Taylor diffusion in falling liquid films

The Taylor diffusion model is applied to the interpretation of residence time distribution measurements in falling liquid films. In a range of Reynolds numbers from 40 to 1000, the application shows considerable systematic deviations. This indicates firstly, that the transverse transport mechanisms are not efficient enough to justify the application of the diffusion model, and secondly, that the transport mechanisms vary considerably through-out the film thickness. These observations are in full agreement with the theory at the wall by Spalding.The data used for this analysis are taken from frequency response measurements, where the Fourier transform is applied to the parameter estimation. By this transform, the effect of the mass transfer between streamlines in a velocity distribution is demonstrated by an interaction matrix from the differential equation for tracer dispersion.     

Conjugate heat transfer in turbulent falling liquid films

Heat transfer characteristics for a falling turbulent liquid film flow over a fin are analyzed using the conjugate convection-conduction theory. Numerical results are obtained from a simultaneous solution of the energy equations of the fluid and the fin. Results are presented for the fin temperature distribution, dimensionless heat transfer coefficients, local heat fluxes, and fin efficiencies.     

液体降膜中Marangoni效应的研究进展

降膜过程中的Marangoni效应是当前流体传递过程与非线性理论研究领域中的热点,对产品质量具有重要影响。回顾了近几年国内外关于Marangoni效应的最新研究进展,重点介绍了有关热Marangoni效应的实验及理论研究成果,并进行了比较和分析。结果发现,Marangoni效应与体系温度和浓度变化等有关,并会影响降膜稳定性。同时,针对目前研究中存在的一些不足,提出了今后研究工作的一些建议。     

Terminal velocity of non-spherical particles falling through a Carreau model liquid

A procedure has been proposed for the estimation of the terminal falling velocity of non-spherical particles moving in a Carreau model fluid in the transition flow region. The procedure is based on a modification of the relationship formerly developed for the fall of spherical particles including the particle dynamic shape factor. The suitability of the proposed procedure has been confirmed by good agreement between experimental and calculated terminal falling velocity data. In the experiments, the terminal falling velocity of short cylinders and rectangular prisms in polymer solutions of different measure of shear thinning and elasticity has been measured.     

Numerical and experimental study of a falling liquid column

The collapsing liquid column phenomenon has been experimentally and theoretically studied. The experimental data demonstrated the development and travel of a shock wave. Point velocities within the flow regime were measured using a hot film probe. The numerical simulation was performed using a finite difference code similar to the Marker and Cell technique. The results were in good agreement with the experimental data. The numerical technique therefore promises to be a valuable aid in studying highly convective, incompressible flows.     

Studies of falling liquid film flow Film thickness on a smooth vertical plate

Investigating the film characteristics of thirteen liquids the author took some 450 hold-up measurements using a vertical column with a smooth plate. The average value of the rippled film thickness is less than the corresponding value with no ripples, i.e. when suitable amounts of surface active agents are used. The film thickness data are an excellent indication of the mode of flow of the falling film.In all the cases considered Kapitsa's theory approximates to the experimental results better than Nusselt's theory in the region for which these theories were intended. On the other hand both these theories compare unfavourably with the universal velocity profile treatment as originally proposed by von Kármán and subsequently extended by Dukler and Bergelin. This is so far the best available approximation to the facts and the assumption of the original universal velocity profile based on full-pipe flow leads to the prediction of the average liquid film thickness in fair agreement with those experimentally determined. Nevertheless, systematic deviations still exist in consequence of the fact that the original velocity profile equations were proposed for full-pipe flow and are in need of modification in the light of the experimental data in falling film thickness.     

规整填料内鼓泡流动下液相流场的测量

采用三维激光多普勒测速仪对Mellapak350Y填料内部鼓泡流动时的液相流场进行了测量,考察了气体流动及填料内部结构对液相时均速度场的影响.实验结果表明,规整填料对气泡具有切割和分散作用;受相间作用力影响,距离气泡越近,液体的速度越大,并且随着气相流量的增大,其对液相流场的影响也逐渐扩大;规整填料特有的内部结构对流速分布也有一定的影响.     

Finite volume method for falling liquid films carrying monodisperse spheres in Newtonian regime

A finite volume method is proposed to study the dynamics of unsteady, falling liquid films carrying monodisperse spheres in Newtonian regime under the action of gravity. The Navier–Stokes equations were rewritten to implement a numerical scheme with interface capturing capability, able to compute discontinuities in the solid volumetric concentration and free surface flows. The interface capturing property is checked with simple benchmarks, showing that experimental data for a vertical settler and the dynamics of the wetting front in a thin liquid film are reproduced with success. Also, the numerical scheme computes with accuracy Kapitza instability or viscous roll waves. This work concludes illustrating the applicability of the model to study viscous resuspension phenomenon in a unsteady, falling suspension film. © 2012 American Institute of Chemical Engineers AIChE J, 58: 2601–2616, 2012     

Gas absorption with or without chemical reaction in laminar non-newtonian falling liquid films

