Stability of viscoelastic liquid curtain

Thin liquid sheets occur in several practical applications. In curtain coating, a thin liquid sheet is formed and falls freely over a considerable height before it impinges onto a moving substrate. Precision curtain coating was developed for multi layer photographic films but its use has expanded to many different applications. One of the important limits of this process is the stability of the liquid curtain, which may define the minimal thickness that can be coated at a given web speed.The condition at which a low viscosity Newtonian liquid curtain breaks was first derived based on a simple balance between inertial and capillary forces. There is a critical flow rate below which the curtain becomes unstable. For viscoelastic liquids, the normal stress related to the stretching of polymer molecules as the liquid accelerates down the curtain changes the force balance. Here, the critical condition at which a viscoelastic liquid curtain breaks was determined as a function of the rheological properties of the liquid. The results show that high extensional viscosity liquids create more stable curtains. Liquid additives could be used to push the limits of curtain flow rates to smaller values and consequently to widen the operability window of the process.     

Effect of viscosity on liquid curtain stability

The effect of viscosity on liquid curtain stability was explored by high‐speed visualization. Measurements of the velocity within the curtain revealed the presence of a viscous boundary layer along the edge guides. The critical condition at the onset of curtain breakup was determined by identifying the flow rate below which the curtain broke for two different edge guide geometries: parallel and convergent. Curtain breakup was initiated by the expansion of a hole within the curtain. For low viscosity liquid, the measured hole retraction speed is independent of the viscosity and equal to the Taylor‐Culick speed. For high viscosity liquids, the retraction speed is lower than the Taylor‐Culick speed due to viscous forces that resist the flow. The results also show the effect of liquid viscosity on the curtain stability is a strong function of the edge guide design. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1448–1457, 2018     

DEM and experimental analysis of the water retention curve in polydisperse granular media

We investigate the water distribution and the link between suction and water content in granular media. Firstly, we examine the effect of suction on the shape and the volume of the liquid bridge by four different methods. Method I is based on the local expression of the capillary force coupled with the gorge method and Method II is based on the Laplace law. These two methods use the toroidal approximation. Methods III and IV are based on the integration of the differential equation that defines the liquid bridge shape (established from the Laplace law). This local behaviour is then used in a discrete element study of a sample composed of several thousands of grains. We focus our study on the pendular state. A liquid film around the grains involving the continuity of the liquid phase is assumed. The water distribution and the water content associated with a given suction are calculated. Then retention curves of the granular media are built. A parametric study is made to bring to light the effect of macroscopic parameters (grain-size distribution) and physical parameters (liquid/air surface tension and contact angle) on the water retention curve. Finally, numerical data are compared to experimental results.     

Resonance penetration of gas bubbles through a thin liquid layer: a capillary resonator and its use for the generation of droplets

As it is well known, a bounded layer of liquid forms an oscillatory system (resonator) for surface waves. We consider a capillary wave resonator that is composed by a thin liquid layer placed on a substrate and surrounded by a solid ring. The dimensions of the system are chosen so that gravity forces are small compared with forces from surface tension. Standing capillary waves are excited by a gas flow supplied through a small orifice in the substrate. Stable oscillations in various resonator modes are described which are accompanied by ordered formation and destruction of gas bubbles producing the regular streams of identical droplets. The mechanism of self-oscillatory behaviour based on the correspondence between bubble growth time and oscillation period is proposed and analysed. Possible applications of the phenomenon, in particular, for the generation of monodisperse droplets without special periodic stimulation, are discussed.     

Decreasing the parameters of an air shock wave using an air-water curtain

The efficiency of using an air-water drop curtain for protection from the force and noise action of an air shock wave generated by an open explosion is studied experimentally. It is shown that the curtain generated by outburst of sprayed water after an advanced underwater explosion of a demolition cord is a reliable means of pressure decrease at the shock-wave front. The dependence of the “effective coefficient of charge-mass reduction” on the position of the curtain relative to the point of explosion, its length, time of evolution, and other conditions was studied. Zones with local pressure increase or decrease in the shock wave were found, which is explained by imposition of secondary compression and expansion waves on the shock wave. Possible physical mechanisms that ensure the protective effect are considered. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 3, pp. 120–130, May–June, 2000.     

