Film Flow Of Fluid Research Articles

A general model for spin coating on a non-axisymmetric curved substrate

We derive a generalised asymptotic model for the flow of a thin fluid film over an arbitrarily parameterised non-axisymmetric curved substrate surface based on the lubrication approximation. In addition to surface tension, gravity and centrifugal force, our model incorporates the effects of the Coriolis force and disjoining pressure, together with a non-uniform initial condition, which have not been widely considered in existing literature. We use this model to investigate the impact of the Coriolis force and fingering instability on the spreading of a non-axisymmetric spin-coated film at a range of substrate angular velocities, first on a flat substrate, and then on parabolic cylinder- and saddle-shaped curved substrates. We show that, on flat substrates, the Coriolis force has a negligible impact at low angular velocities, and at high angular velocities results in a small deflection of fingers formed at the contact line against the direction of substrate rotation. On curved substrates, we demonstrate that, as the angular velocity is increased, spin-coated films transition from being dominated by gravitational drainage with no fingering to spreading and fingering in the direction with the greatest component of centrifugal force tangent to the substrate surface. For both curved substrates and all angular velocities considered, we show that the film thickness and total wetted substrate area remain similar over time to those on a flat substrate, with the key difference being the shape of the spreading droplet.

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.

Revealing the dynamics of stagnant rings of third-grade fluid film with heat transfer in the presence of surface tension

In many engineering applications, including coating and lubrication operations, analyzing the temperature behavior of thin film flows on a vertically upward-moving tube is crucial to improving predictive models. This paper examines a steady third-grade fluid film flow with a surface tension gradient on a vertical tube. The mechanisms responsible for the fluid motion are upward tube motion, gravity, and surface tension gradient. This analysis focuses on heat transfer and stagnant ring dynamics. The formulated highly nonlinear ordinary differential equations are solved using the Adomian decomposition method. The conditions for stagnant rings and uniform film thickness are attained and discussed. The inverse capillary number C, Stokes number St, Deborah number De, and Brinkman number Br emerged as flow control parameters. The temperature of the fluid film rises with an increase in the C, St, De, and Br, whereas it decreases with an increase in thermal diffusion rate. The radius of stagnant rings tends to shrink by the increase in C, St, and De. When the value of De is high, third-grade fluid behaves like solids; only free drainage happens with smaller radius stagnant rings and high temperatures. A comparison between Newtonian and third-grade fluids regarding surface tension, velocity, temperature, stationary rings, and fluid film thickness is also provided.

Stagnant rings and uniform film analysis of Phan-Thien Tanner fluid film flow on a vertically upward moving tube

Analyzing Phan-Thien Tanner fluid film behavior on a vertically upward moving tube can help predictive models in engineering, notably in coating and lubrication operations. This paper provides a theoretical analysis of the dynamics of stagnant rings and uniform Phan-Thien Tanner fluid film adhered to a vertically upward moving tube. Formulated ordinary differential equations are solved to get exact analytic expressions for velocity, flow rate, average velocity, shear stress components, and stagnant rings. Highly nonlinear algebraic equations are solved using Newton's method in MAPLE to find the linear and exponential Phan-Thien Tanner film thicknesses. The uniform film thickness widens with increasing constant tube velocity, while it decreases with increasing Deborah number, Stokes number, and elongation parameter. The analysis delineates that stagnant rings shrink around the tube as the Stokes number, Deborah number, and elongation parameter increase. The minimal Stokes condition for the existence of a realistic stagnant ring is also determined. It has been established that whenever the Stokes number is less than the minimal Stokes condition, stagnant rings do not form. A comparison between the exponential Phan-Thien Tanner, linear Phan-Thien Tanner, upper convected Maxwell, and Newtonian fluids is also provided for stagnant rings and fluid film thickness. Following the application of an efficient approximation on tube geometry, plate geometry is approximated, and the outcomes are consistent with existing literature. The results of this research are significant for a wide range of biofluid applications, including agrochemical uses, paint and surface coating flow behavior, thin films on the cornea and lungs, and chemical and nuclear reactor design.

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.

