Gas absorption in a thin liquid film flow on a horizontal rotating disk

An analytical model for the rate of gas absorption into laminar non-wavy film flow on a horizontal rotating disk is obtained assuming short contact times. Literature data for the oxygen mass transfer coefficient in a wavy film is correlated by means of the dimensionless numbers deriving from the model. The rate enhancement due to waves is found to vary from 6 to 13 times. It is established that the absorption process in the film on the disk as compared to that in a gravitational wavy film flow can be intensified up to 14 times by means of a moderate rotation speed.     

Two-layer film flow on a rotating disk: A numerical study

Development of thin two-layer film over a uniformly rotating disk is studied numerically under the assumption of planar interface and free surface. Similarity transformation is applied to transform the Navier-Stokes equations into a set of coupled non-linear, unsteady partial differential equations. This set of equations are solved numerically by using the finite-difference technique. It is observed that the rate of film thickness varies at different time zone depending on the rate of rotational speed of the disk. A physical explanation is provided to justify this anomalous behaviour. It is observed that, smaller thickness on the top layer enhance the initial rate of film thinning. But the overall effect of density, viscosity and the initial film thickness ratio are found to be insensitive to the final film thickness at large time.     

Surface instabilities of thin liquid film flow on a rotating disk

 Steady flow of a liquid jet from a nozzle onto the centre of a rotating disk is studied with a streak line method to determine the superficial velocity of the spreading liquid film. Good agreement is found with an asymptotic analysis of the unperturbed flow field. Experimentally, the liquid surface is always perturbed by surface waves which appear as regular spirals, steady in the laboratory system in the low Reynolds number range. It could be shown that wave formation is very sensitive to entrance conditions. Therefore, it is assumed that wave generation is an entrance effect which acts as periodic forcing on the forming liquid film. Wave velocities outside the entrance region are measured and proved to be in good agreement with the prediction of a linear stability theory, as long as the flow rate and entrance perturbations are small. At higher flow rates or stronger disturbances, the radial development of the wave velocities takes on the characteristics predicted by nonlinear stability theories and is in qualitative agreement with experiments performed on an inclined plane. Received: 15 January 1998/Accepted: 8 June 1998     

Flow of a Nonlinearly Viscous Fluid over the Surface of a Rotating Flat Disk

The flow of a nonlinearly viscous (power-law) fluid over the surface of a rotating flat disk is investigated. A solution form which makes it possible to reduce the complete system of partial differential equations to a system of ordinary differential equations is found. This system is integrated using the Runge-Kutta method and reduction to a Cauchy problem on the basis of Newton's method. The velocity and pressure fields in a power-law fluid film flowing over the surface of a rotating flat disk are found numerically.     

Experiments on the flow of a thin liquid film over a horizontal stationary and rotating disk surface

Experiments on characterization of thin liquid films flowing over stationary and rotating disk surfaces are described. The thin liquid film was created by introducing deionized water from a flow collar at the center of an aluminum disk with a known initial film thickness and uniform radial velocity. Radial film thickness distribution was measured using a non-intrusive laser light interface reflection technique that enabled the measurement of the instantaneous film thickness over a finite segment of the disk. Experiments were performed for a range of flow rates between 3.0 lpm and 15.0 lpm, corresponding to Reynolds numbers based on the liquid inlet gap height and velocity between 238 and 1,188. The angular speed of the disk was varied from 0 rpm to 300 rpm. When the disk was stationary, a circular hydraulic jump was present in the liquid film. The liquid-film thickness in the subcritical region (downstream of the hydraulic jump) was an order of magnitude greater than that in the supercritical region (upstream of the hydraulic jump) which was of the order of 0.3 mm. As the Reynolds number increased, the hydraulic jump migrated toward the edge of the disk. In the case of rotation, the liquid-film thickness exhibited a maximum on the disk surface. The liquid-film inertia and friction influenced the inner region where the film thickness progressively increased. The outer region where the film thickness decreased was primarily affected by the centrifugal forces. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. At high rotational speeds, spiral waves were observed on the liquid film. It was also determined that the angle of the waves which form on the liquid surface was a function of the ratio of local radial to tangential velocity.     

转移膜的形成对含氢碳膜超低摩擦性能的影响

含氢非晶碳膜在惰性气氛下展现了超低摩擦性能,摩擦系数可达到10~(–3)数量级.本文中通过试验设计验证了转移膜的形成是碳膜超低摩擦性能获得的必要条件.采用含氢非晶碳膜(a-C:H)与钢作为摩擦配副,球盘接触旋转运动,更换接触方式:一种是钢球与镀a-C:H薄膜的钢平板对摩,另一种是镀a-C:H薄膜钢球与钢平板对摩.保持配副材料不变,利用接触方式的差异,来改变转移膜形成的难易程度.第一种方式下,a-C:H可以转移到对偶形成均匀的转移膜,具有超低摩擦性能;在第二种方式下,a-C:H不能转移到对偶形成转移膜,摩擦系数高.而该转移膜是一种含氢的,以sp~2杂化为主的碳结构.氢能够参与钝化碳悬键,从而保证低化学作用活性,sp~2平面分子结构可以具有较低的剪切强度.因此,转移膜的形成和氢的钝化作用对a-C:H薄膜超低摩擦机理均具有重要的贡献.     

