EFFECTS OF MASS TRANSFER ON THE THINNING AND RUPTURE OF A PLANE PARALLEL LIQUID FILM

The effects of mass transfer and physical properties upon the thinning and rupture of adraining plane parallel film are investigated.An equation is derived in which the thinning rate is afunction of bulk properties.surface properties(surface tension,surface viscosities,and the variationof surface tension with surface concentration),intermolecular forces(London-van der Waals forcesand electrostatic double layer forces),adsorption and surface diffusion coefficients,bubble size andfilm thickness.An estimation for the critical thickness at which a film rupture is carried out and thecoalescence time is obtained by integration to the critical thickness,The coalescence time is predictedas a function of bulk and surface properties,London-van der forces,adsorption and surfacediffusion coefficients,and bubble size.     

ON RUPTURE OF A THINNING FILM OF NON-NEWTONIAN POWER LAW LIQUID†

A linear stability analysis of a thinning film of non-Newtonian power law liquid has been employed to predict the critical thickness of rupture of films with immobile interfaces experiencing only van der Waals interactions. The assumption of immobile interfaces makes the above analysis equally applicable to the stability of foam as well as emulsion thin films. Psuedoplastic liquid thin films are found to be significantly less stable than Newtonian films. Power law liquid thin films are more stable for liquids with larger values of power law exponents and larger values of consistency indices. The critical thickness of film rupture is very sensitive to the power law exponent. As expected, the critical thickness of film rupture increases for stronger van der Walls interactions as well as for smaller surface tensions, these effects being more pronounced for psuedoplastic liquid films than their Newtonian counterparts.     

Tunable bands in biased multilayer epitaxial graphene

We have studied the electronic characteristics of multilayer epitaxial graphene under a perpendicularly applied electric bias. Ultraviolet photoemission spectroscopy measurements reveal that there is notable variation of the electronic density-of-states in valence bands near the Fermi level. Evolution of the electronic structure of graphite and rotational-stacked multilayer epitaxial graphene as a function of the applied electric bias is investigated using first-principles density-functional theory including interlayer van der Waals interactions. The experimental and theoretical results demonstrate that the tailoring of electronic band structure correlates with the interlayer coupling tuned by the applied bias. The implications of controllable electronic structure of rotationally fault-stacked epitaxial graphene grown on the C-face of SiC for future device applications are discussed.     

Effect of geometrical arrangement and interdrop forces on coalescence time

According to the Reynolds' equation the time taken for a thin film to reach a critical thickness at which rupture occurs is a function of the film area and applied force. It follows that the coalescence time of a liquid drop is greatly affected by its geometrical configuration. If the drop is unconstrained the coalescence time increases when a vertical force is applied to the drop, but if the drop is constrained by the presence of surrounding drops its coalescence time decreases as the applied force increases. This explains why the rate of coalescence at the disengaging interface of a close-packed dispersion increases with the dispersion height. The coalescence time for a planar film is usually less than for the spherical film formed between a drop and its homophase which explains why near-horizontal surfaces inserted into close-packed dispersion increase the rate of coalescence. The coalescence time of a drop in a close-packed dispersion decreases as it approaches the disengaging interface. This means that the volume rate of coalescence at the interface may equal the disperse phase throughout without the necessity for interdrop coalescence. When the applied pressure is much greater than the van der Waals pressure, as in a close-packed dispersion, the critical film thickness is itself a function of the film area and applied force, but this has little effect on the above conclusions. When the applied pressure is much less than the van der Waals pressure, as in a loose-packed dispersion, the critical film thickness is only a function of the film area and the affect of the applied force on the coalescence time is then increased.     

Microscopic spreading of nonreactive perfluoropolyalkylether film on amorphous carbon surfaces

A spreading mechanism of nonfunctional perfluoropolyalkylehter (PFPE) on carbon surfaces is proposed. For the thin thin-film regime, adsorption-desorption is a main driving force for spreading, and the surface diffusion coefficients increase as the film thickness increases. A two-dimensional virial equation is employed to explain the dependency of surface diffusion coefficient on the film thickness. For the thick thin-film regime, the spreading characteristic is determined by the disjoining pressure gradient. We adopt a slip boundary condition to analyze the thick thin-film regime. This modification of the boundary condition reasonably explains the dependence of surface diffusion coefficients on film thickness.     

