Drainage Of Thin Liquid Films Research Articles

Thin liquid film drainage mechanism for bubble − particle attachment interactions in the low-rank coal flotation in the presence of salt and surfactants

Bubble-particle interaction is a fundamental process in froth flotation, where the attachment of bubbles and particles is the crucial process in effective flotation. However, modeling bubble-particle attachment interaction is challenging. This is because advanced methods like AFM (Atomic Force Microscope) characterizations are difficult to quantify hydrophobic interactions reproducibly for air bubbles and non-spherical particles. This study presents a methodology to obtain the hydrophobic force constants for bubble-particle attachment interaction in the presence of salt (KCl) and surfactants (DTAC and SDS). The hydrophobic interaction constants of bubble-particle interactions were acquired from first principles with the Stefan − Reynolds theory and Glembotsky experimental device. The Stefan − Reynolds theory was successfully applied in the determination of the real hydrophobic constants for bubbles and particles interaction in DI water (deionized water). However, in the coexistence of salt and surfactants, the real hydrophobic constants for bubbles and particles interaction cannot be obtained while the fictive hydrophobic constants were acquired with a linear extrapolation method. The results showed that the addition of inorganic salt and surfactants compressed the electronic double layer’s thickness and presented a higher hydrophobic force constant, enhancing the interaction between a bubble and a low-rank coal particle. In addition, the evaluations of hydrophobic constants reveal that the hydrogen bond energy and salt ions destruction energy should be considered to the comprehension of attachment interaction mechanism and the hydrophobic force source for bubble − particle attachment interactions.

Three-phase contact formation between an air bubble and solid surfaces with different hydrophobicity degrees in liquid

Interactions between gas bubbles and solid particles are crucial in numerous industrial processes, including froth flotation, in which particle-bubble attachment plays a vital role. The process efficiency depends on differences in the surface wettability (i.e., hydrophobicity, expressed by the contact angle) of separated particles. This study aimed to investigate the influence of surface hydrophobicity and zeta potential on the formation of a three-phase contact (TPC) between a single air bubble and planar glass surfaces. Different degrees of hydrophobicity were achieved by esterification with a range of alcohols and time. The interaction between the bubble and surface was monitored using a high-speed camera with a time resolution of 1 ms, allowing for measurements of the time of thin liquid film drainage, time and diameter of TPC formation, TPC line expansion velocity, and dynamic contact angles. The observations suggest that TPC formation occurs when the solid surface has a sufficient degree of hydrophobicity (critical contact angle) and is dependent on the differences in zeta potential values between the air bubble and the solid surface in water. When both surfaces are negatively charged, the limiting value of the water contact angle is ca. 35°, whereas for oppositely charged surfaces, the value slightly decreases to ca. 31°. The results show that increasing surface hydrophobicity enhances the bubble adhesion effectiveness by increasing both the propagation velocity of the TPC perimeter and its size (measured by the diameter of the formed TPC). The article also discusses the mechanism of bubble-solid adhesion in relation to the hydrophobicity and zeta potential of the solid surface based on the obtained results.

Interferometry and Simulation of the Thin Liquid Film between a Free-Rising Bubble and a Glass Substrate.

Because of their practical importance and complex underlying physics, the thin liquid films formed between colliding bubbles or droplets have long been the subject of experimental investigations and theoretical modeling. Here, we examine the possibility of accurately predicting the dynamics of the thin liquid film drainage using numerical simulations when compared to an experimental investigation of millimetric bubbles free-rising in pure water and colliding with a flat glass interface. A high-speed camera is used to track the bubble bounce trajectory, and a second high-speed camera together with a pulsed laser is used for interferometric determination of the shape and evolution of the thin liquid film profile during the bounce. The numerical simulations are conducted with the open source Gerris flow solver. The simulation reliability was first confirmed by comparison with the experimental bubble bounce trajectory and bubble shape evolution during the bounce. We further demonstrate that the simulation predicted time evolution for the shape of the thin liquid film profiles is in excellent agreement with the high-speed interferometry measured profiles for the entire experimentally accessible film size range. Finally, we discuss the implications of using numerical simulation together with theoretical modeling for resolving the complex processes of high velocity bubble and droplet collisions.

