Thin Film Flow Research Articles

Exploration of drag on the thin film of micropolar fluid flow within a permeable medium

Advances in thin film acquired many industrial applications because of their use in several products like electronic devices, magnetic recording media, LED, optical coating, etc. Additionally, thin film has an extensive role in the study of multiferroic materials and superlattices in quantum phenomena. Therefore, it is an urge to predict the importance of drag employing Darcy-Forchheimer on the thin film flow of micropolar liquid through an expanding plate embedding with a permeable medium. Moreover, the current model enriches by incorporating the impact of Soret because of the cross-diffusion process and the radiative heat. By using the appropriate transformed variables, the designed problem is distorted, and further, these sets of equations are handled numerically employing Runge-Kutta shooting technique. The computation is carried out by deploying in-house built-in function bvp4c in MATLAB. The significant operational behavior of the manipulated quantities is accessible graphically and deliberated in the discussion section. The important findings are elaborated as; the angular velocity distribution shows a greater deceleration for the increasing microrotation and the inertial drag effect. Further, the thermo-diffusion due to Soret also attenuates the concentration profile and the solutal thickness became thinner for the higher heavier species.

The Role of the Working Fluid and Non-Ideal Thermodynamic Effects on Performance of Gas Lubricated Bearings

Abstract Small-scale turbomachinery operating at high rotational speed is a key technology for increasing the power density of energy and propulsion systems. A notable example is the turbine of an organic Rankine cycle turbogenerator for thermal recuperation from prime engines and industrial processes. Such systems typically operate with organic compounds characterized by complex molecular structures, to allow the design of efficient fluid machinery and flexibility in matching the heat source and sink temperature profiles. Gas bearings are considered advantageous compared to traditional oil-lubricated rolling element bearings for supporting the turbine rotor, enabling greater machine compactness and reduced complexity, and to avoid contamination of the working fluid. In certain operating conditions, however, the lubricant of the bearing is in thermodynamic states near the saturated vapor line or in the vicinity of the fluid critical point whereby non-ideal effects are relevant and may affect bearing performance. This work investigates the physics of thin film flows in gas bearings operating with fluids made by complex molecules. The influence of non-ideal thermodynamic effects on gas bearing performance is discussed by analysis of the fluid bulk modulus. Reduced values of the non-dimensional bulk modulus near the critical point or saturated vapor line decrease bearing performance. The main parameter characterizing the influence of molecular complexity on bearing performance is shown to be the acentric factor. For complex fluids with large acentric factors, the impact of non-ideal thermodynamic effects on non-dimensional bearing load capacity and rotor-dynamic characteristics is less pronounced.

Modelling Mucus Clearance in Sinuses: Thin-Film Flow Inside a Fluid-Producing Cavity Lined with an Active Surface

The paranasal sinuses are a group of hollow spaces within the human skull, surrounding the nose. They are lined with an epithelium that contains mucus-producing cells and tiny hairlike active appendages called cilia. The cilia beat constantly to sweep mucus out of the sinus into the nasal cavity, thus maintaining a clean mucus layer within the sinuses. This process, called mucociliary clearance, is essential for a healthy nasal environment and disruption in mucus clearance leads to diseases such as chronic rhinosinusitis, specifically in the maxillary sinuses, which are the largest of the paranasal sinuses. We present here a continuum mathematical model of mucociliary clearance inside the human maxillary sinus. Using a combination of analysis and computations, we study the flow of a thin fluid film inside a fluid-producing cavity lined with an active surface: fluid is continuously produced by a wall-normal flux in the cavity and then is swept out, against gravity, due to an effective tangential flow induced by the cilia. We show that a steady layer of mucus develops over the cavity surface only when the rate of ciliary clearance exceeds a threshold, which itself depends on the rate of mucus production. We then use a scaling analysis, which highlights the competition between gravitational retention and cilia-driven drainage of mucus, to rationalise our computational results. We discuss the biological relevance of our findings, noting that measurements of mucus production and clearance rates in healthy sinuses fall within our predicted regime of steady-state mucus layer development.

