Dimensionless Film Research Articles

Effect of Interfacial Velocity Fluctuations on the Enhancement of the Mass-Transfer Process in Falling-Film Flow

To investigate the relationship between surface instability and mass-transport behavior, a laser Doppler anemometer (LDA) system was used to measure the liquid velocity components in a falling film, even very close to the liquid surface. The experimental results show that the presence of countercurrent gas flow tends to reduce and flatten the liquid velocity in the surface region and that the maximum liquid velocity might occur at some distance from the interface. The fluctuating liquid velocity field shows a maximum at a position of 0.8−1.0 in the dimensionless liquid film thickness, and a fluctuation frequency is obtained. Interfacial mass transport in a falling film is strongly dependent on interfacial small-scale convection. The experimental mass-transfer rates are larger than those predicted by penetration theory. The enhanced liquid Sherwood number, ShL, was calculated, and the predicted values were found to be in agreement with the experimental data.

Effect of wear on EHD film thickness in sliding contacts

AbstractA theoretical solution to the elastohydrodynamic (EHD) lubrication problem in sliding contacts, which takes into consideration the effect of the change in shape of the gap due to wear on the load‐carrying capacity, is presented. The model of such a contact is based on assumptions of Grubin and Ertel (von Mohrenstein). The resultant dimensionless Reynolds and film profile equations have been solved numerically for a number of cases with several values of thickness of the worn layer. Iteration of the EHD film thickness is performed by means of the secant method.Values of the calculated dimensionless film thickness are presented as a function of dimensionless wear. The conclusions concern the influence of the linear wear on the film thickness in heavily loaded sliding contacts. Copyright © 2006 John Wiley & Sons, Ltd.

Mixed convection turbulent film condensation on a sphere

The present paper reports a research on condensation heat transfer of an isothermal sphere with an external flow of vapor. The high tangential velocity of the vapor flow is determined from potential flow theory. The transition criterion of the onset turbulence has been given in the local film Reynolds number ( Re Γ ). An eddy diffusivity model along with an expression by [H. Kato, N.N. Shiwaki, M. Hirota, On the turbulent heat transfer by free convection from a vertical plate, Int. J. Heat Mass Transfer, 11(1968) 1117–1125] is used to model turbulence. And the local liquid–vapor interfacial shear which occurs for high velocity vapor flow across a sphere surface is defined by the Colburn analogy. The paper then presents analytical analysis for the local dimensionless film thickness and heat transfer characteristics for the film condensation. And a comparison with those generated by previous theoretical of laminar condensation is discussed. The comparison shows the heat transfer coefficient of turbulent film condensation is higher than laminar film condensation under the high vapor velocity.

Turbulent Film Condensation on an Isothermal Sphere

An investigation is presented of turbulent film condensation on a sphere. It begins by considering the case of vapor flow past an isothermal sphere. The high tangential velocity of the vapor flow at the boundary layer is determined from potential flow theory. The Colburn analogy is used to define the local liquid‐vapor interfacial shear that occurs for high-velocity vapor flow across the spherical surface. The results generated for the local dimensionless film thickness and heat transfer characteristics are discussed. Finally, the results developed in the current study are compared with those generated by previous theoretical and experimental results for laminar flow. It is found that the correlation between the two sets of data is quite satisfactory for low-vapor velocity. However, at the higher vapor velocities, the rate of increase of the coefficient with velocity is greater than that associated with laminar theory. It other words, for high-vapor velocity, the onset of turbulence in the condensate causes discrepancies between the two sets of data. Note that the results of the present study may be used to estimate the heat transfer coefficient more accurately than the result of previous laminar studies.

Impact dynamics of drops on thin films of viscoelastic wormlike micelle solutions