Flow of a Viscoplastic Fluid on a Rotating Disk

ＦＬＯＷＯＦＡＶＩＳＣＯＰＬＡＳＴＩＣＦＬＵＩＤＯＮＡＲＯＴＡＴＩＮＧＤＩＳＫＦａｎＣｈｕｎ（范椿）（ＩｎｓｔｉｕｉｅｏｆＭｅｃｈａｎｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ）（ＲｅｃｅｉｖｅｄＮｏｖ．２０，１９９２；Ｃｏｍｍｕｎｉｃａｔ...     

Peeling behavior of a viscoelastic thin-film on a rigid substrate

In order to study the adhesion mechanism of a viscoelastic thin-film on a substrate, peeling experiment of a viscoelastic polyvinylchloride (PVC) thin-film on a rigid substrate (glass) is carried out. The effects of peeling rate, peeling angle, film thickness, surface roughness and the interfacial adhesive on the peel-off force are considered. It is found that both the viscoelastic properties of the film and the interfacial adhesive contribute to the rate-dependent peel-off force. For a fixed peeling rate, the peel-off force decreases with the increasing peeling angle. Increasing film thickness or substrate roughness leads to an increase of the peel-off force. Viscoelastic energy release rate in the present experiment can be further predicted by adopting a recently published theoretical model. It is shown that the energy release rate increases with the increase of peeling rates or peeling angles. The results in the present paper should be helpful for understanding the adhesion mechanism of a viscoelastic thin-film.     

On the slow translation of a solid submerged in a fluid with a surfactant surface film—II

In Shail & Gooden (1982) the problem of a solid particle translating in a semi-infinite fluid, whose surface is contaminated with a surfactant film, was examined in the quasi-steady Stokes flow régime. Various linearised models governing the variation of film concentration were considered, but the analysis was approximate in that the fluid motion generated was represented by that due to a Stokeslet situated at the centre of the particle. In this paper we remove the latter restriction and treat two specific solids, namely a rigid flat circular disk and a sphere, which move axisymmetrically perpendicular to the fluid surface. This surface is assumed to remain plane throughout the motion. The velocity field in the translating-disk problem is represented in terms of harmonic functions, and the resulting mixed boundary-value problems are reduced, for each of the film behaviours examined, to the solution of sets of simultaneous Fredholm integral equations of the second kind. These equations are solved both iteratively and numerically, and the drag on the disk is computed. For the sphere a stream-function formulation in bispherical coordinates is used. Application of the boundary conditions at the sphere and film results in infinite sets of simultaneous linear equations for the coefficients in the eigenfunction expansion of the stream function. These equations are solved by the method of truncation, and the drag on the sphere is determined.     

Bingham流体在旋转圆盘上流动的数值解

导出了描述Ｂｉｎｇｈａｍ流体在旋转圆盘上流动的基本方程，用差分方法数值解薄膜厚度分布方程，得到二种类型的厚度分布。数值解分别和计算机磁盘的厚度分布，Ｊｅｎｅｋｈｅ等的实验结果定性一致。     

纳米尺度下气体薄膜润滑理论研究

提出了依赖于逆Knudsen数的纳米尺度影响因子Np，修正了目前应用较为普遍的FK-Boltzmann模型，并给出了其数值计算结果。结果表明：当膜厚小于单个空气分子平均自由程时，由于纳米尺度效应的影响，流量因子有所减小，承载能力略微增加。     

The effect of hydrodynamic coupling on the thinning of a film between a drop and its homophase

The rate of thinning of a film trapped between a drop approaching its homophase according to a model incorporating hydrodynamic coupling is dramatically different from earlier, uncoupled models. Implications for film thinning of microflows analyzed in the preceding paper are here investigated using similar analytical methods to derive a nonautonomous, nonlinear evolution equation for the film thickness which has been solved numerically under a variety of conditions after asymptotic analytical behavior has been extracted. The applied force squeezing the film, together with the initial motion in the three phases, determines the rate of film thinning in a complicated manner through the coupling parameter R = (ρ_Aμ_A/ρ_Bμ_B)^{$\text{1}\text{2}$}. Experimental observations that normal drop circulation enhances thinning, whereas reversed drop circulation can cause thickening, are predicted theoretically for the first time. Films much more viscous than their surroundings are found to thin faster than the converse case, a conclusion at odds with offhand intuition but substantiated experimentally; both classes of systems behave differently, often qualitatively so, from predictions of hydrodynamically decoupled systems, and in particular film thinning rates are generally faster because of less resistance to drainage, although the limit of vanishing R does recover the special case of Reynolds' model. For short times, films are shown analytically to thin more rapidly if there is initially outward film motion and normal drop circulation, but with decreasing effectiveness as R increases, in contrast to the effect of R for intermediate and longer times; if there is initially inward film motion, thickening tendencies are enhanced by reverse drop circulation but with decreasing effectiveness as R increases. These and other detailed conclusions, most predicted theoretically for the first time, are not only in qualitative agreement with experimental observations, they are in quantitative agreement with available data.     