A numerical study of fluidization behavior of Geldart A particles using a discrete particle model

This paper reports on a numerical study of fluidization behavior of Geldart A particles by use of a 2D soft-sphere discrete particle model (DPM). Some typical features, including the homogeneous expansion, gross particle circulation in the absence of bubbles, and fast bubbles, can be clearly displayed if the interparticle van der Waals forces are relatively weak. An anisotropy of the velocity fluctuation of particles is found in both the homogeneous fluidization regime and the bubbling regime. The homogeneous fluidization is shown to represent a transition phase resulting from the competition of three kinds of basic interactions: the fluid-particle interaction, the particle-particle collisions (and particle-wall collisions) and the interparticle van der Waals forces. In the bubbling regime, however, the effect of the interparticle van der Waals forces vanishes and the fluid-particle interaction becomes the dominant factor determining the fluidization behavior of Geldart A particles. This is also evidenced by the comparisons of the particulate pressure with other theoretical and experimental results.     

The effect of an electrostatic field on the rupture of a thin viscous static film by van der Waals attractions

This research examines rupture phenomena of a horizontal static thin viscous layer on a solid plate under an electrostatic field generating from a charged foil above the film. The dynamics of the electrified liquid film is formulated to derive a long-wave evolution equation of local film thickness. It determines two-dimensional nonlinear behavior of the film subject to surface tension, viscous, electrically induced forces, and van der Waals attractions. Linear stability analysis is used to obtain the maximum growth rate of a periodic disturbance and its corresponding wavenumber. To see the development of film rupture the strongly nonlinear partial differential equation is numerically solved for the unlimited or limited foil length as part of an initial-value problem with spatially periodic boundary conditions. The stronger electric forces make the thin layer more unstable and speed up its rupture.     

Statistical model of the powder flow regulation by nanomaterials

Fine powders often tend to agglomerate due to van der Waals forces between the particles. These forces can be reduced significantly by covering the particles with nanoscaled adsorbates, as shown by recent experiments. In the present work a quantitative statistical analysis of the effect of powder flow regulating nanomaterials on the adhesive forces in powders is given. Covering two spherical powder particles randomly with nanoadsorbates we compute the decrease of the mutual van der Waals force. The dependence of the force on the relative surface coverage obeys a scaling form that is independent of the used materials. The predictions by our simulations are compared to the experimental results.     

Cohesive forces between particles of fluid-bed catalysts

The importance of van der Waals and capillary interparticle forces with respect to particle weight is discussed. Evaluation of solid to solid interaction on the basis of particle diameter leads to exceedingly high values of cohesive forces. The need for detailed analysis of particle surfaces is shown.Electron scanning microscopy is used to investigate particle surface characteristics of a number of catalytic powders. There are surface irregularities even in the case of apparently perfect microspheres. For some of the materials tested the investigation provides local radii of curvature of particle surface required for the evaluation of particle to particle interactions.     

Characterisation of inter-particle forces within agglomerated metallurgical powders

The strength of agglomerates of nickel flash furnace concentrate and dust was determined from experimental observations of agglomerates forming under controlled conditions, combined with mathematical equations from the literature. It was found that the agglomerates had a tensile strength ranging from 0.01 Pa to 38.7 Pa, while inter-particle forces ranged from 2.2 × 10^− 12 N to 1.5 × 10^− 10 N. These values were compared to the expected magnitude of van der Waals, electrostatic, magnetic and capillary forces within the agglomerates, and it was found that both electrostatic and van der Waals forces are likely to contribute to the cohesion of agglomerates, although sub-micron particles and the presence of sufficiently large asperities on the surface of particles limit the magnitude of van der Waals forces. Magnetic forces are large enough to contribute to the cohesion of dust agglomerates, which is in keeping with the high magnetite content of the recycle dust. It is postulated that electrostatic forces, acting over a longer range than van der Waals forces, may be responsible for initially bringing particles together. The methodology for determining inter-particle forces can be applied to the computer modelling of flash smelting systems, as well as other gas/particle systems such as fluidized beds.     

RUPTURE OF THIN MICROPOLAR LIQUID FILM ON A CYLINDER

The dynamic rupture process of a thin liquid film on a cylinder has been analyzed by investigating the stability to finite amplitude disturbances. The dynamics of the liquid film is formulated using the balance equations including a body force term due to van der Waals attractions. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. A decrease in the cylinder radius will induce a stronger lateral capillary force and thus will accelerate the rupture process. The rupture time increases with the material parameter, Δ.     