A comprehensive study of the liquid transfer from the front to the back of a vertical perforated sheet

Perforations contribute to liquid redistribution in corrugated sheet packings. We focus on a simplified but relevant experimental configuration where a vertical perforated flat sheet is supplied with liquid on its front side. We examine how the perforations irrigate the back of the plate. We successively consider a single perforation, a spanwise row of perforations, and a staggered array of perforations. We quantify the liquid transfer through a single row of perforations and find that the transferred flow rate per unit perforation diameter varies linearly with the supply flow rate per unit width. We also analyze the spreading of the rivulets leaking from the perforations, their merging into a continuous wavy film, and the leveling of this film as it falls down the plate. The spreading and the merging exhibit a power-law behavior in agreement with theoretical models. The leveling exhibits exponential decay behavior.     

Detection and analysis of transition from annular to intermittent flow in vertical tubes

In vertical co-current gas-liquid flow, the transition from annular to intermittent flow occurs when gas core becomes interrupted by liquid bridges due to the instability of the interfacial capillary waves. An analytical model is formulated to explain the liquid bridging in terms of the growth of finite amplitude interfacial capillary waves. Experimental results show that the longest wave length, which is associated with the transition, is about eight times the wave length of waves moving with the velocity of the liquid film.     

Measurement of liquid film profiles by Moiré topography

Area-wide surface topography is continuously monitored with the moiré technique, i.e. measurement of patterns formed by superposition of the warped image of a line grating on a similar reference grating. A simple method for reconstructing liquid film profiles from moir$\text{\$}\text{?}$fringe patterns is developed. The method is tested with a known specimen, a convex lens. Leveling of an uneven liquid film by gravity and capillary force is followed and film profiles are measured at intervals of time. Waves flowing down an inclined plate and disturbances in a liquid curtain are viewed, as are small disturbances caused by the impingement of tiny surface-active particles. Possible application to control of coating operations is pointed out.     

Wave interactions on a viscous film coating a vertical fibre: Formation of bound states

Fibre coating has attracted considerable attention over the past years due to its engineering applications as well as fundamental interest generated by the fascinating complexity of the resulting flow. A liquid film coating axisymmetrically a vertical fibre and flowing under the action of gravity spontaneously breaks up into a regular drop-like wave train. This instability results primarily from the capillary pressure induced by the azimuthal curvature (Rayleigh–Plateau instability) while the pressure induced by the axial curvature has a stabilising effect. Streamwise viscous diffusion plays a dispersive role that dramatically affects the waves selection, speeds and shapes. When both surface tension and viscosity effects are strong, complex wave interactions lead to the formation of bound states. In this study, we investigate experimentally the details of those interactions and show that regular patterns of bound states can be obtained by external forcing. A qualitative theoretical explanation of the experimental findings is provided with a simple model for the flow.     

Pore-network modeling of liquid water transport in gas diffusion layer of a polymer electrolyte fuel cell

A pore-network model is developed to study the liquid water movement and flooding in a gas diffusion layer (GDL), with the GDL morphology taken into account. The dynamics of liquid water transport at the pore-scale and evolution of saturation profile in a GDL under realistic fuel cell operating conditions is examined for the first time. It is found that capillary forces control liquid water transport in the GDL and that liquid water moves in connected clusters with finger-like liquid waterfronts, rendering concave-shaped saturation profiles characteristic of fractal capillary fingering. The effect of liquid coverage at the GDL–channel interface on the liquid water transport inside GDL is also studied, and it is found that liquid coverage at the GDL–channel interface results in pressure buildup inside the GDL causing the liquid water to break out from preferential locations.     