Effect of Velocity, Solid Wettability, and Temperature on Drainage Dynamics of C5PeC11-in-Toluene Liquid Films between Silica and Water Droplet

Properties of thin liquid films between two approaching droplets or between a droplet and a surface are critical for emulsion stability, oil and gas extraction, and mineral flotation. The dynamic force apparatus (DFA)—simultaneous measurement of interfacial film thickness, drainage time, and interaction forces at precisely controlled approach velocities—was used to study the interactions of a water drop with silica surfaces in toluene containing the model asphaltene compound N-(1-undecyldodecyl)-N′-(5-carboxypentyl)-perylene-3,4,9,10-tetracarboxylic bisimide (C5PeC11). A water droplet in toluene containing 0.1 g/L C5PeC11 was driven toward a silica surface of varying wettability (contact angles of 0 and 107°) at two different droplet approach velocities (0.1 and 1 mm/s) and temperatures (22 and 40 °C). Rupture of thin liquid films between a water droplet and silica surfaces was observed, with a moving three phase contact line and strong attachment for hydrophilic silica and minor, local attachment and an easily detachable water drop for hydrophobic silica. Increasing the approach velocity of water droplets toward solid surfaces resulted in a larger dimple and longer film lifetime. Interestingly, higher temperature led to a faster film rupture for hydrophilic silica, in line with industrially observed improvements in removal of water-in-oil emulsions at higher temperatures. The experimentally determined dynamics of the thin liquid film drainage were modeled successfully using the Stokes–Reynolds–Young–Laplace (SRYL) theoretical model.

Thin liquid film drainage mechanism between air bubbles and low-rank coal particles in the presence of surfactant

Flotation strongly depends on bubble–particle attachment interactions. However, modelling of bubble–particle attachment interactions is challenging particularly due to the difficulties in quantifying the hydrophobic interactions between an air bubble and a non-spherical particle using a well-advanced technique such as atomic force microscopy; the reason is that these measurements are not reproducible when particles are non-spherical. This paper proposes a methodology to determine the hydrophobic interaction constants between air bubbles and coal particles in the presence of a surfactant. The bubble–particle hydrophobic constants were determined from first principles using the Navier-Stokes equation and the Glembotsky experimental technique. It was found that the higher the surfactant concentration, the higher the hydrophobic constants. The results showed that the calculated critical film rupture thickness is inversely related to the induction time measurements, and the maximum critical film rupture thickness matched the minimum induction time. The decrease in the electrostatic double layer repulsive energies resulted in the decrease in the induction times.

Effect of Approach Velocity on Thin Liquid Film Drainage between an Air Bubble and a Flat Solid Surface

The dynamic drainage process of the liquid film trapped between an air bubble and a flat silica surface over a wide range of hydrodynamic conditions is studied by a newly developed instrument called integrated thin liquid film force apparatus (ITLFFA) under different salt concentrations. The ITLFFA allows the simultaneous measurement of interaction forces and spatiotemporal film thickness with accurate control of bubble approach velocity in a large range of Reynolds number from 0.005 to 135. Our study demonstrates that increasing the bubble approach velocity plays a significant role in the hydrodynamic pressure and fluid flow within the draining film promoting dimple formation and longer drainage time. The drainage time also depends on the competition between the electrical double-layer and van der Waals interactions, which are repulsive in our system, resulting in a flat equilibrium film at the end. The evolution of the draining film is analyzed using the Stokes–Reynolds–Young–Laplace (SRYL) model. Compa...

Simultaneous measurement of dynamic force and spatial thin film thickness between deformable and solid surfaces by integrated thin liquid film force apparatus.