The impact dynamics of water drops on thin films of viscoelastic wormlike micelle solutions is experimentally studied using a high-speed digital video camera at frame rates up to 4000 frame/s. The composition and thickness of the thin film is modified to investigate the effect of fluid rheology on the evolution of crown growth, the formation of satellite droplets and the formation of the Worthington jet. The experiments are performed using a series of wormlike micelle solutions composed of a surfactant, cetyltrimethylammonium bromide (CTAB), and a salt, sodium salicylate (NaSal), in deionized water. The linear viscoelastic shear rheology of the wormlike micelle solutions is well described by a Maxwell model with a single relaxation time while the steady shear rheology is found to shear thin quite heavily. In transient homogeneous uniaxial extension, the wormlike micelle solutions demonstrate significant strain hardening. The size and velocity of the impacting drop is varied to study the relative importance of Weber, Ohnesorge, and Deborah numbers on the impact dynamics. The addition of elasticity to the thin film fluid is found to suppress the crown growth and the formation of satellite drops with the largest effects observed at small film thicknesses. A new form of the splashing threshold is postulated which accounts for the effects of viscoelasticity and collapses the satellite droplet data onto a single master curve dependent only on dimensionless film thickness and the underlying surface roughness. Additionally, a plateau is observed in the growth of the maximum height of the Worthington jet height with increasing impact velocity. It is postulated that the complex behavior of the Worthington jet growth is the result of a dissipative mechanism stemming from the scission of wormlike micelles.

Effect of Geometric Parameters on Simplex Atomizer Performance

A computational analysis of flow in simplex fuel atomizers using the arbitrary-Lagrangian‐Eulerian method is presented. It is well established that the geometry of an atomizer plays an important role in governing its performance. We have investigated the effect on atomizer performance of four geometric parameters, namely, inlet slot angle, spin chamber convergence angle, trumpet angle, and trumpet length. For a constant mass flow rate through the atomizer, the atomizer performance is monitored in terms of dimensionless film thickness, spray cone half-angle, and discharge coefficient. Results indicate that increase in inlet slot angle results in lower film thickness and discharge coefficient and higher spray cone angle. The spin chamber converge angle has an opposite effect on performance parameters, with film thickness and discharge coefficient increasing and the spray cone angle decreasing with increasing convergence angle. For a fixed trumpet length, the trumpet angle has very little influence on discharge coefficient. However, the film thickness decreases, and spray cone angle increases with increasing trumpet angle. For a fixed trumpet angle, the discharge coefficient is insensitive to trumpet length. Both the spray cone angle and the film thickness are found to decrease with trumpet length. Analytical solutions are developed to determine the atomizer performance considering inviscid flow through the atomizer. The qualitative trends in the variation of film thickness at the atomizer exit, spray cone angle, and discharge coefficient predicted by inviscid flow analysis are seen to agree well with computational results.

Film condensation on a finite-size horizontal wavy plate bounded by a homogenous porous layer

Steady filmwise condensation on a finite-size horizontal wavy plate which covers a homogeneous porous medium layer filled with a dry saturated vapor has been investigated by boundary layer approximations. The dimensionless average Nusselt number Nu ¯ and dimensionless liquid film thickness on the wavy surface are evaluated as a function of seven parameters: Darcy number Da, Jacob number Ja, the wave number n, Prandtl number Pr, modified Rayleigh number Ra, suction parameter S w and the wave amplitude α. It is shown that the condensation heat transfer coefficient can be enhanced by increasing the contact area of the condensate, which corresponds to increasing values of the wave number and amplitude of the wavy surface, and when suction exists at the condensate surface.

The internal electric field originating from the mismatch effect and its influence onferroelectric thin film properties

The influence of the mismatch effect on thin ferroelectric film properties has been studiedin the phenomenological theory framework. The polarization dependent part of the surfaceenergy that defined the boundary conditions for the Euler–Lagrange differentialequation was written as a surface tension energy. The latter was expressed viathe surface polarization and the tension tensor related to the mismatch of thesubstrate and film lattice constants and thermal expansion coefficients. The interfacialstrain caused by the mismatch effect induces the additional surface polarizationPm via a piezoelectric effect that arises near the surface in any film.The new parameter Pm/PS (PS is the known value of the spontaneous polarization in the bulk ferroelectric material atT = 0 K)appeared in the derived phenomenological equations. So we calculate the influence of the parameterPm/PS on the depth distribution of the dimensionless film polarizationP/PS, its dependence on temperature, film thickness and applied electric field,as well as that on the hysteresis loop shape, coercive field values, phasediagram and average dielectric susceptibility temperature dependence. Non-zeroPm/PS values cause a mismatch induced thickness dependent internal electric fieldEm.We have shown that this field drastically influences all the properties. In particular, the polarizationprofile becomes asymmetrical, the polarization temperature dependence resembles that in theexternal electric field and there is a possibility of external field screening by the internal fieldEm. The asymmetry obtained for the hysteresis loop suggests that it is possible that theself-polarization phenomenon recently observed in some films is related to the mismatch effect.The thickness induced ferroelectric–paraelectric phase transition has been shown to exist when|Pm|/PS<1. A largeenough ratio |Pm|/PS>1 could be the physical reason for the ferroelectric phase conservation in ultrathin film. Thepossibility of observing the peculiarities of the film property temperature and thicknessdependences related to the mismatch effect is discussed.

