Aeration in Lubrication With Application to Drag Torque Reduction

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Chinar R. Aphale ◽  
William W. Schultz ◽  
Steven L. Ceccio
Keyword(s):  
Contact Line ◽  
Neumann Boundary ◽  
Rotating Disk ◽  
Contact Angles ◽  
Standard Theory ◽  
Two Phase ◽  
Static Contact ◽  
Interface Contact ◽  
Dirichlet And Neumann Conditions

The aeration of an oil film flowing between the faces of two closely spaced circular plates (one stationary, and one rotating) is examined experimentally, numerically, and with an improved lubrication model. The gap between the plates is small compared to their radii, making lubrication theory appropriate for modeling the flow. However, standard lubrication boundary conditions suggested by Reynolds (1886, "On the Theory of Lubrication and its Application to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil," Philos. Trans. R. Soc. London, 177, pp. 157-234) of p = 0 and pn = 0 (Dirichlet and Neumann conditions on pressure) at the gas-liquid interface do not allow for the inclusion of a contact line model, a phenomenon that is important in the inception of aeration. Hence, the standard theory does not adequately predict the experimentally observed onset of aeration. In the present work, we modify the Neumann boundary condition to include both interfacial tension effects and the dynamics of the interface contact angle. The resulting one-dimensional Cartesian two-phase model is formulated to incorporate the prescribed contact line condition and tracks the interface shape and its motion. This model is then implemented in an axisymmetric, two-dimensional model of the rotating disk flow and used to predict the onset of aeration for varying surface tension and static contact angles. The results of the modified lubrication model are compared with experimental observations and with a numerical computation of the aerating flow using a volume of fluid method.

Two-phase displacement in Hele-Shaw cells: experiments on viscously driven instabilities

1984 ◽  
Vol 141 ◽  
pp. 275-287 ◽  
Author(s):  
C.-W. Park ◽  
S. Gorell ◽  
G. M. Homsy
Keyword(s):  
Viscous Fluid ◽  
Contact Line ◽  
Growth Characteristics ◽  
Recent Theory ◽  
Two Phase ◽  
Quantitative Measurements ◽  
Viscous Oil ◽  
Static Contact ◽  
Growth Constants ◽  
Theory And Experiment

Experiments on the instability of the interface in two-phase displacements in Hele-Shaw cells were conducted using air and a viscous oil as the working fluids. The experiments had two objectives: (i) to provide quantitative measurements of the growth constants of the instability which occurs when a less-viscous fluid displaces a more-viscous one, and (ii) to compare the measured dispersion relations with the predictions of the recent theory of Park & Homsy (1984). The experiments were made by analysing the growth characteristics of between 10 and 20 Fourier modes describing the shape of the interface between displaced and displacing fluids, using still photography. For capillary numbers Ca = μU/γ less than approximately 4 × 10−3 the agreement is only fair, owing to substantial edge effects produced by a nearly static contact line near the lateral boundaries of the cell. For 4 × 10−3 < Ca < 1 × 10−2 theory and experiment agree to within the accuracy of the measurements. Location and verification of the behaviour of modes near the predicted cut-off wavenumber give partial verification of the theory of Park & Homsy.

Metrics for Quantifying Surface Wetting Effects on Vaporization Processes at Nanostructured Hydrophilic Surfaces

2016 ◽  
Author(s):  
Claire M. Kunkle ◽  
Van P. Carey
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angles ◽  
Apparent Contact Angle ◽  
Static Contact Angle ◽  
Sensitive Indicator ◽  
Nanostructured Surfaces ◽  
Hydrophilic Surfaces ◽  
Static Contact ◽  
Spread Area

