Profile and departure size of condensation drops on vertical surfaces

The problem of the equilibrium shape and departure size of two-dimensional dropwise condensation drops on a vertical surface is considered. The equation of the surface of the drop is obtained by minimizing (for a given volume) the total energy of the drop, consisting of surface and gravitational energy, using the techniques of variational calculus. The solution is tractable once the advancing contact angle is known, and is taken as an approximation to the axial meridian profile of a three-dimensional drop. The receding contact angle is obtained as part of the solution. The drop size is specified by imposing its vertical length. Upon increasing this vertical length, a point is reached at which no real solution exists, and this is taken as the departure size of the drop. Comparison with measured departure sizes under various body forces from standard to 100 times earth gravity are good.     

Flows with a moving contact line

The problem of a two-dimensional viscous fluid drop which steadily moves along a horizontal rigid surface is considered. Such motion arises if the rigid surface wettability is nonuniform. A sequence of solutions for the velocity field and the free surface shape with the successively increasing applicability region near the moving contact lines is obtained for small capillary numbers Ca. The solution of the problem is found in the case when the distortion of the free surface of the drop during motion can be neglected. The problem is then reformulated using functions of a complex variable and expanded variables are introduced. In the new variables a more accurate solution of the same problem is found, with a much more narrow inapplicability region near the moving contact lines. In the solution obtained the free surface approaches the receding contact line at an angle of 180° and the advancing line at a zero angle. The solution is applicable up to the receding contact line and here approaches the known asymptotics. Near the advancing contact line the solution is applicable until the angle between the free surface and the rigid substrate becomes of the order of Ca^1/3.     

Compositive effects of orientation and contact angle on critical heat flux in pool boiling of water

An experimental study was carried out to investigate the effects of heat transfer surface orientation and the solid–liquid contact angle on the boiling heat transfer and critical heat flux (CHF) in water pool boiling using a smooth heat-transfer surface under atmospheric pressure. The orientation angle was ranged from 0° (up-facing horizontal position) to 180° (down-facing horizontal position) with a pace of 45°. The three kinds of heat transfer surfaces having different solid–liquid contact angles were the normal surface with a contact angle of 55°, the hydrophilic surface with a contact angle of 30° and the superhydrophilic surface with a contact angle of 0°. The experimental results indicate that orientation and contact angle have complex, coupling effects on heat transfer and CHF. A predicting correlation for the CHF which takes the effects of both orientation and contact angle into account is established. The predicting correlation agrees reasonably well with the experimental data.     

Direct simulation of multiphase flows with modeling of dynamic interface contact angle

We describe a modeling technique for dynamic contact angle between a phase interface and a solid wall using a generalized Navier boundary condition in the context of a front-tracking-based multiphase method. The contact line motion is determined by the generalized Navier slip boundary condition in order to eliminate the infinite shear stress at the contact line. Applying this slip boundary condition only to the interface movement with various slip ratios shows good agreement with experimental results compared to allowing full fluid slip along the solid surface. The interface slip model performs well on grid convergence tests using both the slip ratio and slip length models. A detailed energy analysis was performed to identify changes in kinetic, surface, and potential energies as well as viscous and contact line dissipation with time. A friction coefficient for contact line dissipation was obtained based on the other computed energy terms. Each energy term and the friction coefficient were compared for different grid resolutions. The effect of varying the slip ratio as well as the contact angle distribution versus contact line speed was analyzed. The behavior of drop impact on a solid wall with different advancing and receding angles was investigated. Finally, the proposed dynamic contact model was extended to three dimensions for large-scale parallel calculations. The impact of a droplet on a solid cylinder was simulated to demonstrate the capabilities of the proposing formulation on general solid structures. Widely different contact angles were tested and showed distinctive characteristic behavior clearly.     

Effects of ultrasonic vibration on subcooled pool boiling critical heat flux

The effects of ultrasonic vibration on critical heat flux (CHF) have been experimentally investigated under natural convection condition. Flat bakelite plates coated with thin copper layer and distilled water are used as heated specimens and working fluid, respectively. Measurements of CHF on flat heated surface were made with and without ultrasonic vibration applied to working fluid. An inclination angle of the heated surface and water subcooling are varied as well. Examined water subcoolings are 5°C, 20°C, 40°C and the angles are 0°, 10°, 20°, 45°, 90°, 180°. The measurements show that ultrasonic wave applied to water enhances CHF and its extent is dependent upon inclination angle as well as water subcooling. The rate of increase in CHF increases with an increase in water subcooling while it decreases with an increase in inclination angle. Visual observation shows that the cause of CHF augmentation is closely related with the dynamic behaviour of bubble generation and departure in acoustic field.     