Interactions involving deformable surfaces reveal a number of distinguishing physicochemical characteristics that do not exist in interactions between rigid solid surfaces. A unique fully custom-designed instrument, referred to as integrated thin liquid film force apparatus (ITLFFA), was developed to study the interactions between one deformable and one solid surface in liquid. Incorporating a bimorph force sensor with interferometry, this device allows for the simultaneous measurement of the time-dependent interaction force and the corresponding spatiotemporal film thickness of the intervening liquid film. The ITLFFA possesses the specific feature of conducting measurement under a wide range of hydrodynamic conditions, with a displacement velocity of deformable surfaces ranging from 2 μm s-1 to 50 mm s-1. Equipped with a high speed camera, the results of a bubble interacting with hydrophilic and partially hydrophobic surfaces in aqueous solutions indicated that ITLFFA can provide information on interaction forces and thin liquid film drainage dynamics not only in a stable film but also in films of the quick rupture process. The weak interaction force was extracted from a measured film profile. Because of its well-characterized experimental conditions, ITLFFA permits the accurate and quantitative comparison/validation between measured and calculated interaction forces and temporal film profiles.

The Drainage of Thin Liquid Films on an Inclined Solid Surface

In this paper, we consider the thinning process of an inclined thin liquid film over a solid boundary with an inclination angle to the horizontal in gravity driven flow. Throughout this work, we assumed that the fluid thickness is constant far behind the front and we neglect the thickness of the film at the beginning of the motion. The equation of the film thickness is obtained analytically, using the similarity method by which we can isolate the explicit time dependence and then the shape of the film will depend on one variable only. The solution of the governing equations of the film thickness is obtained numerically by the Rung-Kutta method with the aid of Mat lab(ode45). We present here some of the theoretical aspects of the instability development in an inclined thin liquid films on a solid surface in two dimensional coordinate system with an inclination angle to the horizontal . There are different types of phenomena that can occur, such as drainage, details of rupture, non-Newtonian surface properties in moving contract lines in thin liquid films (1). These phenomena can help to describe the physical processes that occur in our real world. (2,3) have studied the case of contact line instabilities of thin liquid films but with constant flux configuration and also they considered some global models of a moving contact lines. (4) studied the thin liquid films flowing down the inverted substrate in three dimensional flow. (5) investigated the dynamics of an inclined thin liquid films of variable thickness in steady and unsteady cases and when the film is stationary and uniform. (6) considered the stability of thin liquid films and sessile droplets. The stability of the contact line of thin fluid film flows with constant flux configuration is considered by (7). (8) considered the spreading of thin liquid films with small surface tension in the case when the flow is unsteady. The Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field was considered by (9). In this paper we investigate the drainage of the inclined thin liquid films where the gravity and other forces such as viscous and surface tension forces have a significant effect on the flow of the film. We use the similarity method by which we can isolate the explicit time dependence and then the shape of the film will depend on one variable only. The solution of the governing equations of the liquid film thickness is obtained numerically.

Comparative validation of the analytical models for the Marangoni effect on foam film drainage

The aim of this paper is to evaluate four of the well-known models for drainage of thin liquid films, containing non-ionic surfactants, by applying them to different types of draining foam films stabilized by either strong or weak non-ionic surfactants. The effect of non-ionic surfactants on the drainage of foam films under different conditions was studied. The following series of surfactants were employed: (1) methylisobutyl carbinol (MIBC), (2) Dowfroth 200, (3) pentaethyleneglycol monodecyl ether (C 10E 5), (4) pentaethyleneglycol monododecyl ether (C 12E 5), (5) hexaethyleneglycol monododecyl ether (C 12E 6), (6) octaethyleneglycol monododecyl ether (C 12E 8) and (7) tetraethyleneglycol monooctyl ether (C 8E 4). The experimental ‘thickness’ vs ‘time’ dependences were processed with four kinetic models: (1) the model developed by Scheludko on the basis of the Stefan–Reynolds lubrication theory (Scheludko model); (2) the model of Radoev, Dimitrov and Ivanov for foam films confined between partially mobile planar gas–liquid surfaces (RDI model); (3) the model of Ruckenstein and Sharma for foam films with surfaces wrinkled by capillary waves (RSh model); (4) the model of Manev–Tsekov–Radoev for foam films with surfaces corrugated by quasi-stationary inhomogeneities (MTR model). A systematic validation based on the statistical level of uncertainty of the model predictions, as compared to the experimental results was preformed. The test on the model kinetic equations confirmed their validations reported in the literature. In addition, cases in which none of the models is valid were identified as well. Ultimately, it was concluded that thin film drainage is a complex phenomenon, which should be studied further by different experimental techniques and modelling approaches.