Stability of a viscous liquid film flowing down an inclined plane with respect to three-dimensional disturbances

An analysis is presented for the stability of a viscous liquid film flowing down an inclined plane with respect to three-dimensional disturbances under the action of gravity and surface tension. Using momentum-integral method, the nonlinear free surface evolution equation is derived by introducing the self-similar semiparabolic velocity profiles along the flow (x- and y-axis) directions. A normal mode technique and the method of multiple scales are used to obtain the theoretical (linear and nonlinear stability) results of this flow problem, which conceive the physical parameters: Reynolds number Re, Weber number We, angle of inclination of the plane θ and the angle of propagation of the interfacial disturbances ϕ. The temporal growth rate ωi+ and second Landau constant J2, based on which various (explosive, supercritical, unconditional, subcritical) stability zones of this flow problem are categorized, contain the shape factors B and β owing to the non-zero steady basic flow along the y-axis direction. A novel result which emerges from the linear stability analysis is that for any given value of Re, We and θ, any stability that arises in two-dimensional disturbances (ϕ = 0) must also be present in three-dimensional disturbances. For ϕ = 0, there exists a second explosive unstable zone (instead of unconditional stable zone) after a certain value of Re (or θ) due to the involvement of B and β in the expression of J2. This explosive unstable zone vanishes after a certain value of ϕ depending upon the values of Re, We and θ, which confirms the stabilizing influence of ϕ on the thin film flow dynamics irrespective of the values of Re, We and θ.

Evaluation of heat transfer for unsteady thin film flow of mono and hybrid nanomaterials with five different shape features

Recent advancement in nanotechnology brings the idea of hybrid nanomaterials which offer distinguish applications in thermal reservoirs, cooling systems, energy applications, chemical engineering, vehicle engines etc. The understating of shape features for hybrid nanomaterials is quite essential as such consequences highly influenced various thermal properties like viscosity, thermal conductivity, optical properties, stability etc. The objective of current work is to examine heat transfer analysis due to thin film unsteady flow of hybrid nanofluid. The properties of hybrid nanofluid are justified for entertaining the copper (Cu), aluminium oxide (Al2O3) nanoparticles with water (H2O) base fluid. Additionally, applications of viscous dissipation, heat source and nonlinear radiated effects are attributed to current flow problem. The thermal properties of nanoparticles are examined in presence of five shape features consisting of blades, platelets, cylinders, bricks and spheres. Numerical simulations of problem are performed via Runge-Kutta-Fehlberg method. Comparative heat transfer is performed for mono nanofluid (Cu/H2O) and hybrid nanofluid (Cu−Al2O3)//H2O. It has been observed that heat transfer enhancement is more stable for cylindrical particles as compared to spherical nanoparticles. The skin friction enhances due to Hartmann number for both mono nanofluid (MNF) and hybrid nanofluid (HNF). Current results claim applications in coating thin films, lubrication systems, improving the thermal efficiency in thermal and industrial systems, heat exchangers, cooling systems etc.

Existence and Stability of Nonmonotone Hydraulic Shocks for the Saint Venant Equations of Inclined Thin-Film Flow

Extending the work of Yang–Zumbrun for the hydrodynamically stable case of Froude number F<2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F<2$$\\end{document}, we categorize completely the existence and convective stability of hydraulic shock profiles of the Saint Venant equations of inclined thin film flow. Moreover, we confirm by numerical experiment that asymptotic dynamics for general Riemann data is given in the hydrodynamic instability regime by either stable hydraulic shock waves, or a pattern consisting of an invading roll wave front separated by a finite terminating Lax shock from a constant state at plus infinity. Notably, profiles, and existence and stability diagrams, are all rigorously obtained by mathematical analysis and explicit calculation.

Long-time emergent dynamics of liquid films undergoing thermocapillary instability.