Viscoelasticity and Kinetics of Wetting on Rubber

The kinetics of spreading of a liquid drop is usually controlled by conversion of capillary potential energy into viscous dissipation within the liquid when the solid is rigid. However, if the solid is soft, a “wetting ridge” near the solid/liquid/vapour triple line can also be a dissipative sink as the wetting front moves. As a consequence, the kinetics of wetting of rubber may be controlled essentially by viscoelastic losses in the polymer rather than by viscous losses in the liquid drops. Therefore, a direct analogy between the kinetics of wetting and adhesion, respectively, for a liquid and a solid on an elastomeric substrate has been recently proposed. In this paper, the superposition of viscoelastic braking and moderate rubber swelling in the drop spreading phenomenon is considered.     

Single-phase flow model development for macroscopic liquid flow evaluation in gas–liquid reactors, by computational fluid dynamics

This paper proposes a single-phase flow model to simulate the flow induced in a liquid by the injection of gas dispersed in the form of a bubble curtain. It aims at predicting macroscopic liquid flow and mixing time. This single-phase flow model is developed as an alternative to two-phase flow models. The model is based on the assumption that the liquid flow is induced by a density imbalance between the bulk zone and the bubble curtain zone. The density in the bulk is set to the water density while the density in the bubble curtain corresponds to the air–water mixture density and is assessed by numerical simulations, thanks to an iterative procedure. Only the knowledge of the injected air flow rate and the bubble liquid relative velocity is required. The single-phase flow model is applied to assess the liquid flow and the mixing in open quarries having a complex geometry. The liquid velocities and the flow structure in the open quarries simulated with the single-phase flow model are in good agreement with those predicted by numerical simulations based on a two-phase flow model.     

Study of liquid spreading from a point source in a trickle bed via gamma-ray tomography and CFD simulation

Gamma-ray tomography and a liquid collecting device have been used to detect liquid spreading from a single point source in a trickle bed. This basic configuration has been chosen to evaluate the radial spreading of liquid flow through a fixed bed. The experimental data are used to validate the two-dimensional (2D) computational fluid dynamic model (CFD) developed at the CREL laboratory for gas/liquid trickle flows inside a fixed bed [Jiang et al., 2002. A.I.Ch.E. Journal 48, 701-730]. The data obtained show the influence of liquid and gas flow rates and the impact of pre-wetting condition on liquid distribution evolution along fixed bed axis. The comparison between experimental data and simulation results shows a significant effect of the capillary pressure term on prediction of the radial spreading of the liquid flow. Several physical models for the capillary pressure term are tested in order to select the closure law that allows a proper prediction of liquid spreading at trickle flow conditions.     

竖直多孔平板上液膜流动特性的研究

孔结构被广泛应用于传质塔填料中,对填料上的液膜流动和传质行为影响较大。对竖直光板和多孔板上的液膜流动进行了三维模拟,并通过实验验证了模拟的准确性。通过模拟研究了孔结构对液膜流动特性的影响。结果表明,干燥孔会阻碍液膜的铺展,而润湿孔促进液膜的铺展。与光板相比,多孔板上的液膜具有起伏波,这将影响液膜的厚度分布和速度分布。液膜厚度波动和水平方向的速度波动随着孔径的增加而增加,而竖直流动方向的速度随着孔径的增加而降低。当孔径增加到一定值时,毛细波将出现在孔中的液膜中,这大大增加液膜水平方向上的波动速度,而降低流动方向上的速度。当孔径继续增加到临界值时,液膜将破裂。多孔板上孔内和气侧区域存在涡旋,能够促进内部液体交换和增大气侧扰动,从而增强传质能力。     

Numerical Analyses on the Adhesive Contact between a Sphere and a Longitudinal Wavy Surface

The adhesive contact between a sphere and a longitudinal wavy surface is simulated numerically. A modified simulation method is proposed using the Newton BI-CGSTAB method in a rectangular coordinate. The effective Tabor parameter is proposed. It is found that when the amplitude of the wavy surface is larger, the contact area is smaller and the pull-off force is smaller. Jump-in from noncontact phenomena occurs when the Tabor parameter is large. Jumping from one ridge to the next ridge occurs when the effect of the Tabor parameter is large and the amplitude of the wavy surface is not too small. Jumping from noncontact to full contact is affected by the amplitude and the wave number of the wavy surface and is also affected by the Tabor parameter.     