Numerical simulation of bubble formation on orifice plates with a moving contact line

The formation of bubbles on an orifice plate involves a moving contact line, especially in case of poor wetting conditions. The dynamics of the moving contact line and contact angle have a significant impact on the bubble departure size. Therefore, for the numerical simulation, an appropriate contact line boundary condition is essential for a correct prediction of the bubble formation. Numerical tests have been performed on two kinds of contact line models, one is a contact line velocity dependent model (Model-A, a commonly used model) and the other is a stick-slip model (Model-B). The calculation results using Model-A depend greatly on the prescribed maximum contact line velocity. With Model-B a parameter-independent prediction can be obtained provided that the mesh is sufficiently fine. The dynamic advancing and receding contact angles, which are two required inputs to both models, have a significant influence on the predicted bubble departure diameter, if the contact line moves beyond the inner rim of the orifice. The effect of wettability on the bubble departure size is realized via the variation of the maximum contact diameter. When the contact line sticks to a small region near the inner rim of the orifice, such as the bubble formation on a thin-walled nozzle, the effects of the contact angle and contact line models are negligible.     

Bagley correction: the effect of contraction angle and its prediction

The excess pressure losses due to end effects (mainly entrance) in the capillary flow of a branched polypropylene melt were studied both experimentally and theoretically. These losses were first determined experimentally as a function of the contraction angle ranging from 10° to 150°. It was found that the excess pressure loss function decreases for the same apparent shear rate with increasing contraction angle from 10° to about 45°, and consequently slightly increases from 45° up to contraction angles of 150°. Numerical simulations using a multimode K-BKZ viscoelastic and a purely viscous (Cross) model were used to predict the end pressures. It was found that the numerical predictions do agree well with the experimental results for small contraction angles up to 30°. However, the numerical simulations under-predict the end pressure for larger contraction angles. The effects of viscoelasticity, shear, and elongation on the numerical predictions are also assessed in detail. Shear is the dominant factor controlling the overall pressure drop in flows through small contraction angles. Elongation becomes important at higher contraction angles (greater than 45°). It is demonstrated in abrupt contractions (angle of 180°) that both the entrance pressure loss and the vortex size are strongly dependent on the extensional viscosity for this branched polymer. It is suggested that such an experiment (visualisation of entrance flow) can be useful in evaluating the validity of constitutive equations and it can also be used to fitting parameters of rheological models that control the elongational viscosity.     

Speckle technique for dynamic drop profile measurement on rough surfaces

A technique has been developed for measuring three-dimensional instantaneous drop profiles on rough surfaces. The surface is illuminated using a laser and images are captured of the resulting speckle pattern with and without the drop in place. The analysis consists of finding the contact line, measuring the deformation of the speckle field caused by refraction of light at the drop surface, then reconstructing the drop using simulated annealing optimization to find the drop shape whose shift vector field best matches the one measured. An error analysis of the technique was performed using a Monte Carlo technique and comparisons to sideview drop images for a large sample of drops. Mean contact angle measurement error was found to be −1.6° with a 1 − σ error bound of −6.9°, +2.0°.     

A numerical and experimental study of natural convective heat transfer from an inclined isothermal square cylinder with an exposed top surface

Natural convective heat transfer from an isothermal inclined cylinder with a square cross-section which have an exposed top surface and is, in general, inclined at an angle to the vertical has been numerically and experimentally studied. The cylinder is mounted on a flat adiabatic base plate, the cylinder being normal to the base plate. The numerical solution has been obtained by solving the dimensionless governing equations subject to the boundary conditions using the commercial cfd solver, FLUENT. The flow has been assumed to be symmetrical about the vertical center-plane through the cylinder. Results have only been obtained for Prandtl number of 0.7. Values of inclination angle between 0° and 180° and a wide range of Rayleigh number and the dimensionless cylinder width, W = w/h, have been considered. The effects of Dimensionless widths, Rayleigh numbers, and inclination angles on the mean Nusselt number for the entire cylinder and for the mean Nusselt numbers for the various surfaces that make up the cylinder have been examined. Empirical equations for the heat transfer rates from the entire cylinder have been derived.     

