Equilibrium Thickness Research Articles

Effect of the adsorption component of the disjoining pressure on foam film drainage

The present work is trying to explain a discrepancy between experimental observations of the drainage of foam films from aqueous solutions of sodium dodecyl sulfate (SDS) and the theoretical DLVO-accomplished Reynolds model. It is shown that, due to overlap of the film adsorption layers, an adsorption component of the disjoining pressure is important for this system. The pre-exponential factor of the adsorption component was obtained by fitting the experimental drainage curves. It corresponds to a slight repulsion, which reduces not only the thinning velocity as observed experimentally but corrects also the film equilibrium thickness.

Surface-induced weak orientational order and role of isotropic-nematic interface fluctuations in the appearance of an induced nematic film

Recently the nontrivial spatial and temperature dependence of the surface-induced weak planar orientational order parameter Q(z, T) was determined just above the isotropic-nematic (IN) phase transition point (Ji-H. Lee et al., Phys. Rev. Lett. 102, 167801 (2009)). In this paper we present a theoretical explanation of the observed behaviour. We obtain expressions for the short-range and long-range contributions to the interface potential of the induced nematic film and specify the repulsive character of the interaction between the soft IN interface and the external bounding substrate. It is shown that the small value of the IN interfacial tension results in the renormalization of the repulsive interaction potential due to the thermal fluctuations of the soft IN interface. This leads to an increase of the equilibrium thickness of the induced nematic film and the appearance of a step-like orientational order parameter profile. We find that only renormalized short-range and thermal pseudo-Casimir interactions are essential for the appearance of the induced nematic film, which provide the observed thickness, h ~ 30 nm, of this film. The long-range van der Waals interaction is shown to be negligibly small and the dominant role is played by the renormalized short-range repulsion. Fitting of the experimental order parameter profiles (Ji-H. Lee et al. (2009)) with the expressions based on these interactions makes it possible to determine the material parameters of the system, including the amplitudes of the surface interaction, the IN interfacial tension and the interfacial coherence length. The agreement between theory and experiment confirms the importance of the interface fluctuation renormalization of the interface potentials for soft interfaces.

Principal characteristics of a bubble formation on a horizontal downward facing surface

The formation of gas bubbles on downward facing surface and the variation in their shape due to buoyancy and surface tension forces are important fundamental phenomena that contribute significantly to the understanding of the hydrodynamics involve in many gas–liquid systems and particularly in Hall–Héroult aluminium cell.In this paper a cold model and numerical simulation study was carried out to determine the effect of gas injection rates and orifice diameters on the formation of a single bubble arising from an orifice placed on a flat plate submerged horizontally in water and aqueous sodium dodecyl sulphate (SDS) respectively. In the experimental part of the study, high speed camera was used to record the bubble movements followed by a numerical analysis using the phase-field method.The findings indicated that lower surface tension has an influence on equilibrium thickness of the bubble when it grows on a downward facing submerged horizontal plate. The thickness of the bubble can be decreased by 8–10% for a decrease in surface tension from water to aqueous SDS by 0.036N/m. Moreover, the thickness of the bubble was found to be a function of the injection rate and the surface tension of the liquid, whereas the shape change of the bubble during the initial formation was found to be the main cause for the induced flow in the surrounding fluid. The predicted numerical results of the changes in the bubble thickness and its aspect ratios (AR) during initial bubble development were validated against our experimental results. The thickness of the bubble shows a good agreement with the predicted data while the aspect ratio shows similar trend during initial growth.

Stability of vertical films of molten glass due to evaporation

First, we report observations achieved on a gravitationally driven film drainage with molten glass pointing out a stabilizing effect when temperature is larger than 1250°C. A model to describe the change of surface tension with the film thickness due to the evaporation of oxide species is proposed. A lubrication model is derived taking into account the gradient of surface tension. The final system of equations describing the mass and the momentum conservations is numerically solved by an implicit time solver using a finite difference method at a second order scheme in time and space.The numerical procedure is applied to study a film drainage of molten soda–lime–silica glass. The effect of the surface tension gradient is investigated pointing out that with an increase of 0.5% of the surface tension over the spread of the film which is order of few centimeters, the liquid film reaches an equilibrium thickness in agreement with previous experimental work.

Features of the pre-equilibrium charge states of light ions passing through thin celluloid films

A semi-empirical method for establishing of the average charge of ions passing through thin celluloid films is proposed. Calculations for helium (He) and nitrogen (N) ions with different initial velocities (12−18.7 × 108 cm/s for He and 4−12 × 108 cm/s for N) are presented. The equilibrium thickness of a celluloid target in dependence on the initial charge states of incident ions is evaluated.