Flow analysis of temperature-dependent variable viscosity Phan Thien Tanner fluid thin film over a horizontally moving heated plate

Comprehending the temperature-dependent variable viscosity Phan Thien Tanner fluid film flow over a horizontal heated plate with surface tension is essential to enhancing coating and lubrication process prediction models. This paper accords with the flow analysis of a temperature-dependent variable viscosity Phan Thien Tanner fluid film over a horizontal heated plate. The flow over a heated plate occurs as a result of the plate’s motion and the surface tension gradient. The Adomian decomposition method is utilized to solve a system of linear and nonlinear ordinary differential equations, resulting in series-form solutions. The series-form expressions for flow variables such as velocity, temperature, volume flow rate, and surface tension are derived. Moreover, the positions of stationary points are computed using MATHEMATICA. The analysis delineated that when the inverse capillary number, variable viscosity parameter, Deborah number, elongation parameter, and Brinkman number increase, the stationary points move closer to the heated plate. The temperature also rises with an increase in these parameters. The temperature rises with increasing viscous dissipation while it lowers with increasing thermal diffusion. When the Deborah number is high, the Phan Thien Tanner fluid behaves like a solid and the flow is only driven by the motion of the plate. A comparison between Newtonian and Phan Thien Tanner fluids is made for velocity, temperature, and stationary points as a special case.

Impact of variable viscosity, thermal conductivity, and Soret–Dufour effects on MHD radiative heat transfer in thin reactive liquid films past an unsteady permeable expandable sheet

AbstractSignificance of magnetohydrodynamic effect on a viscous (temperature‐dependent) and chemically reactive thin fluid film flow past an unsteady permeable stretchable plate with Soret–Dufour effects, nonlinear thermal radiative, and suction under the action of a convective type of boundary condition is analyzed. The problem consists of nonlinear governing basic equations that are highly nonlinear due to the existence of nonlinear thermal radiative terms in the energy equation. Analytical solutions are challenging to achieve for such types of problems, so a numerical scheme adopts the numerical solution. Computed solutions indicate that decreasing the Dufour number (and simultaneously increasing the Soret number) enhances heat flux, whereas the reverse trend is estimated for the concentration gradient field. The influence of magnetization indicates a decrement in the thin liquid film velocity distribution, whereas an increment is observed in temperature and solutal gradient profiles. Further, an enhancement in thermoradiative values focuses on decreasing the heat flux profiles, whereas a decreasing trend is determined in the solutal gradient by incrementing the Schmidt number. The variations of the velocity field, temperature, and concentration gradients are shown for the unsteady parameter lying in the range [0.8, 1.4]. Similarly, the range of different parameters utilized are [0.0, 1.0], [0.0, 2.0], [0.8, 1.5], [0.5, 2.0], [0.0, 1.0], [0.2, 3.0], [1.0, 2.0], [0.0, 3.0], [0.4, 1.0], and [0.4, 1.0]. The novelty of the present study lies in its analysis of complex fluid dynamics phenomena and their implications for various industrial processes and engineering applications, including coating processes, heat exchangers, microfluidics, and biomedical engineering. The insights gained from the study can contribute to developing more efficient and innovative research in these areas. Further, we have compared the present results with those available in the literature under some special cases and found them to be in excellent agreement.

An Algorithm for Approximating Third-Order Ordinary Differential Equations with Applications to Thin Film Flow and Nonlinear Genesio Problems

Third-order problems have been found to model real-life phenomena such as thick film fluid flow, boundary layer problems, and nonlinear Genesio problems, to name a few. This research focuses on the development of an algorithm using a basis function that combines an exponential function with a power series. This algorithm, called the Exponential Function Induced Algorithm (EFIA), was formulated using the collocation and interpolation techniques. The theoretical analysis of the algorithm was also carried out in this research. The outcome of the analysis showed that the algorithm is consistent, convergent, and zero-stable. The EFIA was applied to solving some real-life third-order problems like thin film flow and nonlinear Genesio problems. The numerical and graphical results obtained showed that the EFIA is accurate, has high precision, and is easy to implement. Algorithm, Exponentially-fitted function, Hybrid block method, Nonlinear Genesio equations, Thin film flow problem, Third-order

Influence of the Reynolds viscosity model and induced magnetic field on a thin Casson fluid film flow between two rotating disks with cross-diffusion effects

