Thin Film Approximation Research Articles

Coupled Discrete Phase and Eulerian Wall Film Models for Drug Deposition Efficacy Analysis in Human Respiratory Airways.

The current study explores the effectiveness of drug particle deposition into human respiratory airways to cure various pulmonary-bound ailments. It has been assumed that drug solutions are inhaled in the form of tiny droplets or mist, which after striking create a thin layer along the inner surface of airways where the virus initially resides to infect the human body. A coupled Eulerian wall film (EWF) and discrete phase model (DPM) based simulation approach is used to capture these dynamics. Here, the Lagrangian DPM technique tracks the dynamics of tiny droplets, while the liquid layer formation after striking is captured using the Eulerian thin film approximations or the EWF model. Previous studies in this field primarily employed only the DPM method, which is inadequate to predict the poststriking dynamics of drug layer deposition and their spread to neutralize the respiratory virus. The drug delivery effectiveness is characterized by three different particle sizes, 1, 5, and 10 μm at the inhalation rates of 15, 30, and 60 L per minute (LPM). It has been found that the size of the drug particles significantly influences drug delivery effectiveness. The film thickness increases monotonically with particle sizes and inhalation rates. However, this increase in averaged film thickness is prominent in the range 5 to 10 μm (≈60%) compared to 1 to 5 μm (≈10%) droplet sizes at generation level 4 (G4). The other deposition parameters, e.g., deposition fraction, deposition density, and area coverage) roughly show similar behavior with the increase in droplet sizes. Therefore, it is recommended to vary the droplet sizes between 5 and 10 μm for better deposition effectiveness. The sizes of more than 10 μm mostly stuck into the oral cavity and cannot reach the targeted generations. In contrast, less than 5 μm may reach much deeper generations than the targeted one.

2D axisymmetric electromagnetic modeling of HTS coils based on T-A formulation with modified Newman boundary conditions

The T-A formulation based on thin film approximation has been widely used in electromagnetic modeling of high temperature superconducting (HTS) coated conductors (CCs). However, with the emergence of no-insulation (NI) HTS coils and its variant HTS coils, the electrical connection of HTS coils has become increasingly complex, and the traditional T-A formulation is challenging to handle the problems of conductors with non-negligible thickness and current sharing. This paper firstly describes the Neumann boundary condition of the T-A formulation under 2D axisymmetric symmetry in detail, as well as the conversion of different boundary conditions. And additional voltage variable is added to correct the Newman boundary condition from the perspective of circuit. Then, considering HTS CCs series or parallel stacking to carry current, the effectiveness of this method is verified by comparing with benchmark model. Finally, we extend the application range of the T-A formulation with modified Newman boundary conditions to simulate thick superconductors, and naturally process current sharing of azimuthal and radial current in circular NI HTS coils.

Dynamics of particle aggregation in dewetting films of complex liquids

We consider the dynamic wetting and dewetting processes of films and droplets of complex liquids on planar surfaces, focusing on the case of colloidal suspensions, where the particle interactions can be sufficiently attractive to cause agglomeration of the colloids within the film. This leads to an interesting array of dynamic behaviours within the liquid and of the liquid–air interface. Incorporating concepts from thermodynamics and using the thin-film approximation, we construct a model consisting of a pair of coupled partial differential equations that represent the evolution of the liquid film and the effective colloidal height profiles. We determine the relevant phase behaviour of the uniform system, including finding associated binodal and spinodal curves, helping to uncover how the emerging behaviour depends on the particle interactions. Performing a linear stability analysis of our system enables us to identify parameter regimes where agglomerates form, which we independently confirm through numerical simulations and continuation of steady states, to construct bifurcation diagrams. We obtain various dynamics such as uniform colloidal profiles in an unstable situation evolving into agglomerates and thus elucidate the interplay between dewetting and particle aggregation in complex liquids on surfaces.

Enhancing electric field calculation in HTS tape simulations for currents exceeding the critical limit using full HTS tape modeling

Superconducting devices are an interesting technological option for improvement of efficiency of energy systems. High-temperature superconducting tapes are among the best choices for power applications. Because of their high non-linearity, the design of devices with superconducting tape requires specific simulation models and methods to correctly represent the superconducting behavior. The J-A formulation has been investigated as an efficient tool to represent the electromagnetic behavior of such devices. It is based on the current density (J) and magnetic vector potential (A), and able to represent both superconducting materials and ferromagnetic materials. With regards to the tapes, the use of thin-film approximation can be successful with the J-A formulation. Usually, only representations considering the superconducting layer of tapes have been investigated. This becomes a problem for operations where the current in the superconductor surpasses the critical current, for example in transient analysis. This paper presents an analysis of the effects the inclusion of all of the tapes’ layers have on simulations with the J-A formulation with thin-film approximations. By considering all layers of the tape, one represents the transition between superconducting and high-loss states of the tape. A simple system, consisting of a single tape with applied current, has been studied as benchmark and simulated with J-A and the more established T-A formulation in two cases: considering all layers; and only the superconducting layers. Results show that results for the J-A and T-A formulations are compatible and the inclusion of all layers improves the stability of the simulation and provides correct assessment of the electric field in the tapes.