The study of viscous thin film flow has led to the development of highly nonlinear partial differential equationsthat model how the evolution of the film height is affected by different forces. We investigate a model of interaction between surface tension and the thermocapillary Marangoni effect, with a particular focus on the long-time limit. In this limit, the model predicts the creation of an infinite cascade of successively smaller satellite droplets near points where the film thickness vanishes. Motivated by recent progress on the analysis of discrete self-similarity in thin film equations, we compute solutions in a space- and time-rescaled coordinate system. Using this rescaled system we observe the dynamics much further in time than has previously been achieved. The observed behavior is close to, but distinct from, previous observations of discretely self-similar thin film flows, in that the rescaled system does not settle down to a periodic solution, but instead has aspects that continue to evolve monotonically in scaled time. This discovery suggests there are as-yet unexplored ways in which discrete self-similarity may be exhibited.

Thermal analysis of MHD unsteady Darcy‐Forchheimer thin film flow in a porous system

AbstractThis study has investigated a Darcy‐Forchheimer thin film flow over an extended horizontal surface with thermal radiation and chemical reaction effects. The governing time‐dependent equations have been non‐dimensionalized using similarity transformations and solved numerically using the fourth‐order Runge‐Kutta method and the shooting technique. The influence of magnetohydrodynamics, non‐uniform heat sourcing, viscous heat radiation, and chemical reactions on temperature, velocity, skin friction, Nusselt, and Sherwood numbers has been examined. Results have shown that porous media, magnetic field, and transient effects decrease the velocity profile, while thermal radiation and variable thermal properties enhance temperature distributions. Findings have indicated that the magnetic field and porosity enhance the skin friction coefficient whereas the heat transfer rate increases with Eckert number and Prandtl number. Rising the chemical reaction parameter from 0.2 to 0.5 rises the mass transfer rate by approximately 9.85%. The thermal analysis of MHD Darcy‐Forchheimer thin film flow in a porous system has been crucial for understanding heat transfer and fluid dynamics in complex environments. It helped in optimizing various engineering processes, such as cooling systems, filtration, and energy conversion, by providing insights into temperature distribution, convective heat transfer, and fluid behavior. This analysis has aided in designing efficient and reliable systems with improved performance and reduced energy consumption.

Thin-film flow due to an asymmetric distribution of surface tension and applications to surfactant deposition

Thin-film equations are utilised in many different areas of fluid dynamics when there exists a direction in which the aspect ratio can be considered small. We consider thin free films with Marangoni effects in the extensional flow regime, where velocity gradients occur predominantly along the film. In practice, because of the local deposition of surfactants or input of energy, asymmetric distributions of surfactants or surface tension more generally, are possible. Such examples include the surface of bubbles and the rupture of thin films. In this study, we consider the asymmetric thin-film equations for extensional flow with Marangoni effects. Concentrating on the case of small Reynolds number $ Re $ , we study the deposition of insoluble surfactants on one side of a liquid sheet otherwise at rest and the resulting thinning and rupture of the sheet. The analogous problem with a uniformly thinning liquid sheet is also considered. In addition, the centreline deformation is discussed. In particular, we show analytically that if the surface tension isotherm $\sigma = \sigma (\varGamma )$ is nonlinear (surface tension $\sigma$ varies with surfactant concentration $\varGamma$ ), then accounting for top–bottom asymmetry leads to slower (faster) thinning and pinching if $\sigma = \sigma (\varGamma )$ is convex (concave). The analytical progress reported in this paper allows us to discuss the production of satellite drops from rupture via Marangoni effects, which, if relevant to surface bubbles, would be an aerosol production mechanism that is distinct from jet drops and film drops.

Hydrodynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

To make progress towards the development of a theory on the motion of inclusions in thin structured films and membranes, we here consider as an initial step a circular disk in a two-dimensional, uniaxially anisotropic fluid layer. We assume overdamped dynamics, incompressibility of the fluid, and global alignment of the axis of anisotropy. Motion within this layer is affected by additional linear friction with the environment, for instance, a supporting substrate. We investigate the induced flows in the fluid when the disk is translated parallel or perpendicular to the direction of anisotropy. Moreover, expressions for corresponding mobilities and resistance coefficients of the disk are derived. Our results are obtained within the framework of a perturbative expansion in the parameters that quantify the anisotropy of the fluid. Good agreement is found for moderate anisotropy when compared to associated results from finite-element simulations. At pronounced anisotropy, the induced flow fields are still predicted qualitatively correctly by the perturbative theory, although quantitative deviations arise. We hope to stimulate with our investigations corresponding experimental analyses, for example, concerning fluid flows in anisotropic thin films on uniaxially rubbed supporting substrates.

Shear-imposed falling film on a vertical moving plate with disrupted time-reversal

We propose a mathematical model to study the stability and dynamics of a shear-imposed thin film flow on a vertical moving plate, incorporating the influence of odd viscosity. This odd viscosity effect is vital in conventional fluids when there is a disruption in time-reversal symmetry. Our motivation to study the dynamics with odd viscosity arises from recent studies (Kirkinis & Andreev, vol. 878, 2019, pp. 169–189; Chattopadhyay & Ji, vol. 455, 2023, pp. 133883) where the odd viscosity effectively reduces flow instabilities under different scenarios. Utilizing a long wave perturbation method, we derive a nonlinear evolution equation at the liquid–air interface, which is influenced by the motion of the vertical plate, imposed shear, odd viscosity, and inertia. We first perform a linear stability analysis of the model to get firsthand information on various flow parameters. Three distinct conditions for the vertical plate, quiescent, upward-moving, and downward-moving, are considered, accounting the imposed shear and odd viscosity. Additionally, employing the method of multiple scales, we conduct a weakly nonlinear stability analysis for the traveling wave solution of the evolution equation and explore its bifurcation analysis. The bifurcation analysis reveals the existence of subcritical unstable and supercritical stable zones for crucial flow parameters: odd viscosity, imposed shear, and motion of the vertical plate. Both linear and weakly nonlinear stability analyses demonstrate that the destabilizing effect induced by the upward motion of the vertical plate can be alleviated by applying uphill shear, while the destabilizing effect of downhill shear can be mitigated when the vertical plate is in a downward motion. Moreover, we define an eigenvalue problem that mirrors the Orr–Sommerfeld (OS) model for analyzing normal modes and identifying the critical Reynolds number. We investigate the dynamics of surface waves through numerical solutions of the OS eigenvalue problem using the Chebyshev spectral collocation method. We observe the consistent enhancement of stabilization in the presence of odd viscosity. In the low to moderate Reynolds number range, vertical plate motion and odd viscosity show similar behavior in OS analysis, while imposed shear exhibits distinct changes. The Benney-type model does not agree with the OS problem when the Reynolds number is moderate with or without the three key parameters: vertical plate motion, imposed shear, and odd viscosity. However, when the Reynolds number is low with or without the three key parameters: vertical plate motion, imposed shear, and odd viscosity, the Benney-type model agrees with the OS. Further, numerical simulations of the evolution equation corroborate the results obtained from linear stability, weakly nonlinear stability, and OS analyses. Finally, the Hopf bifurcation analysis of the fixed point reveals that the wave speed is influenced by both the motion of the plate and the imposed shear while it remains independent of odd viscosity.

Vitamin D3 formation in milk by UV treatment – Novel insights into a rediscovered process