Streaming Potential Effect on the Drainage of Thin Liquid Films Stabilized by Ionic Surfactants

Dynamic effects originating from the electric double layers (EDL) are studied in thin liquid films (TLF) containing ionic and nonionic surfactants. To account for such effects, the EDL are to be incorporated into the differential equations describing the TLF drainage. Numerical simulations in the literature have shown that foam films containing ionic surfactants can drain at a slower rate than that predicted by the Reynolds equation (V(Re)) which postulates rigid planar film surfaces. However, the physical reason of the trend has remained unclarified, and the numerical results have not been validated by any experimental data. In the present study, experiments on the drainage of planar foam films were conducted with the anionic surfactant sodium dodecylsulfate (SDS) in the presence of additional electrolyte (0.02 M NaCl) and with the cationic tetrapentylammonium bromide (TPAB). The obtained results are in accord with the numerical simulations from the literature (V/V(Re) < 1). Such behavior was observed already in our preceding experiments on planar TLF with SDS without added electrolyte. These results were compared to the data of the experiments with TLF containing nonionic surfactant, and differences in the drainage pattern between ionics and nonionics were established. A new theoretical model was developed to account for the dynamic effects arising from EDL. According to the present model, the liquid outflow drags the bulk charges of EDL toward the film border, thus generating streaming potential (as in capillary tubes), which in turn brings the charges back toward the center to maintain the state of zero total electrical current. This creates reverse convection of the liquid near the surfaces, resulting in a velocity of film drainage smaller than V(Re). The present theory predicts kinetic dependence closer to the experiment than the Reynolds equation. The limitations of this new model are specified: it is valid for high ionic strength or low value of the surface potential.

Thin liquid film drainage: Ionic vs. non-ionic surfactants

This paper compares the rate of drainage of thin liquid films (TLF) containing ionic surfactants to that of TLF containing non-ionic surfactants. In essence, the theory of drainage has been developed for films containing non-ionic surfactants, while the validation of the models, based on the theory in the literature, has been performed with experiments on TLF with both, non-ionic and ionic surfactants, usually in the presence of significant background concentrations of electrolyte. Due to the complexity of problem, the dynamic effects on the electrical double layer (EDL) during the film drainage have been ignored for many years in the literature. These effects were finally treated theoretically and the problem solved numerically in a recent work. The new theoretical development however has not yet been validated. In addition, the differences in the kinetics of thinning of TLF with ionic and non-ionic surfactants have not been exposed in the literature until present. This paper is dedicated to revealing these differences. Experiments on kinetics of thinning were conducted with microscopic planar TLF, containing two non-ionic surfactants (tetraethyleneglycol mono-octylether C 8E 4 and n-dodecyl-- d-maltoside C 12G 2) and two ionic surfactants (sodium dodecylsulfate SDS and tetrapentylammonium bromide TPeAB). The TLF with non-ionic surfactants drain according to the well-known theories of Scheludko or Radoev-Manev–Ivanov, which confirms their validity. On the contrary, TLFs with ionic surfactants drain in general at significantly slower rate, as compared to the TLF with non-ionic surfactants, when far from equilibrium. When they are close to the equilibrium conditions, the former drain according to the theory developed for TLF with non-ionic surfactants. An analysis of the experimental results, involving the latest achievements in the field is performed, indicating the complex behaviour of the electrical double layer under dynamic conditions.