Experimental Simulation of Contaminant Deposition on a Film Cooled Turbine Airfoil Leading Edge

A significant challenge of utilizing coal-derived synthetic fuels for gas turbine engines is mitigating the adverse effects of fuel-born contaminant deposits on film cooled turbine surfaces. A new experimental technique has been developed that simulates the key physical, but not the chemical, aspects of coal ash deposition on film cooled turbine airfoil leading edges in order to better understand the interaction between film cooling and deposition and to produce improved film cooling designs. In this large-scale wind tunnel facility, the depositing contaminants were modeled with atomized molten wax droplets sized to match the Stokes numbers of coal ash particles in the engine conditions. The sticking mechanism of the molten contaminants to the turbine surfaces was modeled by ensuring the wax droplets remained somewhat molten when they arrived at the cooled model surface. The airfoil model and wax deposits had thermal conductivities such that they matched the Biot numbers of clean and fouled turbine airfoils at engine conditions. The behavior of the deposit growth was controlled by adjusting the mainstream, coolant, and wax solidification temperatures. Simulated deposits were created for a range of test durations, film cooling blowing ratios, and controlling temperatures. Inspection of the resulting deposits revealed aspects of the flow field that augment and suppress deposition. Deposit thickness was found to increase in time until an equilibrium thickness was attained. Blowing ratio and the difference between mainstream and wax solidification temperatures strongly affected characteristics of the deposits. Model surface temperatures greatly reduced under the deposits as they developed.

Pre-industrial multiple equilibrium sea-ice flow states due to plastic ice mechanics

Abstract Because the Arctic Ocean is largely surrounded by land masses, sea ice mechanics significantly affects the outflow of ice from the Arctic Basin. An important legacy of Dr. Max Coon has been the recognition that Arctic ice pack fails and flows in a plastic manner. Building on this concept we demonstrate here that with reasonable simulation of plastic scaling of sea-ice flow through narrow channels, dynamic–thermodynamic sea ice models have the potential to yield multiple equilibrium flow and hence thickness states for appropriate seasonal daily wind and thermodynamic forcing. These multiple states are due to ‘plastic’ ice mechanics and are not ‘Budyko-Sellers’ albedo feedback multiple states. Each state consists of a mean seasonal ice thickness with annual outflow balancing net growth. Low flow states are thicker. In this paper we first demonstrate that with some caveats, a properly formulated ‘viscous plastic’ sea ice model where ‘rigid’ ice is approximated by very slow flow can successfully simulate plastic ice flow and stoppage of ice flow through narrow channels in agreement with observations and theory. The characteristics of this flow and stoppage are methodically examined by a series of initial value problems of ice flow and advection through various narrowing channels with different ice thicknesses being advected into the channel. Different rheologies are examined and the effect of different creep closure rates on stoppage is investigated using several day mechanistic simulations of flow into the channel employing explicit time stepping. In the case of parallel channels, numerical results are examined in light of analytic solutions. Together with idealized growth rates this simple channel model is used to illustrate the principle of multiple equilibrium states due to ice mechanics. Following this we utilize a 40 km resolution dynamic thermodynamic sea ice model with multiple openings from the Arctic Basin to examine the potential for multiple equilibrium flow states under pre-industrial atmospheric thermodynamic forcing together with daily wind field forcing taken from more current conditions. This potential is assessed by carrying out five year seasonal simulations initialized with different ice thicknesses. Intersection of seasonal averaged net growth and outflow thus obtained are then used to identify potential multiple states and assess their stability. With a coulombic rheology with modest cohesive strength, the results show three states two of which are stable. With an elliptical yield curve having higher cohesive strength only one low flow state is identified. Several ~ 100 year simulations are then carried out to show the existence of the two stable states and their seasonal flow and thickness characteristics. The decay time scales between pre-industrial low flow states and present high flow states are also examined via long term simulations. Finally, a simulation from 1960 to 2040 with estimated climatic warming is carried out and compared with equilibrium thickness states at discrete intervals to show the effect of inertia in the rate of ice decay due to ice mechanics. Forcing data reported in this paper are adequate to test the capability of other dynamic thermodynamic sea ice models to yield multiple flow states.