Vitamin D3 is essential for several functions in the human body and the demand is usually covered by natural reactions in skin with UV radiation delivered by the sun. But living beyond a latitude of 35° can lead to a lack of sufficient exposition to the deciding wavelength. Here, many countries fortify their milk prophylactically with artificial vitamin D3. However, the precursor molecule of vitamin D3 (7-deydrocholesterol) is already naturally located in the milk fat globule membrane. Thus, this study deals with the transformation of the naturally occurring 7-dehydrocholesterol into vitamin D3 through UV treatment of the milk - a mechanism that was observed a century ago only indirectly. Different parameters such as temperature (10 - 50°C), fluid flow regimen (turbulent vs. laminar thin film, i.e., 0.6 mm) and wavelength (254, 280 and 313 nm) were investigated in this study for their efficiencies. The UV dose of each experiment was measured with chemical actinometry delivering the actually applied dose reaching the milk. Thus, the connection between applied UV dose and generated vitamin D3 content in the milk measured quantitively with LC-MS/MS was evaluated here that both were not possible a hundred years ago. The experimental results revealed that temperature generally promotes the vitamin D3 formation at 254 nm. Further, a turbulent flow is not as efficiently treated as a laminar thin film flow that is as narrow as 0.6 mm. As expected from absorbance spectra of the precursor molecule 7-dehydrocholesterol, 280 nm turned out to be the most efficient wavelength, followed by intermediate success through irradiation with 254 nm and almost no effect by 313 nm. Generally, it was shown that vitamin D3 concentration of milk was easily increased by UV treatment with today's technologies and that adjustment of certain physical parameters have a significant effect on the efficiency.

Analytical investigation of convective phenomena with nonlinearity characteristics in nanostratified liquid film above an inclined extended sheet

Abstract This work focuses on the time-variant convective thin-film nanoliquid fluid flow and heat transfer over a stretching, inclined surface under the effect of magnetism for different energy technologies for sustainability. It is crucial to understand how solid materials can be treated with thin films while focusing on the actual ability to improve the body surface features for infiltration, shock resistance, rigidness, brightness, dispersal, absorption, or electrical efficiency. All of these improvements are invaluable, especially in the field of nanotechnology. As with any mass and thermal transport phenomena, the study breaks down important factors such as thermophoresis and Brownian movement, in an attempt to improve the energetic balance and lessen fuel consumption. Utilizing the mathematical model of the temporal evolution on the liquid film flow characteristics over an inclined surface, we obtain a system of nonlinear partial differential equations and convert it to a system of coupled ordinary differential equations appropriately. Finally, the results of the model problem computational analysis are produced using the Laplace Adomian decomposition method (LADM) and are shown both quantitatively and visually. During the flow analysis, the impact of specific flow parameters such as the magnetic, Brownian, and thermophoresis parameters are examined and found to be highly significant. Furthermore, it is found that the effects of ( M M ) and (Nt) factors on ( F F ), ( Φ \Phi ), and ( ϕ \phi ) lead to decreased conduction. Conversely, the thermal gradient within the liquid films rises in proportion to the (Nb) factor. This research is distinguished from similar attempts made in the past in terms of thin-film nanoliquid flow from inclined planes and application of LADM approach toward modeling. The findings have provided tangible use in coming up with new methods of cooling electronics gadgets, energy harvesting for solar energy, and eco-friendly industrial processes.

Unsteady thin film flow of a hybrid nanoliquid with magnetic effects

Unsteady thin film flow of a hybrid nanoliquid with magnetic effects

Gravity-driven thin film flow of a third-grade fluid on a movable inclined plane with slip boundary condition

The prime aim and essence of this study are to present a closed-form solution of the unidirectional velocity field for thin film flow generated by a third-grade liquid moving over a fixed or movable inclined plane in the presence of partial slip boundary condition. Consideration of partial slip makes this problem different from other published research works. Here lies the novelty of this study. The nondimensional, unidirectional velocity profiles rely on the material parameter of third-grade fluid, slip parameter and initial velocity of the movable plane. Study discloses that the fluid’s velocity decelerates with raising the material property of grade-3 fluid and it accelerates with the slip parameter and initial velocity of the inclined plane. The outcomes of this study are deliberated physically at length.