Thin film modelling of magnetic soap films

Magnetic soap films under the forcing of an inhomogeneous magnetic field are governed by a wide range of interconnected physics. The study of magnetic soap films requires the development of comprehensive models to support experimental observations. In this study, the thin film approximation is applied to the Navier–Stokes equations to derive a model for the film thickness of magnetic soap films that incorporates the effects of interfacial mobility, surfactant transport and magnetite nanoparticle (NP) transport. This derived model consists of a coupled system of equations for the film thickness, interfacial velocity, interfacial surfactant concentration and magnetite NP concentration. Simulations are performed for both soap films and magnetic soap films by solving the system of equations using the Galerkin finite element method, and results are compared with experiments. Simulation results highlight that interfacial flows can dominate the rate of film thinning and that accounting for the dependence of the magnetisation on the local magnetite NP concentration can influence the predicted speed of magnetically driven flows. Furthermore, simulation results demonstrate that the model is able to predict marginal regeneration in qualitative agreement with the experiments for soap films; the model also predicts the same flow pattern as seen in the experiments for magnetic soap films. Overall, this study advances the state of soap film and magnetic soap film modelling and will contribute to acquiring control over the drainage and stability of magnetic soap films in the long term.

A three-phase model for biofilm formation on a porous solid surface

We investigate the growth kinetics of bacterial biofilms on porous substrates. A three-phase model is developed, which accounts explicitly for the cell phase, extracellular matrix (ECM), and nutrient-rich aqueous phase. We use the thin-film approximation as the characteristic height of the biofilm is much smaller than its characteristic radius. We use the 2D axisymmetric model to capture biofilm growth on a porous agar substrate. Our model accounts for osmotic flux and predicts the spatiotemporal variations of the volume fractions of the different phases and the nutrient concentrations in the biofilm and the substrate. An increase in surface tension helps redistribute biomass radially. Our model captures the behavior of different kinds of biofilms: films characterized by low (yeast) and high (bacterial) ECM content. The predictions of our model are quantitatively validated with the experimental data from the literature. Our model provides insights on the role of different parameters on biofilm growth, which can be used to develop strategies to prevent or accelerate biofilm formation on surfaces.

Nonlinear flow of couple stress fluid layer over an inclined plate

The issue of stability of a thin couple-stress liquid layer flows on an inclined plane was inspected. The thin-film approximation was employed to obtain a Benney-like differential equation, that described the time record of the interface profile The linear transition state and reduction ratio of maximum classical (Newtonian) growth-rate were discussed. The complete evolution equation was solved numerically using the method of lines in order to support the novelty of the work. The linear stability could be enhanced by increasing the couple-stress coefficient and surface tension as well as reducing the inclination. However, the ordinary viscosity played an irregular role. The linear results predicted conditions (windows) in which the non-Newtonian film was more stable than its Newtonian counterpart. The nonlinear stimulation anticipated the existence of sock waves in certain situations. The appearance of instability through the linear subcritical region as well as irregular influences with respect to surface tension and couple-stress property was revealed. The nonlinear approach was more accurate in describing the stability issue than the linear one. Such results could be employed to attain the optimum statuses with regard to the film stability, and control the shock waves. They would not only enable accurate practical implementation in the design of inertial confinement fusion capsules and supernova explosions and implosions modeling, but also would allow for precise numerical simulation.

Surfactant amplifies yield-stress effects in the capillary instability of a film coating a tube.