In models of fluid dynamics, the magnetic field is essential for preserving the stability of flow streams and found applications in magnetic resonance imaging, magnetic levitation, and geophysical exploration. Recognizing the significance of this magnetic influence, we aim to investigate the behavior of flow within a three-dimensional squeezed film of Casson fluid situated between two rotating disks, under the influence of an induced magnetic field and the Reynolds viscosity model. The study also meticulously examines the heat and mass transfers, taking into account the effects of thermo-diffusion and diffusion-thermo. The resulting torque on both the upper and lower surfaces is analyzed and presented in a tabulated format. The normalized system of equations is transformed into a set of first-order differential equations, which are then solved using the bvp4c numerical solver in MATLAB. The impacts of various parameters are graphically illustrated in two different scenarios ( ϒ = 0.0 , 0.5 ) , i.e., constant and variable viscosity. It is observed that when the variable viscosity parameter is set to zero, the azimuthal velocity profile experiences a more pronounced increase as the rotational parameter rises. Conversely, the azimuthal magnetic profile exhibits a more significant decrease when considering the influence of the variable viscosity parameter. Finally, the results are compared with previous studies in the literature for a limiting case, and error is reduced between 0.000003% and 0.000002%.

Stagnant points and uniform film analysis of Eyring fluid film flow on a vertically upward moving slippery flat plate

In this paper, we analyze how Eyring fluid film behavior on a vertically upward moving slippery flat plate can help predictive models in engineering, notably in coating and lubrication operations. This paper deals with the stagnant points and uniform film analysis of Eyring fluid film flow on a vertically upward moving slippery flat plate. The formulated ordinary differential equation is solved for exact analytic solution. Exact analytic expressions for velocity, flow rate, average velocity, shear stress components, and stagnant points are derived. A highly nonlinear algebraic equation is derived for film thickness. Equation is solved by Newton’s method using Maple code. The thickness of film widens with increasing relaxation time, constant plate velocity, and fluid density, while it decreases with increasing fluid viscosity and constant slip parameter. The analysis delineates that the positions of stagnant points tend to relocate closer the slippery plate as the Stokes number, Deborah number, and constant slip parameter increase. A high Deborah number enhances drainage, causing stagnant points to relocate closer to the slippery plate and the development of a stable elastic layer adjacent to the plate. For stagnant points and fluid film thickness, a comparison between the Eyring fluid and existing studies (EPTT, LPTT, UCM, and Newtonian fluid) is also provided. The validity of this paper with the existing studies is also presented by reducing Eyring fluid model to Newtonian model. The results of this research are significant for a wide range of biofluid applications, including agrochemical uses, paint and surface coating flow behavior, thin films on the cornea and lungs, and chemical and nuclear reactor design.

Film Flow of Nano-Micropolar Fluid with Dissipation Effect

Film Flow of Nano-Micropolar Fluid with Dissipation Effect

Thin film Maxwell-Power Law Fluid Flow on an extending surface

In this research article, the examination is done on film flow of two-dimensional fluid along with transfer of heat in a magnetic field on an unsteady extending sheet. To gain the appropriate outputs for the flow efficiency and rate of transfer of heat, the Power law fluids are mixed with the viscoelastic fluids which reduce the viscosity of the fluids. The heat transfer rate is further improved with the inclusion of nanoparticles. The flow and heat transmission characteristics of a Maxwell, Power-law-model-fluid along with Joule absorption and changeable liquid sheet thickness are examined. The combined model of the two non-Newtonian fluids also incorporated the nanofluid's influence. To create the coupled comparable ordinary differential equations (ODEs) that the homotopy analytical method (HAM) along with appropriate similarity transformations are used. Impacts of variations of different significant factors like and number of fluid flow of fluid film with the transfer of heat are perceived. The influence of the unsteadiness factor on a thin film is discovered analytically for various estimations. Despite this, the implanted factors utilized for understanding the physical demonstration, like magnetic factor , inertial parameter , Eckert number , penetrability factor , Prandtl number Pr and Deborah number have been offered by graphs and deliberated in detail.

