scholarly journals Suppression of the Kapitza instability in confined falling liquid films

2018 ◽  
Vol 860 ◽  
pp. 608-639 ◽  
Author(s):  
Gianluca Lavalle ◽  
Yiqin Li ◽  
Sophie Mergui ◽  
Nicolas Grenier ◽  
Georg F. Dietze
Keyword(s):  
Linear Stability ◽  
Pressure Difference ◽  
Film Surface ◽  
Water Film ◽  
Narrow Channel ◽  
Liquid Films ◽  
Interfacial Instability ◽  
Critical Conditions ◽  
Driving Mechanism ◽  
Strong Confinement

We revisit the linear stability of a falling liquid film flowing through an inclined narrow channel in interaction with a gas phase. We focus on a particular region of parameter space, small inclination and very strong confinement, where we have found the gas to strongly stabilize the film, up to the point of fully suppressing the long-wave interfacial instability attributed to Kapitza (Zh. Eksp. Teor. Fiz., vol. 18 (1), 1948, pp. 3–28). The stabilization occurs both when the gas is merely subject to an aerostatic pressure difference, i.e. when the pressure difference balances the weight of the gas column, and when it flows counter-currently. In the latter case, the degree of stabilization increases with the gas velocity. Our investigation is based on a numerical solution of the Orr–Sommerfeld temporal linear stability problem as well as stability experiments that clearly confirm the observed effect. We quantify the degree of stabilization by comparing the linear stability threshold with its passive-gas limit, and perform a parametric study, varying the relative confinement, the Reynolds number, the inclination angle and the Kapitza number. For example, we find a 30 % reduction of the cutoff wavenumber of the instability for a water film in contact with air, flowing through a channel inclined at $3^{\circ }$ and of height 2.8 times the film thickness. We also identify the critical conditions for the full suppression of the instability in terms of the governing parameters. The stabilization is caused by the strong confinement of the gas, which produces perturbations of the adverse interfacial tangential shear stress that are shifted by half a wavelength with respect to the wavy film surface. This tends to reduce flow-rate variations within the film, thus attenuating the inertia-based driving mechanism of the Kapitza instability.

scholarly journals The linear stability of a Stokes layer subjected to high-frequency perturbations

2014 ◽  
Vol 764 ◽  
pp. 193-218 ◽  
Author(s):  
Christian Thomas ◽  
P. J. Blennerhassett ◽  
Andrew P. Bassom ◽  
Christopher Davies
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
High Frequency ◽  
Wall Motion ◽  
Critical Reynolds Number ◽  
Narrow Channel ◽  
Critical Conditions ◽  
Stokes Layer ◽  
Quantitative Results ◽  
Sinusoidal Wall

AbstractQuantitative results for the linear stability of planar Stokes layers subject to small, high-frequency perturbations are obtained for both a narrow channel and a flow approximating the classical semi-infinite Stokes layer. Previous theoretical and experimental predictions of the critical Reynolds number for the classical flat Stokes layer have differed widely with the former exceeding the latter by a factor of two or three. Here it is demonstrated that only a 1 % perturbation, at an appropriate frequency, to the nominal sinusoidal wall motion is enough to result in a reduction of the theoretical critical Reynolds number of as much as 60 %, bringing the theoretical conditions much more in line with the experimentally reported values. Furthermore, within the various experimental observations there is a wide variation in reported critical conditions and the results presented here may provide a new explanation for this behaviour.

scholarly journals Direct observation of anisotropic growth of water films on minerals driven by defects and surface tension

2020 ◽  
Vol 6 (30) ◽  
pp. eaaz9708 ◽  
Author(s):  
Sibel Ebru Yalcin ◽  
Benjamin A. Legg ◽  
Merve Yeşilbaş ◽  
Nikhil S. Malvankar ◽  
Jean-François Boily
Keyword(s):  
Surface Tension ◽  
Water Vapor ◽  
Film Growth ◽  
High Surface ◽  
Film Surface ◽  
Water Film ◽  
Element Cycling ◽  
Water Films ◽  
Nanoscale Topography ◽  
Underlying Mechanisms