Turbulent film condensation on a vertical wedge

The present paper develops for the study of turbulent film condensation on a vertical wedge plate. It begins by considering the case of vapour flow past an isothermal wedge. Potential flow theory is used to determine the high tangential velocity of the vapour, and the Colburn analogy is used to define the local liquid–vapour interfacial shear which occurs when the high velocity vapour flows across the wedge surface. The paper then presents a discussion of the results obtained for the local dimensionless film thickness and heat transfer characteristics. Finally, the results developed in this study are compared with those generated by previous theoretical results.

On the breakup of a thin liquid film subject to interfacial shear

The breakup of a thin non-evaporating liquid film that is either flowing down or climbing on a vertical or inclined surface and subject to cocurrent or countercurrent interfacial shear (or gas flow) is investigated analytically. Analytical expressions for the dimensionless liquid film thickness, for a climbing water film on a vertical surface are in good agreement with reported experimental data for a wide range of cocurrent gas velocities.

Experimental investigation of splash and crown formation during single drop impact on wetted surfaces

Experimental results concerning crown formation during liquid drop impact on wetted surfaces are reported. Different liquids and numerous impact conditions are investigated. In particular, crown-splash (C-S) and deposition-crown (D-C) limits are determined on the basis of the experimental observations. These limits converge for dimensionless film thickness thinner than 0.03, leaving the outcome of crown formation unobserved. The sole Weber number and dimensionless film thickness cannot explain the phenomenon. It appears that all these data can be described using a combination of Weber and Ohnesorge numbers versus dimensionless film thickness.

Turbulent film condensation on a half oval body

The paper is an investigation of turbulent film condensation on a half oval body. The high tangential velocity of the vapor flow at the boundary layer is determined from potential flow theory. The Colburn analogy is used to define the local liquid–vapor interfacial shear which occurs when the high velocity vapor flows across the body surface. The paper then presents a discussion of the results obtained for the local dimensionless film thickness and heat transfer characteristics. Furthermore, the present paper discusses the influence of Froude number, sub-cooling temperature and system pressure on mean Nusselt number.

Analytical investigation of forced convection film condensation on a vertical porous-layer coated surface

A problem of forced convection condensation in a thin porous layer is considered. The flow in the porous region is described by the Darcy-Brinkman-Forchheimer model (DBF) while classical boundary layer equations without inertia and enthalpie terms are used in the pure condensate region. In order to resolve this problem, an analytical method is proposed. Then, analytical solutions for the flow velocity, temperature distributions and for the local Nusselt number are obtained. The results are essentially presented in the form of the velocity and temperature profiles within the porous layer, the dimensionless film thickness and the heat transfer represented by the local Nusselt number. The comparison of the (DBF) model and the Darcy-Brinkman (DB) one is carried out. The effects of the effective viscosity (Reynolds numberReK), permeability (Darcy numberDa) and dimensionless thickness of porous coating H* on the flow and the heat transfer enhancement are also documented.

Numerical Solution of a Rimming Flow Problem Using a Moving Mesh Method

AbstractWe consider the evolution of a thin film of viscous fluid on the inside surface of a cylinder with the horizontal axis, rotating with a constant angular velocity about this axis. We use a lubrication approximation extended to the first order in the dimensionless film thickness (including the small effects of the variation of the film pressure across its thickness and the surface tension) and numerically we compute the time evolution of the film to a steady state.

