was increased. The accompanying fluid behavior around the heated region was also recognized. In addition, the agreement between the experimental results and numerical simulation clarifies that the primary factor for the change of the microflow structure is the locally controlled viscous force.     

Application of PIV to velocity measurements in a liquid film flowing down an inclined cylinder

PIV technique is applied for measurements of instant velocity distributions in a liquid film flowing down an inclined tube in the form of a wavy rivulet. An application of special optical calibration is applied to correct distortion effects caused by the curvature of the interface. A vortex flow of liquid is observed inside a wave hump in the reference system moving with wave phase velocity. Conditionally averaged profiles of longitudinal and transverse components of liquid velocity are obtained for different cross-sections of developed non-linear waves. It is shown that the increase in wave amplitude slightly changes the location of the vortex center. The analysis of modification of vortex motion character due to wavy flow conditions, such as tube inclination angle, film Reynolds number, wave excitation frequency, is fulfilled.     

A multiphase,micro-scale PIV measurement technique for liquid film velocity measurements in annular two-phase flow

Prediction methods for two-phase annular flow require accurate knowledge of the velocity profile within the liquid film flowing at its perimeter as the gradients within this film influence to a large extent the overall transport processes within the entire channel. This film, however, is quite thin and variable and traditional velocimetry methods have met with only very limited success in providing velocity data. The present work describes the application of Particle Image Velocimetry (PIV) to the measurement of velocity fields in the annular liquid flow. Because the liquid is constrained to distances on the order of a millimeter or less, the technique employed here borrows strategies from micro-PIV, but micro-PIV studies do not typically encounter the challenges presented by annular flow, including very large velocity gradients, a free surface that varies in position from moment to moment, the presence of droplet impacts and the passage of waves that can be 10 times the average thickness of the base film. This technique combines the seeding and imaging typical to micro-PIV with a unique lighting and image processing approach to deal with the challenges of a continuously varying liquid film thickness and interface. Mean velocity data are presented for air–water in two-phase co-current upward flow in a rectangular duct, which are the first detailed velocity profiles obtained within the liquid film of upward vertical annular flow to the authors’ knowledge. The velocity data presented here do not distinguish between data from waves and data from the base film. The resulting velocity profiles are compared with the classical Law of the Wall turbulent boundary layer model and found to require a decreased turbulent diffusivity for the model to predict well. These results agree with hypotheses previously presented in the literature.