Knowledge of the occurrences of water films on minerals is critical for global biogeochemical and atmospheric processes, including element cycling and ice nucleation. The underlying mechanisms controlling water film growth are, however, misunderstood. Using infrared nanospectroscopy, amplitude-modulated atomic force microscopy, and molecular simulations, we show how water films grow from water vapor on hydrophilic mineral nanoparticles. We imaged films with up to four water layers that grow anisotropically over a single face. Growth usually begins from the near edges of a face where defects preferentially capture water vapor. Thicker films produced by condensation cooling completely engulf nanoparticles and form thicker menisci over defects. The high surface tension of water smooths film surfaces and produces films of inhomogeneous thickness. Nanoscale topography and film surface energy thereby control anisotropic distributions and thicknesses of water films on hydrophilic mineral nanoparticles.

The Thermocapillary Convection in Locally Heated Laminar Liquid Film Flow Caused by a Co-Current Gas Flow in Narrow Channel

2003 ◽  
Author(s):  
E. Y. Gatapova ◽  
Y. V. Lyulin ◽  
I. V. Marchuk ◽  
O. A. Kabov ◽  
J.-C. Legros
Keyword(s):  
Free Surface ◽  
Analytical Solution ◽  
Liquid Film ◽  
Gas Flow ◽  
Surface Deformation ◽  
Plane Channel ◽  
Film Surface ◽  
Local Heat ◽  
Narrow Channel ◽  
Liquid Film Flow

A two-dimensional model of a steady laminar flow of liquid film and co-current gas flow in a plane channel is considered. It is supposed that the height of a channel is much less than its width. There is a local heat source on the bottom wall of the channel. An analytical solution for the temperature distribution problem in locally heated liquid film is obtained, when the velocity profile is linear. An analytical solution of the linearized equation for thermocapillary film surface deformation is found. A liquid bump caused by the thermocapillary effect in the region where thermal boundary layer reaches the film surface is obtained. Damped oscillations of the free surface may exist before the bump. This is obtained according to the solution of the problem in an inclined channel. It depends on the forces balance in the film. The defining criterion is found for this effect. The oscillations of free surface do not exist for horizontally located channel.

scholarly journals Stability of liquid films down an inclined plane

2006 ◽  
Vol 28 (4) ◽  
pp. 219-224
Author(s):  
Phan Thi Thu Phuong ◽  
Tran Van Tran
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Linear Stability ◽  
Viscous Liquid ◽  
Difference Method ◽  
Liquid Films ◽  
Inclined Plane ◽  
Wave Numbers

In this paper, the problem of linear stability of viscous liquid films down an inclined plane is solved by finite difference method. It is applicable for moderate values of Reynolds and wave numbers. The obtained results by this method is compared with ones of some papers and with experimental data.

The Influence of Evaporation in Shear-Driven Liquid Film on Heat Removal From Local Heater

2006 ◽  
Author(s):  
Elizaveta Gatapova ◽  
Oleg Kabov
Keyword(s):  
Liquid Film ◽  
Thin Liquid Film ◽  
Heat Removal ◽  
Film Surface ◽  
Numerical Data ◽  
High Heat ◽  
Liquid Films ◽  
High Heat Flux ◽  
Maximal Surface ◽  
High Heat Transfer

The present work focuses upon shear-driven liquid film evaporative cooling of high heat flux local heater. Thin evaporating liquid films may provide very high heat transfer rates and can be used for cooling of high power microelectronic systems. Thermocapillary convection in a liquid film falling down a locally heated substrate has recently been extensively studied. However, non-uniform heating effects remain only partially understood for shear-driven liquid films. The combined effects of evaporation, thermocapillarity and gas dynamics as well as formation of microscopic adsorbed film have not been studied. The effect of evaporation on heat and mass transfer for 2D joint flow of a liquid film and gas is theoretically and numerically investigated. The convective terms in the energy equations are taken into account. The calculations reveal that evaporation from film surface essential influences on heat removal from local heater. It is shown that the thermal boundary layer plays significant role for cooling local heater by evaporating thin liquid film. Measured by an infrared scanner temperature distribution at the film surface is compared with numerical data. Calculations satisfactorily describe the maximal surface temperature value.