Analysis of heat transfer in [formula omitted]-immiscible layers of a horizontal Jeffrey fluid film flow

This paper deals with theoretical analysis of heat transfer in n-immiscible layers of a horizontal Jeffrey fluid film, driven by a heated plate and surface tension gradient. The formulation of the horizontal n-immiscible layers is based on mass, momentum, and energy conservation laws. The resulting systems of coupled linear ordinary differential equations are solved to obtain exact solutions for velocity, temperature, volume flow rate, shear stress, and rate of heat transfer. The effects of flow control parameters of interest, such as the inverse capillary number C, thermal conductivity of fluid χ, and Brinkmann number Br, on the velocity and temperature of the 5-immiscible layers, are investigated through graphical analysis. It is observed that increasing C leads to an increase in the velocity of all 5-immiscible layers. The temperature of all 5-immiscible layers also rises with increasing values of C, χ, and Br. The analysis of these 5-immiscible layers provides significant knowledge and understanding that may be applied to systems with a higher or lower number of immiscible layers utilizing the expressions derived for n-immiscible layers of a fluid film. Moreover, a comparison between immiscible layers of Newtonian fluid and Jeffrey fluid films is made in terms of velocity and temperature.

Heat transfer analysis of temperature dependent viscosity Johnson–Segalman fluid film flow on a vertical heated belt

Understanding the behaviour of temperature dependent viscosity thin film flows on a vertically upward moving heated belt is crucial for improving predictive models in various engineering applications, such as in coating and lubrication processes. This paper presents the heat transfer analysis of temperature-dependent viscosity fluid flow on a vertical upward moving heated belt. The formulated coupled system of nonlinear ordinary differential equations is solved using the Adomian decomposition method. The study investigates the impact of flow controlling parameters: Stokes number St, Brinkmann number Br, variable viscosity parameter β, Weissenberg number We, effective viscosity ϕ and slip parameter e is observed on velocity, temperature, and stationary points. It is perceived that the temperature of the fluid decreases with the increase of St, Br, β, and ϕ, while it increases with the increase of We and e. Positions of stationary points relocate towards the heated belt surface by the increment of St, Br, β, and ϕ. On the other hand, their positions relocate away from the heated belt surface by the increment of We and e. The analysis also highlights the influence of heat generated by viscous dissipation and heat transported by thermal diffusion on the velocity, temperature, and stationary points. Moreover, the flow variables discussed for the temperature dependent viscosity Johnson–Segalman fluid are also discussed for the temperature dependent viscosity Newtonian fluid, and an analogy between both is provided.

A new elastic instability in gravity-driven viscoelastic film flow

We examine the linear stability of the gravity-driven flow of a viscoelastic fluid film down an inclined plane. The viscoelastic fluid is modeled using the Oldroyd-B constitutive equation and, therefore, exhibits a constant shear viscosity and a positive first normal stress difference in viscometric shearing flows; the latter class of flows includes the aforesaid film-flow configuration. We show that the film-flow configuration is susceptible to two distinct purely elastic instabilities in the inertialess limit. The first instability owes its origin entirely to the existence of a free surface and has been examined earlier [Shaqfeh et al., “The stability of gravity driven viscoelastic film-flow at low to moderate Reynolds number,” J. Non-Newtonian Fluid Mech. 31, 87–113 (1989)]. The second one is the analog of the centermode instability recently discovered in plane Poiseuille flow [Khalid et al., “Continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow,” Phys. Rev. Lett. 127, 134502 (2021)] and owes its origin to the base-state shear; it is an example of a purely elastic instability of shearing flows with rectilinear streamlines. One may draw an analogy of the aforesaid pair of unstable elastic modes with the inertial free-surface and shear-driven instabilities known for the analogous flow configuration of a Newtonian fluid. While surface tension has the expected stabilizing effect on the Newtonian and elastic free-surface modes, its effect on the corresponding shear modes is, surprisingly, more complicated. For both the Newtonian shear mode and the elastic centermode, surface tension plays a dual role, with there being parameter regimes where it acts as a stabilizing and destabilizing influence. While the Newtonian shear mode remains unstable in the limit of vanishing surface tension, the elastic centermode becomes unstable only when the appropriate non-dimensional surface tension parameter exceeds a threshold. In the limit of surface tension being infinitely dominant, the free-surface boundary conditions for the film-flow configuration reduce to the centerline symmetry conditions satisfied by the elastic centermode in plane Poiseuille flow. As a result, the regime of instability of the film-flow centermode becomes identical to that of the original channel-flow centermode. At intermediate values of the surface tension parameter, however, there exist regimes where the film-flow centermode is unstable even when its channel-flow counterpart is stable. We end with a discussion of the added role of inertia on the aforementioned elastic instabilities.