An equilibrium model for tungsten fuzz in an eroding plasma environment

A model equating the growth rate of tungsten fuzz on a plasma-exposed surface to the erosion rate of the fuzzy surface is developed to predict the likelihood of tungsten fuzz formation in the steady-state environment of toroidal confinement devices. To date this question has not been answered because the operational conditions in existing magnetic confinement machines do not necessarily replicate those expected in future fusion reactors (i.e. high-fluence operation, high temperature plasma-facing materials and edge plasma relatively free of condensable impurities). The model developed is validated by performing plasma exposure experiments at different incident ion energies (thereby varying the erosion rate) and measuring the resultant fuzz layer thickness. The results indicate that if the conditions exist for fuzz development in a steady-state plasma (surface temperature and energetic helium flux), then the erosion rate will determine the equilibrium thickness of the surface fuzz layer.

Foam films from mixed solutions of bovine serum albumin and n-dodecyl-β- d-maltoside

New data for foam films from mixed aqueous solutions of important components non-ionic surfactant “ n-dodecyl-β- d-maltoside” (C 12G 2) and globular protein “bovine serum albumin” (BSA) are presented. Based on the equilibrium surface tension isotherm of mixed aqueous solutions of BSA (10 −6 M) with C 12G 2, obtained by Wilhelmy method it is found that protein–surfactant complexes are formed at concentration region from 3 × 10 −6 to 1.5 × 10 −5 M C 12G 2. Thinning of the films stabilized by mixtures with a composition corresponding to the special points of the isotherm is recorded and compared with this of the individual components. It is found that the films from mixed protein–surfactant solutions, exhibit irregular thinning behaviour and thickness nonhomogeneity. The critical and equilibrium thickness of stable films is measured interferometrically and discussed based on the specificity of interactions between the components. Films from pure BSA solutions are thinnest (11 nm) and their thickness corresponds to Newton black (NB). It is found that the thickness of mixed films is larger (17 nm) than that of films from pure BSA and corresponds to thickness of common black films, irrespectively that they visually look like Newton film (NF). The larger value of these thicknesses is explained with an increase in the thickness of adsorption layers due to the bigger hydrodynamic radius of complexes or reorientation of BSA molecule to the volume face during its displacement by C 12G 2 domains.

Interfacial Tension and Spreading Coefficient of Thin Films: Review and Future Directions

The surface tension of a very thin film deviates from its thermodynamic thick film analogue. Generalized surface tension expressions can be obtained from intermolecular forces in order to calculate some important parameters such as the spreading coefficient of very thin films and the equilibrium shape and thickness of a pancake drop. These expressions become important for ultrathin films such as those relevant for oil extraction and for some biological calculations (in relation to vesicles and liposomes). We discuss such uses either when a thin surfactant layer covers a surface modifying its effective surface tension as a function of the surfactant layer thickness, or when a thin liquid layer is covering a surface and the thin film itself has a lower surface tension than the bulk value. Possible research directions in the field are outlined.

Thin wetting film from aqueous solution of polyoxyalkylated DETA (Diethylenetriamine) polymeric surfactant

Thin wetting films from aqueous solutions of the polymeric surfactant polyoxyalkylated diethylenetriamine (DETA), have been studied on hydrophilic SiO 2-glass surface. The wetting (receding) contact angles θ r of the solution on the glass surface have been measured, using the sessile drop method. Also the contact angle θ aq of a drop of doubly distilled water on the same glass surface pre-treated with DETA polymeric surfactant solution has been measured. The receding contact angles θ r versus polymeric surfactant concentration C s curves showed a maximum at θ r ≈ 22° in the concentration range of 10 −6–2 × 10 −5 mol dm −3 DETA. The equilibrium thickness h of wetting films from DETA aqueous solution on hydrophilic SiO 2-glass surface, pre-treated with surfactant solution, has been measured using the micro-interferometric method at various concentrations, C s. At very low C s (between 10 −11 and 10 −8 mol dm −3) the h-values are almost constant, then they increase with increasing C s reaching a maximum at 1.5 × 10 −6 mol dm −3, after which they decrease with further increase in C s. Both θ r and h exhibit largest values in the concentration range between 2 × 10 −6 and 2 × 10 −5 mol dm −3 DETA. The analysis of the results obtained shows that the stability of the wetting films from aqueous solutions of DETA is determined by the electrostatic, steric, and hydrophobic components of disjoining pressure, respectively by the adsorption and orientation of the polymeric DETA molecules on the SiO 2-glass surface.