A numerical inquiry of the MHD radiative thin film nanofluid flow and heat transfer augmentation for Ni and Ta nanoparticles of different shapes dispersed in C 12 H 26–C 15 H 32 over an unsteady, curved stretching surface

Thin films are a versatile technology used in various industries, including light-emitting diodes, magnetic recording media, electronic device manufacturing, and optical coating. They are crucial for studying quantum phenomena, superlattices, and multiferroic materials. Their small size allows for better thermal transport studies due to the combination of thin film flow and nanoparticles. Therefore, this study aims to investigate thin film flow and heat transfer with the effects of thermal radiations, magnetic field, and velocity slip in association with tantalum ( Ta ) and nickel ( Ni ) nanoparticles that emerged in kerosene oil ( C 12 H 26 − C 15 H 32 ) toward a curved stretching surface. A review of the pertinent literature indicates that no research has previously been done on the present problem of an unsteady thin film flow across a curved stretching surface. The problem under consideration is modeled by choosing the curvilinear coordinate system. The controlling nonlinear system of partial differential equations is transformed into the system of ordinary differential equations by using an appropriate similarity transformation and then solved numerically using the BVP 4 C technique in MATLAB . The impact of significant physical parameters on velocity, temperature, skin friction, and Nusselt numbers are depicted through graphs and radar charts. The investigation highlights the significant influence of magnetohydrodynamics ( MHD ) , thermal radiation, volumetric fraction, and velocity slip on the enhancement of nanofluid temperature. It is also noted that cylindrical-shaped Ta nanoparticles exhibited the maximum velocity, while blade-shaped Ni nanoparticles showed the lowest. Moreover, the maximum and minimum temperatures were observed for blade-shaped Ni nanoparticles and cylindrical Ta nanoparticles, respectively. Additionally, the maximum and minimum values of skin friction are found for cylindrical Ni nanoparticles and blade-shaped Ta nanoparticles, respectively. Similarly, the maximum and minimum Nusselt numbers are recorded for cylindrical Ta nanoparticles and blade-shaped Ni nanoparticles, respectively.

Unsteady MHD‐radiative thin film flow with heat transfer over a stretching surface in porous media

AbstractThis study conducts a computational analysis to explore how magnetic fields, radiation, heat, and mass transfer collectively influence a horizontal stretching sheet within a porous medium. The research focuses on elucidating the dynamics of thin film flow through the formulation of time‐dependent equations and subsequent transformation of fluid flow equations into ordinary differential equations via similarity transformation. The numerical solution is attained employing the Runge–Kutta fourth‐order method coupled with a shooting technique. MATLAB software is utilized to generate graphs and numerical values, offering a detailed representation of engineering‐relevant physical quantities in tabular form. The investigation revealed notable trends associated with varying parameters. Increasing unsteadiness parameters lead to a reduction in velocity, temperature, and concentration fields, while the temperature distribution demonstrates a positive correlation with radiation parameters. Moreover, elevated Prandtl numbers and unsteadiness parameters correspond to augmented heat and mass flux, respectively. Of particular significance is the observed heightened heat transfer rate during the transition from a Prandtl number of 1 (representing air) to 2 (representing oil), alongside an increased mass transfer rate with the escalation in Schmidt number from 0.62 (representing hydrogen) to 0.78 (representing ammonia). A comparative analysis of the numerical findings with existing literature demonstrates excellent agreement, affirming the validity and relevance of the present study. These insights offer valuable implications for understanding and optimizing heat and mass transfer processes in porous media, with potential applications in various engineering and scientific domains.

Numerical investigation of electrically conducting thin film flow and heat transfer improvement for various shaped $$Sn-PG$$ and $$W-PG$$ nanofluids over an unsteady curved stretching surface

Numerical investigation of electrically conducting thin film flow and heat transfer improvement for various shaped $$Sn-PG$$ and $$W-PG$$ nanofluids over an unsteady curved stretching surface

Liquid film flow rate from measurements of disturbance wave characteristics for applications in thin film flow

Liquid film flow rate from measurements of disturbance wave characteristics for applications in thin film flow

Thin-film flow between a rotating sphere and a nearly vertical moving plate

When a sphere rotates near a rigid boundary coated with a thin layer of viscous liquid, ‘tracks’ are generated both behind and over the sphere. This paper describes a theory for the simplest one-track configuration which can occur under particular experimental conditions. The theoretical predictions are in good agreement with experimental observations.