Heat transfer in a power-law fluid film over a unsteady stretching sheet

In this paper the problem of momentum and heat transfer in a thin liquid film of power-law fluid on an unsteady stretching surface has been studied. Numerical solutions are obtained for some representative values of the unsteadiness parameter S and the power-law index n for a wide range of the generalized Prandtl number, 0.001 ≤ Pr ≤ 1000. Typical temperature and velocity profiles, the dimensionless film thickness, free-surface temperature, and the surface heat fluxes are presented at selected controlling parameters. The results show that increasing the value of n tends to increase the boundary-layer thickness and broadens the temperature distributions. The free-surface temperature of a shear thinning fluid is larger than that of a Newtonian fluid, but the opposite trend is true for a shear thickening fluid. For small generalized Prandtl numbers, the surface heat flux increases with a decrease in n, but the impacts of n on the heat transfer diminish for Pr greater than a moderate value (approximately 1 ≤ Pr ≤ 10, depending on the magnitude of S).

Droplet Entrainment From a Shear-Driven Liquid Wall Film in Inclined Ducts: Experimental Study and Correlation Comparison

The primary objective of the present study is to clarify the droplet disintegration mechanism and the film properties of liquid oil films driven by shear stress, which is induced by a co-current gas flow. This work focuses on the flow behavior within the starting length of the complex two-phase flow and the effect of inclination on the entrainment rate. Many investigations have been performed in the past to determine the droplet entrainment in the gas core for fully developed flow conditions with respect to their relevance in pipes of power plants and various chemical engineering systems. In more recent work the effect of inclination has been studied in detail. Nevertheless, a lack of knowledge can be realized for droplet entrainment within the starting length of this complex flow type. Thus, fundamental experiments have been carried out to provide a data base for droplet entrainment of liquid disintegrated from an oil film within its starting length at several inclination angles of the flow. The experimental results have been compared with correlations from literature. Additionally, the wall film thickness has been measured to allow a fully coupled modeling of entrainment and liquid film properties depending on global flow parameters. Based on film Reynolds number, Weber number, a dimensionless film flow length, and a modified Froude number, taking into account the angle of inclination, correlations have been developed, where those from literature are not applicable.

A mechanism for linear instability in two-dimensional rimming flow

In rimming flow, a thin film of viscous liquid coats the inside of a cylinder whose axis is horizontal and which is rotating with constant angular velocity. It has been established experimentally that such flows are often unstable with a variety of secondary flow regimes having been observed experimentally [15]. We use a lubrication approximation extended to the first order in the dimensionless film thickness (including the small effects of the variation of the film pressure across its thickness and the surface tension) and study the stability of the steady solutions to two-dimensional disturbances. The modified evolution equation is found to have both asymptotically stable and unstable solutions arising from the pressure terms. Surface tension effects place a restriction on the critical wave number when instability occurs: in many cases, surface tension prevents instability.

A model of chaotic evolution of an ultrathin liquid film flowing down an inclined plane

Chemical and colloidal transport processes in partially saturated porous and fractured media are dependent on liquid flow along a solid surface, which may be chaotic even for small Reynolds numbers. This paper presents the derivation of a one-dimensional evolution equation describing the slow motion (small Reynolds numbers, R<<1) of a very thin liquid film flowing down an inclined impermeable plane. In this equation, gravitational, capillary, and molecular forces are taken into account. The addition of the molecular force term leads to a highly nonlinear equation governing the spatial and temporal evolution of film thickness. In a weakly nonlinear limit, this evolution equation is rescaled to a canonical form. The latter predicts a chaotic hydrodynamic instability for the film surface. This chaotic behavior is illustrated using the 3D projections of pseudo-phase space attractors for the spatial and temporal variations of the dimensionless film thickness.

Inertia Effects in a Curved Non-Newtonian Squeeze Film

Inertia Effects in a Curved Non-Newtonian Squeeze Film

Experimental analysis of a spray impinging on a conical surface

The details of droplet–droplet and droplet–liquid film interactions on solid surfaces are believed to have significant role in spray impingement phenomena, yet details of this interaction have not been clearly identified. After impact, droplet interactions affect droplet collisions, coalescence and liquid splashing; this interaction affects secondary atomization and droplet dispersion characteristics of the impingement process. In this study detailed measurements are performed in liquid sprays with a phase-Doppler velocimeter: simultaneous measurements of droplet size and velocity are obtained. The analysis is oriented towards secondary droplets behaviour. One general conclusion of this paper is that, working with a mean dimensionless film thickness between 1 and 3, the size and velocity distribution of secondary droplets are sensitive to the film thickness.