A static contact angle is most often used as a means of quantifying the wetting characteristics of the liquid phase in vaporization processes at a solid surface. This metric is often convenient to measure and intuitive in its interpretation, but when a surface is superhydrophilic, the resulting low contact angles are difficult to measure accurately from photographs of sessile droplet profiles or contact line regions. For droplets at ultra low contact angles, small changes of contact angle can produce very large changes in wetted surface area, which makes small uncertainties in contact angle result in large uncertainties in wetted area. For hydrophilic nanostructured surfaces, another disadvantage is that the relationship of the macroscopic (apparent) contact angle to the nanoscale interaction of the liquid and vapor contact line with the nanostructured surface is not always clear. In this study, a new wetting metric based on spreading characteristics of sessile droplets is proposed that can be easily measured for hydrophilic surfaces. This metric also has the advantage that it is a more direct and sensitive indicator of how a droplet spreads on the surface. The spread area directly impacts heat transfer interactions between the droplet and the surface, therefore affecting evaporation time. Consequently, a metric that more directly illustrates the spread area provides an indication of how the wetting will affect these mechanisms. Use of the proposed new metric is explored in the context of evaporation and boiling applications with superhydrophilic surfaces. Characteristics of this metric are also compared to static contact angle and other choices of wetting metrics suggested in earlier studies, such as dynamic advancing and receding contact angles, and spreading coefficients. The effects of nanoscale structure and/or roughness on the proposed wetting metric are analyzed in detail. A model is developed that predicts the dependence of the proposed wetting parameter on intrinsic material wettability for rough, nano-structured surfaces. The model results demonstrate that the proposed metric is a more sensitive indicator of macroscopic wetting behavior than apparent contact angle when the surface is superhydrophilic. This characteristic of the proposed new metric is shown to have advantages over other wetting metrics in the specific case of superhydrophilic nanostructured surfaces. Application of the proposed wetting metric is demonstrated for some example nanostructured surfaces. The results of our study indicate that this proposed new metric can be particularly useful for characterizing the effects of variable wetting on vaporization processes on highly wetted nanostructured surfaces.

scholarly journals Thick drops climbing uphill on an oscillating substrate

2018 ◽  
Vol 840 ◽  
pp. 131-153 ◽  
Author(s):  
J. T. Bradshaw ◽  
J. Billingham
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Contact Angles ◽  
Boundary Integral ◽  
Static Contact Angle ◽  
Rise Velocity ◽  
Contact Lines ◽  
Weakly Nonlinear ◽  
Static Contact

Experiments have shown that a liquid droplet on an inclined plane can be made to move uphill by sufficiently strong, vertical oscillations (Brunet et al., Phys. Rev. Lett., vol. 99, 2007, 144501). In this paper, we study a two-dimensional, inviscid, irrotational model of this flow, with the velocity of the contact lines a function of contact angle. We use asymptotic analysis to show that, for forcing of sufficiently small amplitude, the motion of the droplet can be separated into an odd and an even mode, and that the weakly nonlinear interaction between these modes determines whether the droplet climbs up or slides down the plane, consistent with earlier work in the limit of small contact angles (Benilov and Billingham, J. Fluid Mech. vol. 674, 2011, pp. 93–119). In this weakly nonlinear limit, we find that, as the static contact angle approaches $\unicode[STIX]{x03C0}$ (the non-wetting limit), the rise velocity of the droplet (specifically the velocity of the droplet averaged over one period of the motion) becomes a highly oscillatory function of static contact angle due to a high frequency mode that is excited by the forcing. We also solve the full nonlinear moving boundary problem numerically using a boundary integral method. We use this to study the effect of contact angle hysteresis, which we find can increase the rise velocity of the droplet, provided that it is not so large as to completely fix the contact lines. We also study a time-dependent modification of the contact line law in an attempt to reproduce the unsteady contact line dynamics observed in experiments, where the apparent contact angle is not a single-valued function of contact line velocity. After adding lag into the contact line model, we find that the rise velocity of the droplet is significantly affected, and that larger rise velocities are possible.

Determination of specific interfacial areas in swirled two-phase flow

1983 ◽  
Vol 48 (3) ◽  
pp. 842-853
Author(s):  
Kurt Winkler ◽  
František Kaštánek ◽  
Jan Kratochvíl
Keyword(s):  
Interfacial Area ◽  
Liquid Volume ◽  
Upward Flow ◽  
Two Phase ◽  
Flow Rates ◽  
Mist Flow ◽  
Interfacial Areas ◽  
Correlation Parameters ◽  
Flow Components

Specific gas-liquid interfacial area in flow tubes 70 mm in diameter of the length 725 and 1 450 mm resp. containing various swirl bodies were measured for concurrent upward flow in the ranges of average gas (air) velocities 11 to 35 ms-1 and liquid flow rates 13 to 80 m3 m-2 h-1 using the method of CO2 absorption into NaOH solutions. Two different flow regimes were observed: slug flow swirled annular-mist flow. In the latter case the determination was carried out separately for the film and spray flow components, respectively. The obtained specific areas range between 500 to 20 000 m3 m-2. Correlation parameters are energy dissipation criteria, related to the geometrical reactor volume and to the static liquid volume in the reactor.

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