The effect of adsorption modeling on the stability of surfactant-laden liquid film flow

The primary instability of gravity-driven, liquid film flow is examined when the liquid contains a soluble surfactant. It is shown that the model adopted for the description of adsorption equilibrium affects significantly the prediction of the critical Reynolds number, Rec. Weak attractive/repulsive van der Waals forces between adsorbed molecules stabilize/destabilize the film, whereas strong, attractive van der Waals forces result in non-monotonic variation of Rec with surface coverage. Ionic surfactants form an electric double layer at the interface, whose repulsive potential destabilizes the film. The intensity of electrostatic effects varies inversely with the solution ionic strength, and two asymptotic limits—zero and high concentration of an indifferent salt—are examined. The competition between electrostatic and van der Waals forces results in a very rich behavior, with the critical Reynolds number increasing or decreasing with surface coverage. The parametric variation of Rec is physically understood in terms of the effectiveness of surfactant mass exchange (between the interface and the bulk) in short-circuiting the basic stabilization mechanism, i.e., Marangoni stresses. © 2017, Springer-Verlag GmbH Austria

A numerical study of interfacial transport to a gas-sheared wavy liquid

Interfacial transport of a passive scalar from a gas to a thin liquid film is considered. The base flow in the liquid is laminar, with linear velocity profile produced by gas shear. The velocity disturbances imposed by waves are simulated by an inviscid, constant-vorticity model. Numerically computed roil waves are shown to enhance interfacial transport by modifying the convection pattern below the crest and by inducing a mixing effect on the substrate. It is argued that the entire wave spectrum is active in this enhancement of interfacial transport. (C) 1998 Elsevier Science Ltd. All rights reserved

Laminar film flow along a periodic wall

Laminar, gravity-driven flow of a liquid down an inclined wall with large-amplitude sinusoidal corrugations is studied numerically by a spectral spatial discretization method. The synchronous resonance between the wall and the free surface is investigated for corrugations with wavelength 0.002 m, which - according to linear theory - lead to strongest interaction. Free surface profile and flow structure are studied as a function of the film Reynolds number and the wall amplitude. Streamline patterns are computed and conditions leading to flow reversal are established. The distribution of the shear stress along the wall and of the normal velocity gradient close to the free surface are computed and related to heat/mass transport

Non-linear dynamics of a viscoelastic film subjected to a spatially periodic electric field

We investigate the non-linear dynamics of the electrohydrodynamic instability of a viscoelastic polymeric film under a patterned mask. We develop a computational model and carry out 2D numerical simulations fully accounting for the flow and electric field in both phases. We perform a thorough parametric study and investigate the influence of the various rheological parameters, the applied voltage and the period of the protrusions of the mask in order to define the fabrication limits of this process in the case of patterned electrodes. Our results indicate that the effect of elasticity is destabilizing, in agreement with earlier studies in the literature based on linear stability analysis for homogeneous electric fields. However, the significance of the normal and shear polymeric stress components is found to change drastically as deformation advances, rendering inappropriate the lubrication approximation that neglects normal stresses. We also find that for low values of the Ca number a metastable state arises with finite interfacial deformation, the amplitude of which compares favourably with experimental observations in contrast with earlier predictions using linear theory. Though the critical voltage for this metastable state appears to be unaffected by the elasticity of the material, viscoelasticity affects the fabrication limit on the period of the protrusions of the top electrode. (C) 2015 Elsevier B.V. All rights reserved

Surfactant-laden film lining an oscillating cap: Problem formulation and weakly nonlinear analysis

A surfactant-laden liquid film that lines the inside of an oscillating spherical cap is considered as a model of lung alveoli. Pulmonary surfactant solubility is described by Langmuir adsorption kinetics, modified by incorporating the intrinsic compressibility of the adsorbed monolayer. A novel boundary condition, supported by experimental data and scaling arguments, is applied at the rim. The condition enforces mass conservation of water and surfactant by matching the 'large-scale' dynamics of the alveolus to 'small-scale' equilibrium over mid-alveolar septa of small but finite thickness. Linear and weakly nonlinear analysis around the conditions in a non-oscillating cap indicates that the occurrence of shearing motion in the liquid is related to the non-zero film thickness over the rim, and shearing velocity at the interface is predicted an order-of-magnitude lower than the velocity of radial oscillation. Marangoni stresses dominate the interfacial dynamics, but capillary stresses affect significantly the interior flow field. In particular, they produce spatial modulations in flow rate, surface concentration of surfactant and wall shear stress, whose length scale varies with Ca-1/3, i.e. is determined by a balance between capillary and viscous forces. Non-zero adsorption kinetics modifies at first order only the amplitude and phase of surface concentration, but affects all other variables at second order. In particular, it sets a steady drift of surfactant away from the alveolus and towards the rim. Finally, an attempt is made to relate the present predictions to physiological findings about air flow and particle deposition inside alveoli, and about shear stress-inflicted damage in diseased lungs. © The Author(s), 2022. Published by Cambridge University Press