To assess how the presence of surfactant in lung airways alters the flow of mucus that leads to plug formation and airway closure, we investigate the effect of insoluble surfactant on the instability of a viscoplastic liquid coating the interior of a cylindrical tube. Evolution equations for the layer thickness using thin-film and long-wave approximations are derived that incorporate yield-stress effects and capillary and Marangoni forces. Using numerical simulations and asymptotic analysis of the thin-film system, we quantify how the presence of surfactant slows growth of the Rayleigh-Plateau instability, increases the size of initial perturbation required to trigger instability and decreases the final peak height of the layer. When the surfactant strength is large, the thin-film dynamics coincide with the dynamics of a surfactant-free layer but with time slowed by a factor of four and the capillary Bingham number, a parameter proportional to the yield stress, exactly doubled. By solving the long-wave equations numerically, we quantify how increasing surfactant strength can increase the critical layer thickness for plug formation to occur and delay plugging. The previously established effect of the yield stress in suppressing plug formation [Shemilt et al., J. Fluid Mech., 2022, vol. 944, A22] is shown to be amplified by introducing surfactant. We discuss the implications of these results for understanding the impact of surfactant deficiency and increased mucus yield stress in obstructive lung diseases.

A thin-film modeling approach for analysis of carbon capture sorbent-based devices

The threat of climate change has driven scientists and engineers to develop new methods reducing carbon emitted as well as capturing CO2 from the atmosphere and other point sources. Carbon capture technology is still in its infancy and requires significant system efficiency improvements before commercial or industrial adoption is not cost prohibitive. Contactor designs must optimize capture efficiency while minimizing pumping losses through this stage, and typical contactors employ a packing material that is wetted with a fluid spray to create a film. The capture efficiency is determined by a complex relationship of operating parameters, contactor geometry, and the chemical kinetics of the CO2 and chosen capture fluid. Due in part to the large parameter space, as well as the physical difficulty of accurately determining capture efficiency, numerical modeling has become an important tool in research and development of contactors for carbon capture. Historically, modeling approaches used for CO2 capture simulations have been too computationally intensive for design work. This work examines the effectiveness of using a thin-film approximation approach to model the reacting fluid, thus avoiding the expensive grid resolution requirements of the volume-of-fluid (VOF) method. Results showed that changes in the reaction model and dissolution constants have a significant impact in the capture efficiency predictions. CO2 capture was largely dictated by the supply of MEA in the film, with capture efficiency reductions as MEA was depleted. Changes in gas temperatures and velocities also had some impact in the CO2 mass transfer. Overall the results validation shows that in a non-flooded contactor, the thin-film approximation is capable of predicting experimental results with sufficient accuracy. Therefore, this model can be used to quickly evaluate contactor designs.

Three-Dimensional Self-Similarity of Coalescing Viscous Drops in the Thin-Film Regime.

Coalescence and breakup of drops are classic problems in fluid physics that often involve self-similarity and singularity formation. While the coalescence of suspended drops is axisymmetric, the coalescence of drops on a substrate is inherently three-dimensional. Yet, studies so far have only considered this problem in two dimensions. In this Letter, we use interferometry to reveal the three-dimensional shape of the interface as two drops coalescence on a substrate. We unify the known scaling laws in this problem within the thin-film approximation and find a three-dimensional self-similarity that enables us to describe the anisotropic shape of the dynamic interface with a universal curve.

A newly developed screening current simulation method for REBCO pancake coils based on extension of PEEC model

Since the screening current (SC) in rare earth-barium-copper-oxide (REBCO) coated conductor (CC) generates an undesired magnetic field, it must be accurately estimated, especially for magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR). Moreover, in recent years, it was pointed out that the screening current enhanced the stress/strain in REBCO CC, when an REBCO magnet was operated as an insert under an ultrahigh magnetic field. The previously reported SC simulation methods may be roughly categorized into finite element method (FEM) and equivalent circuit method. The FEM-based method often adopted an axisymmetric model or a thin film approximation model, while the circuit-based are the simple equivalent circuit model and the network equivalent circuit model, so-called the partial element equivalent circuit (PEEC) model. The latter is newly developed in this paper. Features of those SC simulation models are briefly compared to each other in this paper. Each SC simulation models have pros & cons. We have to adequately chose an SC simulation model depending on a purpose. We extended the original PEEC model to simulate SC. The extended model is named the advanced partial element equivalent circuit (A-PEEC) model. It is also extendable to an SC simulation of no-insulation REBCO pancake coils. To simulate the SC of a simple coil model and the LBC3 magnet, we investigated the screening current distribution maps, and the simulated screening current-induced fields were compared with the measurements. We have confirmed the validity of the newly developed A-PEEC model.