A polyethylene chain investigated with replica exchange molecular dynamics simulation: Equilibrium lamellar thickness and melting point, ordering and free energy

In the present work, a polyethylene chain with N=200 CH2 units was simulated using replica exchange molecular dynamics (REMD). Simulations were performed in a broad temperature range and for intra-chain interactions varying from the fully interacting to the ideal spring chain.Our work demonstrates that REMD is a very efficient method to obtain equilibrium data. It is found that the coil-to-globule transition is dominated by the vdW energy, whereas the globule-to-folded chain transition is accompanied by transitional behavior in the torsion and vdW energies. Our data clearly show that for the chain length considered here, the chain folded crystal to globule transition is a continuous transition. Nevertheless, we can establish with good accuracy the equilibrium transition temperature for the chain folded crystal to globule transition.A set of orientational order parameters was used to investigate the order in the polymer chain. At the globule-to-folded chain transition an abrupt change in the value of the order parameter is observed, whereas there is no or almost no change in the value of the order parameter at the coil-to-globule transition temperature. The (apparent) order in the disordered globular and coiled states indicated by some studied order parameters is related to the definition of the order parameter and depends on the chain length of the polymer.Below the equilibrium melting temperature the (largest principal component of the) radius of gyration and the equilibrium lamellar thickness of the folded chain crystal decrease with increasing temperature, which gives support to the theory of Muthukumar but is opposite to the prediction of classical crystallization theories. The agreement between simulations and theory may hint to universal behavior of the relative equilibrium thickness versus the relative super cooling.

Hygroscopic thickness swelling rate of wood polymer nanocomposite

In this study, the effects of nanoclay and coupling agent content on the clay dispersion and thickness swelling behavior of PP/WF composites were investigated. To meet this objective, the blend nanocomposites were prepared by melt mixing PP and beech WF at 50% weight ratios, with various amounts of nanoclay (0, 3, and 6 phc) and MAPP (0, 2, and 4 phc) in Hakee internal mixer. The samples were then made by injection molding. The thickness swelling rate of the composites was evaluated by immersing them in water at room temperature for several weeks (up to 3000 h). A swelling model developed by Shi and Gardner (2006) was used to study the thickness swelling process of composites, from which the parameter, K SR, can be used to quantify the swelling rate. The results indicated that equilibrium thickness swelling and also shorter equilibrium time (the time to reach the equilibrium thickness swelling) decreased with increase of clay loading, and also the effect of compatibilizer was positive in terms of enhancing the dimensional stability of the composites. The swelling model developed was a good predictor of the hygroscopic swelling process of wood plastic composites. The composites containing PP had a higher KSR than those containing MAPP or nanoclay. The minimum KSR values were observed in composites made of 3 phc of nanoclay and 4 phc of MAPP. The micrographs of XRD and TEM confirmed the intercalation morphology in nanocomposite samples.

Effect of surface anisotropy on the melting temperatures of free-standing gold nanofilms

A systematic study of the effect of surface anisotropy on the melting temperatures of free-standing gold nanofilms for various film thicknesses was carried out using molecular dynamics (MD) simulations. Caloric curves obtained from progressive heating of nanofilms showed sharp increase in energy at the transition temperatures due to the absorption of latent heat of melting. The importance of identifying the correct transition point (i.e., lower transition point) as the melting temperature was demonstrated. Melting temperatures of nanofilms were found to be lower than the bulk melting point. Significant decrease in the melting temperature with film thickness was observed for thicknesses below ∼6 nm. Among the films with low index crystallographic surfaces, those with {1 1 0} surface (least close-packed and highest surface energy) showed lowest melting temperatures whilst those with {1 1 1} surface (most close-packed and lowest surface energy) showed highest melting temperatures. Prolonged isothermal heat treatment demonstrated that there is no coexistence of equilibrium thickness of liquid layer with solid, in the case of free-standing nanofilm, below its melting temperature.

Theoretical study on the structure and energetics of intergranular glassy film in Si3N4-SiO2ceramics

AbstractMolecular dynamics simulations have been performed to investigate intergranular glassy film in Si3N4–SiO2ceramics. A 90°-twist grain boundary was employed as a representative random grain boundary and an amorphous structure of the intergranular glassy film was introduced in the calculations. It is found that the presence of the intergranular glassy film at the grain boundary significantly decreases the number of dangling bonds at the interface originating from geometric strain due to misorientation of adjacent Si3N4grains. Calculations with a several of thicknesses of the intergranular glassy film revealed that the excess energy significantly decreased with the increase in the thickness smaller than 7.0Å, while further increase in the thickness did not contribute to a release in the geometric strain energy. Equilibrium thickness of the intergranular glassy film was estimated from the calculations. A new approach to estimating the equilibrium thickness is proposed. A possible explanation of the disparity between intergranular glassy film thicknesses of the intergranular glassy film measured by high-resolution electron microscopy and electron energy-loss spectroscopy is given in terms of ordering of atoms at the interface.