Effect of Film Curvature on Drainage of Thin Liquid Films

Thin liquid films are considered to be the basic structural elements of foam and emulsion systems. Consequently, the structure and stability of macro-dispersions are highly dependent on the dynamic structure formation and stability of a single, thin, curved film between unequal-sized bubbles and droplets as in a polydispersed foam and emulsion system. A novel experimental technique based on the differential microinterferometric method has been used to investigate the dynamic behavior of such curved foam films. The simple theoretical drainage model of Reynolds was used to calculate the drainage time for both curved and plane-parallel films, and the results were compared with the experimental observations. It was found that for thicker films (i.e., greater than 100 nm), the curved film drained twice as slowly as the plane-parallel film. However, at a film thickness less than 100 nm, the plane-parallel film has a lower rate of thinning compared to the curved film.

Determination of Bulk and Surface Diffusion Coefficients from Experimental Data for Thin Liquid Film Drainage

This note presents a method for the determination of the surface diffusion coefficient and surface diffusion flux. The theoretical considerations are based on the Onsager linear theory for the definition of the surface diffusion flux and on the Einstein theorem for the definition of the surface diffusion parameter. In this interpretation the surface diffusion coefficient differs from the one commonly defined in the literature. It does not depend on the surfactant concentration and it is a function only of the type of surfactant and the liquid/liquid interface. The theoretical calculations indicate that the effect of the surface diffusion on the film drainage is stronger than that predicted by previous theoretical studies. The experimental data for thin liquid film drainage in the case of low surfactant concentration in the continuous phase could be used for the calculation of the bulk and surface diffusion coefficients. In the present study we utilized the experimental data for the drainage of nitrobenzene films stabilized by different concentrations of dodecanol.

Measurement of thin liquid film drainage using a novel high-speed impedance analyzer

This work describes the design and implementation of a new instrument, called the thin film impedance analyzer, which measures the rate of drainage of thin oil films. The instrument forms an oil film by elevating a planar oil–water interface into a water drop hanging from a stainless steel capillary tube immersed in the oil. The instrument measures the magnitude of the impedance of the matter between the capillary tube and a screen electrode immersed in the lower water phase. Under appropriate conditions, the capacitance of the oil film dominates the impedance. The instrument records the increase in the magnitude of the admittance associated with the draining and thinning of the oil film. The features of the drainage curves vary considerably with the type, amount, and location of surfactants in the oil and water phases, as well as with user-specified values of drop volume, drop equilibration time, and extent of drop compression. For this reason, the instrument has utility as a screening tool for selecting surfactants for emulsion formulations. Potential future uses include accelerated prediction of emulsion stability and extraction of oil–water interfacial rheological parameters.

Molecular Diffusion and Drainage of Thin Liquid Films Stabilized by Bovine Serum Albumin−Tween 20 Mixtures in Aqueous Solutions of Ethanol and Sucrose

The drainage characteristics and surface lateral diffusion properties of thin liquid films (foam lamellae) formed by BSA (bovine serum albumin) and Tween 20 were studied using optical microscopy including epi-illumination and fluorescence recovery after photobleaching. The concentrations of the surfactant and protein at the aqueous phase interface, the composition of the interface (BSA, Tween 20, and BSA-Tween 20 mixtures), and the aqueous phase composition (1 M ethanol and 0.5 M sucrose) were the variables studied. This study has revealed many complicated effects arising from film-film and film-subphase interactions as a function of the variables studied. The interactions between Tween 20 and BSA at the interface were found to dependent not only on the interfacial composition but also on the subphase composition.

Dimple formation in the thin film beneath a drop or bubble approaching a plane surface

The fourth-order differential equation governing the shape of the dimple as a function of time during the drainage of thin liquid film, derived by Hartland (1969, Chem. Engng Prog. Symp. Ser. No. 91, 65, 82-89), is solved numerically. The required four boundary conditions are obtained from the geometric symmetry of the system and the shape of the drop or bubble. The present theory applies to both large and small films, and predicts the drainage for any axisymmetric initial profile. In particular, planar and parabolic initial profiles quickly predict identical development of the dimpled profile as do bell-shaped initial profiles. Similarly, the initial film thickness does not affect the subsequent development of the dimpled film. Comparison with the experimental profiles measured by Hartland (1969) for large drops and by Platikanov (1964, J. phys. Chem. 68, 3619-3624) for air bubbles shows good agreement.