RUPTURE OF THIN MICROPOLAR LIQUID FILM ON A CYLINDER

The dynamic rupture process of a thin liquid film on a cylinder has been analyzed by investigating the stability to finite amplitude disturbances. The dynamics of the liquid film is formulated using the balance equations including a body force term due to van der Waals attractions. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. A decrease in the cylinder radius will induce a stronger lateral capillary force and thus will accelerate the rupture process. The rupture time increases with the material parameter, Δ.     

Capillary and van der Waals force between microparticles with different sizes in humid air

It is well known that surface effect forces, such as van der Waals force and capillary force, are the major contributions to adhesion when microsized particles are in contact in humid environment. But it is very complex to calculate the adhesion force between two smooth unequal particles. In conventional approaches, the effective particle radius approximation and the constant half-filling angle assumptions are often used for computing the van der Waals forces between two microparticles. However, the approximation and the assumption are actually difficult to accurately model the forces between unequal particle sizes when the surfaces are with different properties. In this paper, we present a theoretical study of the van der Waals force and capillary force between two microparticles with different radii and the surface properties linked by a liquid bridge. The proposed model provides the adhesion force predictions in good agreement with the previous formula and existing experiment data. Considering the solid particles are partially wetted by the liquid bridge, the van der Waals force is calculated by divided the particle surface into a wetted part and a dry portion in our stimulation. Since the wetted surface portion of the particle is determined by the half-filling angle, the relationship between two half-filling angles of the unequal size particles is developed from the geometrical consideration, which is relate to the size ratio of the particles, the contact angle, and the separation distance. Then, the van der Waals force is determined using the surface element integration. Moreover, the influences of humidity, particles size, contact angle, and separation distance toward the adhesion forces are discussed using the proposed method. Simulations indicate that a higher relative humidity leads to bigger liquid bridges, suggesting a higher capillary force, but at the same time, the van der Waals force decreases due to the decrease in surfaces energy. As for the influence of contact angle, results show that a higher contact angle, that is, a more hydrophobic surface, reduces the capillary force but increases the van der Waals force (absolute value). The simulations also show that the both the capillary force and the van der Waals force (absolute value) increase as the particle size increases. When the particles are separated from each other, the capillary force and van der Waals force decreases gradually. These results are helpful to understand and utilize the adhesion interaction between particles with unequal sizes at the ambient condition.     

Molecular modeling and atomistic simulation strategies to determine surface properties of perfluorinated homopolymers and their random copolymers

Molecular mechanics (MM) and molecular dynamics (MD) simulations on ten perfluoroalkyl methacrylates and four copolymers derived from methyl methacrylate (MMA) and 1,1-dihydroperfluorohendecyl methacrylate (F10MA) in different ratios have been performed to predict surface properties. 1,1-Dihydroperfluorohendecyl methacrylate, which contained highest number of fluorine atoms, exhibited lowest surface energy, a trend that is in accordance with experimental observations. Density calculations on selected perfluoroalkyl methacrylates have been performed using NPT dynamics, for which no experimental data are available. Computations were performed to obtain bulk properties like cohesive energy density and solubility parameter through MM and MD simulations in the NVT ensemble under periodic boundary conditions. From the equilibrated structures, surface energies were computed, which compared well with the experimental data reported in the literature. Surface energies of copolymers decreased with increasing number of perfluoroalkyl groups. Various components of energetic interactions have been examined in detail in order to gain a better insight into interactions between bulk structure and the film. The dominant contributions are from van der Waals and Coulombic energy terms. The computed mass density profile for thin films gave an indication whether the film is of sufficient thickness so that the interior of the film is indistinguishable from the bulk structure. The total pair correlation and bond correlation functions have been analyzed to confirm the amorphous nature of the simulated structures.     

Thin Glass Film between Ultrafine Conductor Particles in Thick-Film Resistors

Thick-film resistors arc electrical composites containing ultrafine particles of ruthenate conductor (Pb₂Ru₂O₇ in the present materials) distributed in a highly modified silicate glass. We show that conductor particles remain flocced in the absence of any applied or capillary pressures, but are separated at equilibrium by a nanometer-thick film of glass. Microstructures show evidence for liquid-phase sintering, i.e., contact flattening of particles, under van der Waals attraction alone. Titania addition, which in dilute concentrations markedly increases the resistivity, decreases the temperature coefficient of resistance, and improves voltage stability and noise, is found to increase the equilibrium film thickness between particles by a few angstroms. STEM analyses show that the added titania preferentially concentrates in the silicate-rich grain boundary film, as well as at particle–glass interfaces. The roles of interparticle forces and adsorption on the glass film thickness with and without titania are discussed. The large increase in resistivity caused by titania additions is attributed to the increase in Film thickness as well as to local chemical changes of two possible types. Titania enrichment within the glass film itself is expected to decrease the local ruthenium ion solubility, and this along with the possible formation of a more insulating titania-substituted surface layer on ruthenate grains will decrease the tunneling conductivity between conductor grains.     