Linear stability analysis of two-way coupled particle-laden density current

2017 ◽  
Vol 95 (3) ◽  
pp. 291-296 ◽  
Author(s):  
Pouriya Amini ◽  
Ehsan Khavasi ◽  
Navid Asadizanjani
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Base Flow ◽  
Interfacial Instability ◽  
Linear Stability Theory ◽  
Flow Density ◽  
Density Current ◽  
Density Currents

Stability of two-way coupled particle-laden density current is studied with the aim of linear stability analysis. Interfacial instability can be found in density currents, which effects entrainment and the rate of effective mixing. In this paper, we investigate the density current interfacial instability using linear stability theory, considering the particles attendance. The ultimate goal is to extract the governing equation for current with particles and study the effect of different parameters on stability of such currents. Base flow has velocity and density profiles of tangent hyperbolic type. Main current and particles are studied in two separate phases. It is found that current will be more stable as M0 (M0 = S∗N∗/ρ∗ where ρ∗ is the non-dimensional flow density, S∗ is the Stokes’ drag coefficient, and N∗ is the particles’ number density) grows, this is a result of number of particles and their radius, and also viscosity effects. The current is more stable as the growth rate increases. As the Richardson number in M0 rises, the growth rate value decreases. As the slope of the river bed increases, the current is less stable.

Effect of Longitudinal Mini-Grooves on Flow Stability and Wave Characteristics of Falling Liquid Films

2007 ◽  
Author(s):  
Klaus Helbig ◽  
Ralph Nasarek ◽  
Tatiana Gambaryan-Roisman ◽  
Peter Stephan
Keyword(s):  
Wave Propagation ◽  
Film Thickness ◽  
Linear Stability ◽  
Propagation Speed ◽  
Wave Theory ◽  
Liquid Films ◽  
Transport Processes ◽  
Thickness Variation ◽  
Experimental Findings ◽  
Falling Liquid Films

Falling liquid films are used in many industrial apparatuses. In many cases the film flow along a wall with topography is considered advantageous for intensification of the transport processes. We use the shadow method and the chromatic white light sensor (CHR) method to study the wavy structure of falling films on flat walls and on walls with longitudinal grooves. We show that the wavy pattern substantially changes on walls with topography. The wave frequency, the wave propagation velocity and the area of the liquid-gas interface decrease on grooved walls. The linear stability of the film has been analyzed using the long-wave theory, which relies on the assumption that the average film thickness is much smaller than the scale of the film thickness variation. The linear stability analysis predicts that the disturbance growth rate, the frequency of the fastest growing disturbance mode and the wave propagation speed decrease on a tube with longitudinal mini-grooves in comparison with a smooth tube. These results agree well with the experimental findings.

Multi-Zone Ice Accretion and Roughness Models for Aircraft Icing Numerical Simulation

2016 ◽  
Vol 8 (5) ◽  
pp. 737-756 ◽  
Author(s):  
Chengxiang Zhu ◽  
Chunling Zhu ◽  
Tao Guo
Keyword(s):  
Numerical Simulation ◽  
Mass Distribution ◽  
Water Film ◽  
Heat Transfer Process ◽  
Critical Conditions ◽  
Ice Accretion ◽  
Flow State ◽  
Aircraft Icing ◽  
Equilibrium Equations ◽  
Airfoil Surface