A dimensionally-reduced fracture flow model for poroelastic media with fluid entry resistance and fluid slip

We develop a model which couples the flow in a discrete fracture to a deformable porous medium. To account for the discrete representation of the fracture, a dimensionally-reduced fluid flow model is proposed. The fluid flow model incorporates both a reduced permeability of the fracture walls due to the skin effect, and a slip of fluid flowing along the permeable fracture walls. Biot's model for poroelastic media is coupled to a fracture flow model based on a thin-film approximation of the compressible Navier-Stokes equations. The fracture flow model incorporates a fluid entry resistance parameter to relate the leak-off through the fracture walls to a pressure jump across the fracture walls, and the Beavers-Joseph-Saffman slip rate coefficient to represent the fluid slip along the fracture walls. The numerical model is based on a thermodynamic framework in which all energy storage and dissipative mechanisms in the problem are identified, including the mechanisms related to the interface effects. The thermodynamic framework is employed to solve the nonlinear coupled problem up to a specified energy range through a Picard iteration technique and to study the model and its results. Studies are presented for a range of fluid entry resistance parameters and Beavers-Joseph-Saffman slip rate coefficients, showing the capability of the model to simulate skin and slip effects in a dimensionally-reduced fracture setting.

MATHEMATICAL DESCRIPTION OF THE PROCESS OF FILM CONDENSATION OF VAPORS FROM STEAM-GAS MIXTURES

This article presents an analysis of the mathematical description of the process of film condensation of vapors from vapor-gas mixtures. Taking into account the considerable variety of effects that occur during the flow of films in processes in which phase transformations occur, the complexity of the mathematical description of the flow of condensate films becomes obvious. This complexity of describing the process is aggravated by the combination of heat and mass transfer, non- isothermic, and changes in such properties as surface tension, viscosity, and density. To describe the flow rate and film thickness during film condensation, a fundamental system of equations is used, and the equations of dynamics and continuity in the long-wave approximation are also taken into account. The estimation of the propagation length of nonlinear waves in condensate films with varying flow rates showed that with an increase in the condensation intensity, the role of the proposed corrections increases, but within the limits of the validity of the thin-film approximation does not become decisive and significant. During the description of the process of film condensation of vapors from steam-gas mixtures, it was found that when the basic conditions are met, the influence of undulation manifests itself mainly through an increase in the heat exchange surface, and the contribution of surface forces to the intensification of the process, i.e., an increase in condensate consumption, is no more than 10-12%

A steady-state semi-analytical approximation of melt pool evolution in pulsed laser surface melting

Pulsed laser surface melting (pLSM) is a technique that offers an efficient and effective way to modify the geometry surfaces without any addition or removal of material. The resultant surface geometry plays a critical role in several applications. This paper presents a steady-state thin-film approximation of the melt pool created by pLSM and the resulting semi-analytical solution for the evolved surface geometry. These predictions of the semi-analytical solution are then compared with a validated numerical solution. The comparison demonstrates a good match with errors ranging from ~4% to ~25% across several pulse durations. Larger errors are observed at comparatively lower and higher pulse duration. Smaller errors are observed for intermediate pulse duration values because of the deviation of non-dimensional numbers from their assumed orders. Overall, the thin-film solution is a reasonable and useful approximation of the evolved surface geometry through the pLSM process, thus saving significant computational costs.

Optical Characterization of Few-Layer PtSe2 Nanosheet Films.

Thin films of transition-metal dichalcogenides are potential materials for optoelectronic applications. However, the application of these materials in practice requires knowledge of their fundamental optical properties. Many existing methods determine optical constants using predefined models. Here, a different approach was used. We determine the sheet conductance and absorption coefficient of few-layer PtSe2 in the infrared and UV–vis ranges without recourse to any particular model for the optical constants. PtSe2 samples with a thickness of about 3–4 layers were prepared by selenization of 0.5 nm thick platinum films on sapphire substrates at different temperatures. Differential reflectance was extracted from transmittance and reflectance measurements from the front and back of the sample. The film thickness, limited to a few atomic layers, allowed a thin-film approximation to calculate the optical conductance and absorption coefficient. The former has a very different energy dependence in the infrared, near-infrared, and visible ranges. The absorption coefficient exhibits a strong power-law dependence on energy with an exponent larger than three in the mid-infrared and near-infrared regions. We have not observed any evidence for a band gap in PtSe2 thin layers down to an energy of 0.4 eV from our optical measurements.

Role of suction pressure in the stability of a gravity-driven thermoviscous liquid film flow down the interior surface of a cylinder.