Drainage of thin liquid films between relatively smooth surfaces

Using a new surface force apparatus, static and dynamic measurements have been conducted to investigate the squeeze of a liquid from the contact between a relatively smooth sphere and a plane. Simple liquids and polymer melts (polyisoprene) have been studied, with different solid surfaces (mica, cobalt, gold, platinum, and steel). It has been found that an ‘‘immobile’’ layer of fluid is present on each solid surface which does not participate in the hydrodynamic flow of the liquid. The thickness of this film is relatively independent of the roughness of the solid, corresponds to a small number of molecular layers (1 to 5), and is influenced by the structure of the molecule. These fluids shows two different behaviors: for small molecules the thickness of the ‘‘immobile’’ layer is proportional to the viscosity; for larger molecules the thickness is proportional to the one-tenth power of the viscosity. During the squeeze process, when the solid surfaces are close, a ‘‘confined’’ layer occurs due to molecule entanglement. This phenomenon is described for a semirigid hydrocarbon.

Hole formation and sheeting in the drainage of thin liquid films

Foam, emulsion, and pseudoemulsion films stabilized by surfactants above the critical micelle concentration exhibit pronounced stepwise thinning or stratification. Dynamic removal of a layer is initiated by the formation and subsequent sheeting of a hole (or holes) at each step of the stratified thinning. We outline a nonlinear hydrodynamic stability analysis which successfully models the dynamics of hole formation and sheeting by accounting for an equilibrium oscillatory structural component in the disjoining pressure isotherm. Initiation of a hole is attributed to the nonlinear growth of a hydrodynamic instability during film thinning under the action of a constant capillary pressure and an oscillatory disjoining pressure. Subsequent growth or sheeting of the hole is explained by outward fluid flow within the inhomogeneous thin film as radial pressure gradients develop from curvature variations and viscous resistance to flow. Qualitative comparison is made between the proposed hydrodynamic theory and experimental observations of thinning events and rates. 32 refs., 6 figs.

The drainage of thin liquid films between solid surfaces

We present measurements of the thickness as a function of time of liquid films as they are squeezed between molecularly smooth mica surfaces. Three Newtonian, nonpolar liquids have been studied: octamethylcyclotetrasiloxane, n-tetradecane, and n-hexadecane. The film thicknesses are determined with an accuracy of 0.2 nm as they drain from ∼1 μm to a few molecular layers. Results are in excellent agreement with the Reynolds theory of lubrication for film thicknesses above 50 nm. For thinner films the drainage is slower than the theoretical prediction, which can be accounted for by assuming that the liquid within about two molecular layers of each solid surface does not undergo shear. In very thin films the continuum Reynolds theory breaks down, as drainage occurs in a series of abrupt steps whose size matches the thickness of molecular layers in the liquid. The presence of trace amounts of water has a dramatic effect on the drainage of a nonpolar liquid between hydrophilic surfaces, causing film rupture which is not observed in the dry liquids.

The effect of double layer interaction on the drainage of thin liquid films

The drainage of thin liquid films of an aqueous solution containing anionic surfactant and inorganic electrolyte between platinum and a mercury pool electrode was examined by the capacitance method. The system consisted of either symmetrical or unsymmetrical potentials of diffuse double layers which were estimated by differential capacitance measurements. The results showed that the drainage of the liquid film initially took place quickly and then slowly attained an equilibrium thickness. This general tendency could be explained qualitatively by the theoretically calculated disjoining pressure but the equilibrium thickness of 7–13 nm was too small to be explained in terms of electrostatic repulsion and van der Waals attraction. Hence, it was supposed that other forces, such as steric hindrance, are acting to thicken the film in addition to the above mentioned disjoining pressure. The force acting on the film obtained from the Reynolds equation also indicates the presence of other forces which are acting to thin the film in addition to gravity.