On the relationship between porosity and interparticle forces

This paper presents an attempt to quantify the relationship between porosity and interparticle forces for mono-sized spheres. Two systems are considered: the packing of wet coarse spheres where the dominant interparticle force is the capillary force, and the packing of dry fine spheres where the dominant force is the van der Waals force. The interrelationships between porosity, capillary force and liquid content are first discussed based on the well-established theories and experimental observations. The resultant relationship between porosity and capillary force is then applied to the packing of fine particles to quantify the van der Waals force in a packing. A generalised relationship between porosity and interparticle forces results as an extension of this analysis. The usefulness of this relationship is finally demonstrated in depicting the fundamentals governing the relationship between porosity and particle size.     

Molecular beam growth of micrometer-size graphene on mica

We demonstrate molecular beam growth of graphene on biotite mica substrates at temperatures below 1000 °C. As indicated by optical and atomic force microscopy, evaporation of carbon from a high purity solid-state source onto biotite surface results in the formation of single-, bi-, and multilayer graphene with size in the micrometer regime. It is shown that the graphene grown directly on mica surface is of very high crystalline quality with the defect density below the threshold detectable by Raman spectroscopy. The interaction between graphene and the mica substrate is studied by comparison of the Raman spectroscopy and atomic force microscopy data with the corresponding results obtained for graphene flakes mechanically exfoliated onto biotite substrates. Experimental insights are combined with density functional theory calculations to propose a model for the initial stage of the van der Waals growth of graphene on mica surfaces. This work provides hints on how the direct growth of high quality graphene on insulators can be realized in general without exceeding the thermal budget limitations of Si technologies.     

Possible Electrical Double-Layer Contribution to the Equilibrium Thickness of Intergranular Glass Films in Polycrystalline Ceramics

The plausibility of the entropic repulsion of electrical double layers acting to stabilize an equilibrium thickness of intergranular glass films in polycrystalline ceramics is explored. Estimates of the screening length, surface potential, and surface charge required to provide a repulsive force sufficiently large to balance the attractive van der Waals and capillary forces for observable thicknesses of intergranular film are calculated and do not appear to be beyond possibility. However, it has yet to be established whether crystalline particles in a liquid-phase sintering medium possess an electrical double layer at high temperatures. If they do, such a surface charge layer may well have important consequences not only for liquid-phase sintering but also for high-frequency electrical properties and microwave sintering of ceramics containing a liquid phase.     

A new state model of liquid-vapor interfaces—to yield analytical expression for surface tension

Based on the van der Waals fluid model, a simple equation of state, unique for non-uniform fluids, is developed. It is applied to the liquid-vapor interface, to derive the density profile in the interfacial region. The density profile is used in conjunction with the gradient theory, to yield an expression for the surface tension of a saturated fluid as a function of temperature and fluid properties. The non-dimensionalized influence parameter of the gradient theory is assigned best-fit values, which are of a unity order of magnitude, as expected. The predicted surface tension values are in good agreement with experimental data, for a variety of fluids.     

Self-organization in unstable thin liquid films: dynamics and patterns in systems displaying a secondary minimum

Dynamics, stability, morphology, and dewetting of a thin film (<100 nm) under the influence of a long-range van der Waals attraction combined with a short-range repulsion are studied based on numerical solutions of the nonlinear two-dimensional (2-D) thin film equation. Area and connectivity measures are used to analyze the morphology and the distinct pathways of evolution of the surface instability. The initial disturbance resolves into an undulating structure of uneven 'hills and valleys'. Thereafter, the morphology depends on the mean film thickness relative to the minimum of the force curve. Relatively thin films to the left of the minimum transform directly into an array of droplets via the fragmentation of ridges. At long times, the droplets merge due to ripening. In contrast, relatively thick films are dewetted by the formation and growth of isolated, circular holes. Coalescence of holes eventually leads to the formation of ridges and drops. Films of intermediate thickness display a rich combination of different morphologies. Thus, the morphology and the sequence of evolution depend crucially on the form of the potential and the film thickness relative to the location of the minimum in the force vs. thickness curve. Different types of patterns can, therefore, even co-exist on a heterogeneous surface.