Analytical Solutions for Unsteady Thin Film Flow with Internal Heating and Radiation

This study determines Lie point symmetries for differential equations that mathematically express a time-dependent thin film fluid flow with internal heating and thermal radiation to construct invariants. These invariants are used in the derivation of similarity transformations for reducing the flow equations into systems of equations that possess only one independent variable. The homotopy analysis method is employed to analytically solve the reduced system of equations. The new similarity transformations and the corresponding analytical solutions comprehensively consider flow dynamics and heat transfer under multiple physical conditions. These solutions are presented graphically to demonstrate the effects of variations in the radiative heat flux with internal heating on the flow dynamics and heat transfer properties. Moreover, the variations in fluid dynamics are described graphically using the obtained analytical homotopy solution under different values of the unsteadiness parameter and Prandtl number.

Revisiting Shikhmurzaev’s Approach to the Contact Line Problem

In this paper, we revisit a model for the contact line problem which has been proposed by Shikhmurzaev (Int. J. Multiph. Flow 19(4):589–610, 1993). In the first part, in addition to rederiving the model, we study in detail the assumptions required to obtain the isothermal limit of the model. We also derive in this paper several lubrication approximation models, based on Shikhmurzaev’s approach. The first two lubrication models describe thin film flow of incompressible fluids on solid substrates, based on different orders of magnitude of the slip length parameter. The third lubrication model describes a meniscus formation where a wedge-shaped solid immerses in a thin film of fluid.

Analysis of Fractional Thin Film Flow of Third Grade Fluid in Lifting and Drainage via Homotopy Perturbation Procedure

Analysis of thin film flows is an important topic in fluid dynamics due to the large number of industrial applications such as food processing, chip manufacturing, irrigation, oil refining process, painting finishing, etc. Analysis involves studying the effects of various parameters in absolute conditions. These parameters may be film thickness, volumetric flux, liquid velocity profile, viscosity, shear stress, gravity, density, and different boundary formations. We have expanded the formulations of non-Newtonian third grade fluid for lifting and draining in fractional space. Fractional calculus along with Homotopy Perturbation Method is used for the solution and analysis purposes. The suitability and consistency of the solutions is determined by detecting residuals in each case. Velocity profile, average velocity, and volume flow for lifting and drainage cases are calculated. To the best of authors knowledge, thin film flow of fractional third grade fluid is not attempted before in lifting and drainage. Investigation shows increase in value of fractional parameter that decreases the velocity profile in lifting while increases the velocity in drainage scenario. Also, the frictional parameter and the gravitational parameter have opposite, while material constant has direct relationship with the velocity profile in lifting case. All the parameters showed inverse effect on the velocity in drainage case.

Investigation of Film Fluid Flow in Perforated Cylindrical Channel of Regularly Structured Packing

Investigation of Film Fluid Flow in Perforated Cylindrical Channel of Regularly Structured Packing

Unsteady MHD Thin Film Flow of a Second-Grade Fluid past a Tilted Plate under the Impact of Thermal Radiation and Chemical Reaction

This paper explores the impact of chemical reaction and thermal radiation on time-dependent hydromagnetic thin-film flow of a second-grade fluid across an inclined flat plate embedded in a porous medium. The thermal radiation based on the Rosseland approximation is incorporated in the energy equation. Uniform applied magnetic field and first-order homogenous chemical reaction are included in the momentum and concentration equations, respectively. The novel mathematical flow model is constructed by using a set of partial differential equations (PDEs). The PDEs are then transformed into an equivalent set of ordinary differential equations (ODEs) and solved by applying the Laplace transform method. However, the time domain solutions are obtained by using the INVLAP subroutine of MATLAB. Physical parameters influencing thin-film velocity, temperature, and concentration are illustrated graphically, while those affecting skin friction, heat, and mass transfer rates are presented in a tabular form. It is found that thin-film velocity and temperature boost with increasing values of thermal radiation, but thin-film velocity decreases with increasing values of chemical reaction and magnetic field. The current investigation is to enhance heat and mass transfer in the design of mechanical systems involving the thin film flow of second-grade fluids over an inclined flat plate after applying thermal radiation and chemical reaction.