Evaporation in a capillary tube of square cross-section: application to ion transport

Modelling of evaporation of a pure liquid within a capillary tube of circular cross-section is a classic problem which has been the subject of many studies. Here we consider the case of tubes of polygonal cross-section. This case leads to quite different results owing to the liquid flow along the tube edges induced by the capillary forces. Various evaporation regimes can be distinguished depending on the competition between capillary, gravity and viscous forces. We concentrate on the regime dominated by the capillary forces. It is shown that the position z₀ of the bulk meniscus should scale as z₀∝t in this case. The prefactor depends on the liquid distribution within the entrance region of the tube. A simplified model for a tube of square cross-section is then presented and calibrated against data from three-dimensional simulations. The last part of the paper is devoted to an analysis of ion transport during evaporation in a tube of square cross-section. The results suggest that the ion transport by liquid film can be a very effective mechanism for explaining the formation of efflorescence at the surface of porous media.     

Residence time study of a two-phase mixture in a horizontal cylindrical vessel

A cold model of a rotary holding furnace was studied using water and a kerosene-LIX^® 973N organic mixture which are immiscible. The flow of the feed was found to behave similar to a gravity current where the feed preferentially moved along the liquid–liquid interface. Visual observation and residence time distribution obtained showed that the flow of the lighter feed mixture was similar to a laminar flow but with a preferential route along the wall with the outlet spout. In the commercial-scale rotary holding furnace, plug flow conditions are considered desirable while mixing or short-circuiting is considered undesirable. The flow in the cold model was fitted to a plug flow and three CSTRs all in series and a particular depth of the upper layer of organic was found where mixing with the bath fluid was a maximum. Air bubbling in the centre of the cold model showed that at low air flow rates, the air curtain acted to limit mixing but as the air flow rates increased, the increased circulation caused by the air flow increased mixing and negated the air curtain effect.     

Factors Affecting the Significance of Gravity on the Infiltration of a Liquid into a Porous Solid

A mathematical model is formulated to illustrate the significance of gravity on the infiltration of a liquid in a porous solid. The result indicates that the relative significance of gravity on the infiltration depth depends on the infiltration time as well as the properties of the permeating liquid and the porous solid. The effect of gravity can be neglected for a short infiltration time, and for infiltration systems with the infiltrating liquid having a large value of surface energy, a small value of wetting angle on the solid, and a low density, and the porous solid having a small equivalent capillary radius and a small tortuosity.     

Capillary forces between two solid spheres linked by a concave liquid bridge: Regions of existence and forces mapping

This article focuses on the capillary interactions arising when two spherical particles are connected by a concave liquid bridge. This scenario is found in many situations where particles are partially wetted by a liquid, like liquid films stabilized with nanoparticles. We analyze different parameters governing the liquid bridge: interparticle separation, wetting angle and liquid volume. The results are compiled in a liquid volume‐wetting angle diagram in which the regions of existence (stability) or inexistence (instability) of the bridge are outlined and the possible maximum and minimal particle distances for which the liquid bridge may be found. Calculations of the capillary forces discriminate those conditions for which such force is repulsive or attractive. The results are plotted in form of maps that allow an easy understanding of the stability of a liquid bridge and the conditions at which it may be produced for the two particle model. © 2009 American Institute of Chemical Engineers AIChE J, 2009