This study aims to analyze the stability of a gravity-driven thin film flow in the heated/cooled interior surface of a vertical hollow cylinder. The model development involves simplifying the flow and energy equations using the usual thin-film approximation, where the average film thickness is considered to be much smaller than the radius of cylinder. A dispersion relation is then derived to study the temporal stability of the system in order to quantify the effect of various non-dimensional parameters present in the model, such as the thermoviscous number, Marangoni number, Biot number, and Bond number. Another non-dimensional parameter is introduced by considering an opposing suction pressure in the annulus region. The thermocapillary stress and the thermoviscous effect are shown to strongly affect the temporal stability of the flow. It is shown that although the suction pressure affects the velocity profile of the flow, it does not affect the temporal stability results. The suction pressure is then shown to have some effect on the spatiotemporal stability. Critical condition is presented for the transition between absolutely and convectively unstable systems, and parameter regimes are presented to quantify the effect of the above-mentioned parameters.

Analysis of Contact Occurrence in Fluid–Structure Interaction System Under the Thin Film Approximation

In this paper, we consider the interactions between a 2D film of an incompressible viscous fluid deposited on a solid substrate and an elastic 2D structure delimiting the upper boundary of the film. The system is strongly coupled since we assume continuity of velocities and normal stresses at the fluid/structure interface. A general model including a fractional power of the laplacian is chosen to model the structure dynamics. We derive two asymptotic models in the thin film approximation depending on the relative size of the structure mechanical parameters. We then discuss the influence of the power exponent on possible collapse of the film in the various reduced models.

Streamlines in the Two-Dimensional Spreading of a Thin Fluid Film: Blowing and Suction Velocity Proportional to the Spatial Gradient of the Height

The aim of this investigation is to determine the effect of fluid leak-off (suction) and fluid injection (blowing) at the horizontal base on the two-dimensional spreading under the gravity of a thin film of viscous incompressible fluid by studying the evolution of the streamlines in the thin film. It is assumed that the normal component of the fluid velocity at the base is proportional to the spatial gradient of the height of the film. Lie symmetry methods for partial differential equations are applied. The invariant solution for the surface profile is derived. It is found that the thin fluid film approximation is satisfied for weak to moderate leak-off and for the whole range of fluid injection. The streamlines are derived and plotted by solving a cubic equation numerically. For fluid injection, there is a dividing streamline originating at the stagnation point at the base which separates the flow into two regions, a lower region consisting mainly of rising fluid and an upper region consisting mainly of descending fluid. An approximate analytical solution for the dividing streamline is derived. It generates an approximate V-shaped surface along the length of the two-dimensional film with the vertex of each section the stagnation point. It is concluded that the fluid flow inside the thin film can be visualised by plotting the streamlines. Other models relating the fluid velocity at the base to the height of the thin film can be expected to contain a dividing streamline originating at a stagnation point and dividing the flow into a lower region of rising fluid and an upper region of descending fluid.

Streamlines in the Two-Dimensional Spreading of a Thin Fluid Film: Blowing and Suction Velocity Proportional to the Height

The two-dimensional spreading under gravity of a thin fluid film with suction (fluid leak-off) or blowing (fluid injection) at the base is considered. The thin fluid film approximation is imposed. The height of the thin film satisfies a nonlinear diffusion equation with a source/sink term. The Lie point symmetries of the nonlinear diffusion equation are derived and exist, which provided the fluid velocity at the base, vn satisfies a first order linear partial differential equation. The general form has algebraic time dependence while a special case has exponential time dependence. The solution in which vn is proportional to the height of the thin film is studied. The width of the base always increases with time even for suction while the height decreases with time for sufficiently weak blowing. The streamlines of the fluid flow inside the thin film are plotted by first solving a cubic equation. For sufficiently weak blowing there is a dividing streamline, emanating from the stagnation point on the centre line which separates the fluid flow into two regions, a lower region consisting of rising fluid and dominated by fluid injection at the base and an upper region consisting of descending fluid and dominated by spreading due to gravity. For sufficiently strong blowing the lower region expands to completely fill the whole thin film.

Modelling of Thin CNTs Nanoliquid Film Flow Over a Bi-directional Stretching Surface

Unsteady flow of water and ethylene-glycol based carbon nanotubes (CNTs) nanoliquid film is examined on a bi-directional stretching surface under influence of transverse magnetic field and thermal radiation. Single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) are considered within the base liquid for investigation. Guiding full Navier–Stokes and energy equations were simplified using the thin film approximations and solved using the method of the asymptotic expansion. The result shows that nanoliquid thinning rate diminishes with rising values of CNTs volume fraction, Hartmann number and Biot number. The result also indicates that the thinning rate is more for MWCNTs with reference to the SWCNTs. It is seen that film thinning rate enhances for water-MWCNTs nanoliquid but reverse scenario is found for ethylene-glycol MWCNTs nanoliquid. The effect of various physical parameters on temperature profile has been discussed.