AbstractA mathematical multi-zone ice accretion model used in the numerical simulation of icing on airfoil surface based on three water states, namely, continuous film, rivulets and beads is studied in this paper. An improved multi-zone roughness model is proposed. According to the flow state of liquid water and film flow, rivulets flow governing equations are established to calculate film mass distribution, film velocity, rivulet wetness factor and rivulet mass distribution. Force equilibrium equations of droplet are used to establish the critical conditions of water film broken into rivulets and rivulets broken into beads. The temperature conduction inside the water layer and ice layer is considered. Using the proposed model ice accretion on a NACA0012 airfoil profile with a 4° angle of attack under different icing conditions is simulated. Different ice shapes like glaze ice, mixed ice and rime ice are obtained, and the results agree well with icing wind tunnel experiment data. It can be seen that, water films are formed on the surface, and heights of the films vary with icing time and locations. This results in spatially-temporally varying surface roughness and heat transfer process, ultimately affects the ice prediction. Model simulations indicate that the process of water film formation and evolution cannot be ignored, especially under glaze ice condition.

Sliding instability of draining fluid films

2018 ◽  
Vol 857 ◽  
pp. 111-141 ◽  
Author(s):  
Georg F. Dietze ◽  
Jason R. Picardo ◽  
R. Narayanan
Keyword(s):  
Stability Analysis ◽  
Transient Stability ◽  
Water Film ◽  
Interfacial Instability ◽  
Pressure Gradients ◽  
Fluid Films ◽  
Steady Regime ◽  
Sliding Motion ◽  
Residual Film ◽  
Sliding Instability

The aim of this paper is to show that the spontaneous sliding of drops forming from an interfacial instability on the surface of a wall-bounded fluid film is caused by a symmetry-breaking secondary instability. As an example, we consider a water film suspended from a ceiling that drains into drops due to the Rayleigh–Taylor instability. Loss of symmetry is observed after the film has attained a quasi-steady state, following the buckling of the thin residual film separating two drops, whereby two extremely thin secondary troughs are generated. Instability emanates from these secondary troughs, which are very sensitive to surface curvature perturbations because drainage there is dominated by capillary pressure gradients. We have performed two types of linear stability analysis. Firstly, applying the frozen-time approximation to the quasi-steady base state and assuming exponential temporal growth, we have identified a single, asymmetric, unstable eigenmode, constituting a concerted sliding motion of the large drops and secondary troughs. Secondly, applying transient stability analysis to the time-dependent base state, we have found that the latter is unstable at all times after the residual film has buckled, and that localized pulses at the secondary troughs are most effective in triggering the aforementioned sliding eigenmode. The onset of sliding is controlled by the level of ambient noise, but, in the range studied, always occurs in the quasi-steady regime of the base state. The sliding instability is also observed in a very thin gas film underneath a liquid layer, which we have checked for physical properties encountered underneath Leidenfrost drops. In contrast, adding Marangoni stresses to the problem substantially modifies the draining mechanism and can suppress the sliding instability.

The flow of thin liquid films between rollers

1961 ◽  
Vol 11 (1) ◽  
pp. 33-50 ◽  
Author(s):  
E. Pitts ◽  
J. Greiller
Keyword(s):  
Flow Regime ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Experimental Results ◽  
Critical Conditions ◽  
Theoretical Treatment ◽  
Uniform Thickness ◽  
Full Agreement ◽  
Low Speeds

When rollers, placed horizontally and side by side so that each is half immersed in a tank of liquid, rotate in opposite directions, liquid is carried through the gap between them and divides to form a sheet over each roller. At low speeds the sheets are of uniform thickness across the width of the rollers, but at higher speeds they are regularly ridged owing to alternate increase and decrease in thickness. Preliminary observations led to the development of an approximate theoretical treatment of the even-flow régime and the critical conditions when the ribbed flow is about to begin. Results of this work are in full agreement with detailed experimental results.

Sign in / Sign up

Export Citation Format

Share Document