The role of surfactants on the mechanism of the long-wave instability in liquid film flows

The analysis for the physical mechanism of the long-wave instability in liquid film flow is extended to take into account the presence of a surfactant of arbitrary solubility. The Navier-Stokes equations are supplemented by mass balances for the concentrations at the interface and in the bulk, by a Langmuir model for adsorption kinetics at the interface, and are expanded in the limit of long-wave disturbances. The longitudinal flow perturbation, known to result from the perturbation shear stress which develops along the deformed interface, is shown to contribute a convective flux that triggers an interfacial concentration gradient. This gradient is, at leading order, in phase with the interfacial deformation, and as a result produces Marangoni stresses that stabilize the flow. The strength of the interfacial concentration gradient is shown to be maximum for an insoluble surfactant and to decrease with increasing surfactant solubility. The decrease is explained in terms of the spatial phase of mass transfer between interface and bulk, which mitigates the interfacial flux by the flow perturbation and leads to the attenuation of Marangoni stresses. Higher-order terms are derived, which provide corrections for disturbances of finite wavelength

A model of lung surfactant dynamics based on intrinsic interfacial compressibility

A minimum model for the description of lung surfactant dynamics during consecutive compression/relaxation cycles is proposed. The model is based on Frumkin/Langmuir equilibrium and on an equation of state that includes rigorously the intrinsic compressibility of the densely packed monolayer. Adsorption/desorption dynamics is taken to be kinetically-limited, and film collapse during extreme compression is accounted for by a sublayer reservoir and a simple kinetic expression for monolayer replenishment during re-expansion. The model is validated and found to agree quantitatively with independent data in the literature, taken at physiologically relevant conditions. The best-fit values of the key model parameters are discussed and found to be physically meaningful. Finally, the characteristics of dilatational elasticity, as predicted by the model, are considered. © 2021 Elsevier B.V

Observations of solitary wave dynamics of film flows

Experimental results are reported on non-stationary evolution and interactions of waves forming on water and water-glycerol solution flowing along an inclined plane. A nonlinear wave generation process leads to a large number of solitary humps with a wide variety of sizes. A fluorescence imaging method is applied to capture the evolution of film height in space and time with accuracy of a few microns. Coalescence - the inelastic interaction of solitary waves resulting in a single hump - is found to proceed at a timescale correlated to the difference in height between the interacting waves. The correlation indicates that waves of similar height do not merge. Transient phenomena accompanying coalescence are reported. The front-running ripples recede during coalescence, only to reappear when the new hump recovers its teardrop shape. The tail of the resulting solitary wave develops an elevated substrate relative to the front, which decays exponentially in time; both observations about the tail confirm theoretical predictions. In experiments with water, the elevated back substrate is unstable, yielding to a tail oscillation with wavelength similar to that of the front-running ripples. This instability plays a key role in two complex interaction phenomena observed: the nucleation of a new crest between two interacting solitary humps and the splitting of a large hump (that has grown through multiple coalescence events) into solitary waves of similar size

Decomposition of NH3 on Pd and Ir - Comparison with Pt and Rh

The unimolecular decompositions of NH3 on polycrystalline wires and foils of Pd and Ir are examined and compared with the corresponding ones on Pt and Ph. The reactions were carried out in a differential flow reactor, at pressures from 0.01 to 1 Ton and temperatures from 500 to 1900 K. It was found that the rates of product formation could be fit by Langmuir-Hinshelwood unimolecular rate expressions, with an accuracy of +/- 20% under all conditions. Ammonia decomposes to N-2 and the rate of decomposition is fastest on Ir by several orders of magnitude when compared with that on the other metals, becoming flux limited above about 750 K. Ir appears to be the choice catalyst for dehydrogenating ammonia. The heats of adsorption of NH3, on Pt, Ph and Pd are similar and equal to 16.7, 16.8 and 17.4 kcal/mol, respectively. The apparent activation energy for this reaction is similar on Pt and Ph and equal to 21 kcal/mol, while for Pd and Ir it is 26.2 and 31.2 kcal/mol, respectively

Mass transfer in gas-liquid flow in small-diameter tubes

Data on the rate of liquid-phase controlled mass transfer in a small-diameter tube (ID 4 mm) are presented. The motivation is to model the performance of compact contact devices consisting of short, narrow passages. The mean volumetric mass transfer coefficient, K(L)a, is measured for a wide range of superficial gas and liquid velocities (U-GS = 0.1-30 m s(-1) and U-LS = 0.01-1 m s(-1)). Results are related to flow regime transitions and are correlated in terms of Jepsen's (1970, A.I.Ch.E. J. 16, 705-711) fractional energy dissipation parameter. (C) 1997 Elsevier Science Ltd. All rights reserved