Analysis of cooling of a conducting fluid film of non-uniform thickness on a rotating disk

The unsteady thin conducting liquid film of non-uniform thickness on a rotating disk which is cooled axisymmetrically from below has been analysed numerically by solving the evolution equation of the free surface. Transient film profiles for different initial liquid film distributions have been obtained. The results reveal that the thinning process and film planarisation are markedly influenced by the heat dissipating or cooling parameter β, Prandtl number σ and Reynolds number Re.     

Dynamical responses of non-isothermal flow between two independently rotating disks with time-dependent wall conditions

The present work develops a theoretical model of rotational convection and uses it to investigate the dynamical responses of the flow and heat transfer between two disks rotating at different rates under the influences of time-dependent disturbances. The unsteady non-isothermal flow model is formulated by extending a recently developed steady-state similarity model of axi-symmetric rotational convection. In the new model all the rotation-induced buoyancy forces are considered. Using one disk as reference, effects of the time-dependent changes in wall temperature or rotating rate of the other disk on the flow and heat transfer are explored. Various rotational modes with asymptotic or fluctuating change in boundary condition of temperature or disk rotation are studied. The present time-dependent model for this non-isothermal rotating flow is numerically solved by a finite-difference method. By using the present results, the complicated flow and heat transfer mechanisms with thermal-flow coupling in the class of time-dependent rotational convection are manifested.     

Stability of a vertical liquid film with consideration of the marangoni effect and heat exchange with the environment

The stability of a free vertical liquid film under the combined action of gravity and thermocapillary forces has been studied. An exact solution of the Navier-Stokes and thermal conductivity equations is obtained for the case of plane steady flow with constant film thickness. It is shown that if the free surfaces of the film are perfectly heat insulated, the liquid flow rate through the cross section of the layer is zero. It is found that to close the model with consideration of the heat exchange with the environment, it is necessary to specify the liquid flow rate and the derivative of the temperature with respect to the longitudinal coordinate or the flow rate and the film thickness. The stability of the solution with constant film thickness at small wave numbers is studied. A solution of the spectral problem for perturbations in the form of damped oscillations is obtained.     

Effects of air-flow and evaporation on the development of thin liquid film over a rotating annular disk

Axisymmetric flow of thin pure liquid film on a spinning horizontal annular disk is studied under the action of air shear at the liquid–air interface and evaporation. The non-linear evolution equation that is obtained by singular perturbation method is solved analytically, for small Reynolds number, by using the method of characteristic and numerically by the use of Newton–Kantorovich method for any Reynolds number. Font breakdown time and its location from the center of the disk is predicted both by analytically and numerically. The result shows that the thinning of the initial film increases as air stress increase, same result is also escalated in presence of evaporation.     

The slow rotation of an axisymmetric solid submerged in a fluid with a surfactant surface layer—I The rotating disk in a semi-infinite fluid

A formulation in terms of a Fredholm integral equation of the first kind is given for the axisymmetric problem of a solid rotating in a bounded viscous fluid whose surface is contaminated with an immiscible surfactant film. The particular case of a rotating thin circular disk immersed in a semi-infinite body of fluid is studied in detail, the problem being reduced to the solution of a Fredholm integral equation of the second kind. This equation is solved both asymptotically and numerically, and the resistive torque on the disk and surface velocity profiles are computed for varying values of the ratio of the coefficient of surface shear viscosity to the coefficient of viscosity of the substrate fluid, and depth of the disk below the surface.     

薄膜润滑中双电层效应的理论分析与实验研究

建立了考虑双电层效应的有限宽组合滑块薄膜润滑数学模型,并利用组合滑块与圆盘的滑动摩擦试验对双电层效应进行研究,利用实验结果修正了润滑过程中双电层效应的计算,给出电粘度的计算公式并进行数值分析.结果表明:在薄膜厚度较薄的情况下,双电层效应使得流体的等效粘度随膜厚减小而迅速增加;随着膜厚增加,双电层的电粘度效应逐渐减弱;随着电场强度增加,双电层的电粘度效应增加,当电场强度达到一定程度时,双电层的电粘度效应开始减弱.     

Incompressible viscous flows resulting from the steady rotation of a finite disk

Low Reynolds number solutions are obtained for two flows which are generated by the steady rotation of a finite disk of zero thickness in its own plane. The disk is assumed to be either immersed in an infinite body of fluid or else coplanar with a solid stationary plane with the fluid filling the half space on one side of it. In both cases the swirl is strong near the source of disturbance and weakens with the distance from the disk. Spatial variations of the centrifugal acceleration give rise to radial outflow near the disk as well as to inflow along the axis of symmetry. Since the disk is taken to be finite the analysis presented accounts for the conditions prevailing at the rim and beyond it. Thus, it is found that when the solid stationary plane is absent the flow is faster than when that partition is present. The retarding effect is noticeable even in the vicinity of the origin.