An analytical solution is presented for gas absorption with or without a first-order or zero-order chemical reaction in a laminar non-Newtonian power-l model falling liquid film. For physical absorption, the first ten eigenvalues, series coefficients and related quantities are computed accurately by a quasinumerical method which shows considerable improvement over previous investigations. The range of applicability of the penetration theory solution is also established to indicate in what regions will the finite film thickness and complete velocity profile be important in determining the absorption rate. It is found that the range of dimensionless axial contact length X* in which the penetration theory is valid diminishes rapidly with increasi values of the power-law index n. For chemical absorption, the solution can be obtained by a linear superposition principle in terms of a “transie part” in which the effect of hydrodynamics within the liquid film is of importance and a “steady part” in which the reaction rate is controlling. In the “transient part” solution, the first ten eigenvalues and related quantities are reported for a variety of values of n and the dimensionl reaction rate parameter k_l* or k₀*. Certain asymptotic solutions from the penetration theory are also given and their range of applicab estimated. For any given n, it is estimated that only when k₁* or k₀* is less than approximately 10 will the finite film thickness and velocity profile have any effect on the absorption rate as compared to that calculated from the penetration theory with chemical reaction. The non-Newt character of the liquid film also has a significant influence on the absorption rate. At a fixed X*, the absorption enhancement due to reaction is when n = ∞ and is smallest when n = 0. The solutions obtained in this work are useful either for predicting absorption rates or for deter molecular diffusivity (and reaction rate constant) of gases in non-Newtonian falling liquid films.     

Modeling and experimental studies of large amplitude waves on vertically falling films

Experimental data on the amplitude of large waves on vertically falling films are presented over a wide range of fluid properties and flow rates. Attempts are made to correlate the amplitude of these naturally excited and saturated waves to the Weber (We) and Kapitza numbers (Ka), the two dimensionless groups characterizing the film. For viscous fluids (with 2<Ka<200), the wave amplitude increases with the reciprocal of the Weber number and saturates at values around 3 (h_max/h_N∼3) while the dependence on Ka is found to be weak. For less viscous fluids (200<Ka<3890), the waves are found to be much more dynamic with amplitudes saturating at much higher values of around 10. The film roughness, or more precisely, the standard deviation (r.m.s) of the film thickness is also found to be correlated with the reciprocal of the Weber number. Scaling arguments are used to explain the initial increase in wave amplitudes. A two-equation h-q model is used to study the spatio-temporal dynamics of waves on long domains with periodic inlet forcing. The model is used to examine the amplitude-celerity relation for three families of solitary waves: the slow moving γ₁ family, the fast moving γ₂ family and the very fast moving ‘tsunami (Γ₂) family’ having Nusselt film as the substrate. It is found that the film profile at short distances depends on the forcing amplitude and frequency but once the wave amplitude exceeds a critical value, the amplitude-celerity relationship is linear for all solitary waves that exist on the film and is independent of the forcing frequency or amplitude. It is also found that for a fixed set of fluid properties and flow rate (We and Ka), the Γ₂ wave has the largest amplitude and wavelength. Local bifurcation and computational results are used to explain the experimentally observed wave amplitudes on naturally excited films.     

An experimental method for measuring the spreading velocity of surface active substances on thin films of liquid substrate

This paper reports the development of a new experimental method suitable for the determination of the spreading velocity of surface active substances on a thin film of liquid substrate over a solid surface. Previous research showed that when oil and surfactants spread on the surface of a deep body of water, the spreading velocity is usually quite high, being in the range of several tens of centimeters per second. However, the spreading velocities of these substances on a thin water film are much slower. This is because that the spreading of an oil or a surfactant on water surface is not just a two dimension phenomenon, but a phenomenon involving the movement of water in a small depth below the surface. An additional process impeding oil or surfactant spreading in this situation is the interaction of the spreading molecules with the liquid/soild interface underneath water surface. The experimental method developed in this work uses a Wilhelmy balance to monitor the average spreading velocity of surface active substances on a thin water film over a porous solid substrate. The spreading of cellulose hydrophobization agents over wet paper web during the papermaking process is used as an example to demonstrate the capability of the method.     

Hydrodynamic entrance lengths of laminar falling films

An integral method is used to obtain a closed form expression for the determination of hydrodynamic entrance length for falling liquid films emerging from a flat slit and flowing in laminar flow along an inclined flat plate. The results obtained from the present analysis are compared with the experimental data and numerical solutions and found to be in good agreement with them.     

Specular X-ray reflectivity analysis of adhesion interface-dependent density profiles in nanometer-scale siloxane-based liquid films

Nanometer-scale thick liquid films of poly(methylhydro-dimethyl)siloxane copolymer (PMDMS) deposited on hydrophilic and hydrophobic solid organic films have been studied using synchrotron X-ray specular reflectivity (XRR). The physico-chemical properties of liquid PMDMS at the interfacial level are controlled by the nature of the solid surface. Detailed analysis of the XRR-data revealed the formation of a low-density region in the liquid PMDMS film in the vicinity of the hydrophobic surface, whereas a densely packed molecular layer is formed at the liquid PMDMS-hydrophilic substrate interface. Non-covalent polymer chains are ‘frozen’ at the solid-liquid interfaces in the confined liquid films and interactions with the substrate surfaces (i.e. hydrogen bonding) are responsible for distinctly different density profiles.