Theoretical description of the adsorption of transition metal ions on metal surfaces with the formation of submonolayer ferromagnetic films

The influence of the temperature and ferromagnetic ordering on the adsorption of Fe, Co, and Ni transition metal ions on a copper paramagnetic substrate with the formation of a submonolayer film is described in terms of the spin-density functional theory for the first time. The conditions for the formation of magnetic monoatomic films stable with respect to island adsorption with a change in the coverage parameter Θ are revealed. Four model cases of the electron density distribution as a function of the equilibrium distance between the film and the substrate and the equilibrium thickness of the adsorption layer are considered. It is demonstrated that the inclusion of the ferromagnetic ordering substantially affects the adsorption energy and leads to its considerable increase.

Description of the adsorption of magnetic ions on metallic surfaces using the spin-density-functional method

The effect of temperature on the adsorption of magnetic ions of transition metals on a paramagnetic metallic substrate is described for the first time with allowance for the effects of ferromagnetic ordering in a submonolayer film. Conditions have been determined necessary for the formation of magnetic monatomic films stable relative to the island adsorption with changes in the coverage Θ. Four model cases of electron-density distribution depending on the equilibrium distance between the film and the substrate and the equilibrium thickness of the adsorption layer are considered. It is shown that the allowance for the effects of ferromagnetic ordering exerts a substantial influence on the adsorption energy, leading to its noticeable increase.

Variable charge molecular dynamics simulations of the intergranular films in SiC

Variable charge molecular dynamics simulations of SiC intergranular glassy films have been performed based on the iterative fluctuation charge model. The atomistic structures of different configurations of the intergranular films are simulated. Charge transfer between the films and their neighboring crystals is observed and the equilibrium film thickness is found to be dependent on the charge transfer. Our results provide a direct proof for the existence of space charges and show that electrostatic interaction contributes to the equilibrium thickness of the intergranular films.

Kinetics of layer hopping in a diblock copolymer lamellar phase

In the ordered state, symmetric diblock copolymers self-assemble into an anisotropic lamellar morphology. The equilibrium thickness of the lamellae is the result of a delicate balance between enthalpic and entropic energies, which can be tuned by controlling the temperature. Here we devise a simple yet powerful method of detecting tiny changes in the lamellar thickness using optical microscopy. From such measurements we characterize the enthalpic interaction as well as the kinetics of molecules as they hop from one layer to the next in order to adjust the lamellar thickness in response to a temperature jump. The resolution of the measurements facilitate a direct comparison to predictions from self-consistent field theory.

Adsorption layer and foam film properties of mixed solutions containing β-casein and C 12DMPO

The interrelations between adsorption layer properties and surface forces in thin foam films of protein/surfactant mixtures were investigated. The adsorption from β-casein/dodecyl dimethyl phosphine oxide (C 12DMPO) mixed solutions was studied by Profile Analysis Tensiometry (PAT). The adsorption of protein/surfactant mixtures at the air/water interface is of competitive nature. The obtained adsorption isotherms suggest a gradual displacement of the protein molecules from the interface with increasing surfactant concentration. Foam films were studied by microinterferometry, originally introduced by Scheludko and Exerowa. The obtained experimental results show that the composition of the mixed adsorption layers changes with increasing amount of added surfactant. At a certain mixing ratio the corresponding foam film thickness decreases dramatically. This change happens above the surfactant concentration where the surface tension of the protein–surfactant mixtures approaches the values obtained for the respective pure surfactant solutions. The thickness, refractive index and adsorbed amount of the respective adsorption layers were determined by ellipsometry. These results correlate with the above-mentioned PAT and foam film data. The refractive index and adsorbed amount decrease monotonically and reach values close to those for pure surfactant solutions. On the contrary, a continuous increase can be observed in the layer thickness up to the above-mentioned concentration, indicating the formation of a more diffuse layer at the air–water interface formed by β-casein and C 12DMPO molecules upon increase of surfactant concentration. For foam films the electrolyte concentration can change the equilibrium thickness of the films and the Π(h)-isotherms significantly.