Experimental investigation of inclined liquid water jet flow onto vertically located superhydrophobic surfaces

In this study, the behaviour of an inclined water jet, which is impinged onto hydrophobic and superhydrophobic surfaces, has been investigated experimentally. Water jet was impinged with different inclination angles (15°–45°) onto five different hydrophobic surfaces made of rough polymer, which were held vertically. The water contact angles on these surfaces were measured as 102°, 112°, 123°, 145° and 167° showing that the last surface was superhydrophobic. Two different nozzles with 1.75 and 4 mm in diameters were used to create the water jet. Water jet velocity was within the range of 0.5–5 m/s, thus the Weber number varied from 5 to 650 and Reynolds number from 500 to 8,000 during the experiments. Hydrophobic surfaces reflected the liquid jet depending on the surface contact angle, jet inclination angle and the Weber number. The variation of the reflection angle with the Weber number showed a maximum value for a constant jet angle. The maximum value of the reflection angle was nearly equal to half of the jet angle. It was determined that the viscous drag decreases as the contact angle of the hydrophobic surface increases. The drag force on the wall is reduced dramatically with superhydrophobic surfaces. The amount of reduction of the average shear stress on the wall was about 40%, when the contact angle of the surface was increased from 145° to 167°. The area of the spreading water layer decreased as the contact angle of the surface increased and as the jet inclination angle, Weber number and Reynolds number decreased.     

Visualization of boiling phenomena in inclined rectangular gap

An experimental study was performed to investigate the pool boiling critical heat flux (CHF) in one-dimensional inclined rectangular channels by changing the orientation of a copper test heater assembly. In a pool of saturated water under the atmospheric pressure, the test parameters included the gap sizes of 1, 2, 5, and 10 mm, and the surface orientation angles from the downward-facing position (180°) to the vertical position (90°). Tests were conducted on the basis of the visualization of boiling phenomena in the narrowly confined channel and open periphery utilizing a high-speed digital camera. To prevent the heat loss from the water pool and copper test heater, a state-of-the-art vacuum pumping technique was introduced. It was observed that the CHF generally decreased as the surface inclination angle increased and as the gap size decreased. In the downward-facing position (180°), however, the vapor movement was enhanced by the gap structure, which produced the opposing result; that is, the CHF increased as the gap size decreased. Phenomenological characteristics regarding the interfacial instability of vapor layer were addressed in terms of visualization approaching the CHF. It was found that there exists a transition angle, around which the CHF changes with a rapid slope.     

Shape of hexagonal hydrostatic menisci

A numerical method is implemented for computing the shape of an infinite, hexagonal, doubly periodic, hydrostatic meniscus originating from contact lines whose projections in the horizontal plane are circles. The contact lines themselves may lie on vertical cylinders or spherical objects. The Laplace–Young equation determining the meniscus shape is solved by a finite‐difference method in orthogonal curvilinear coordinates generated by conformal mapping. The elevation of the contact lines is either prescribed or computed as part of the solution to ensure a specified contact angle. The results illustrate that the contact line spacing has an important effect on the contact angle or contact line distribution. Meniscus shapes exist only for a limited range of pressure differences between the upper and lower fluid that depend on the capillary length. Copyright © 2009 John Wiley & Sons, Ltd.     

Equilibrium shapes of strained islands with non-zero contact angles

The equilibrium morphology of a strained island on an elastic substrate is determined. The island is assumed to partially wet the substrate (Volmer-Weber growth) and thus makes a non-zero contact angle with the surface. Both isotropic and anisotropic misfit strain are allowed. Two- and three-dimensional equilibrium island shapes are determined by using expressions for the elastic strain energy in the small-slope approximation. In this limit, the problem can be reduced to a singular integral-differential equation for the island thickness. We find that when there is a non-zero contact angle, all island shapes, for a given ratio of the elastic stress to surface energy, attain a form that is independent of the specific contact angle under an appropriate scaling. We show that for islands with non-zero contact angles, as the island volume increases, the shape approaches the geometry of a completely wetting island. But when the volume decreases, these islands approach a point while islands with a zero contact angle, approach a finite length line segment of zero volume. Multiple-hump equilibrium shapes are found. Single-humped islands are shown to have a lower chemical potential than multiple-humped islands, implying that they are the most stable. This conclusion is shown to be consistent with a stability analysis of the two-dimensional case. The effects of a tetragonal misfit strain on the three-dimensional island shape is investigated.     

Control of surface wettability via strain engineering

Reversible control of surface wettability has wide applications in lab-on-chip systems, tunable optical lenses, and microfluidic tools. Using a graphene sheet as a sample material and molecular dynamic simulations, we demonstrate that strain engineering can serve as an effective way to control the surface wettability. The contact angles θ of water droplets on a graphene vary from 72.5 to 106 under biaxial strains ranging from 10% to 10% that are applied on the graphene layer. For an intrinsic hydrophilic surface (at zero strain), the variation of θ upon the applied strains is more sensitive, i.e., from 0 to 74.8 . Overall the cosines of the contact angles exhibit a linear relation with respect to the strains. In light of the inherent dependence of the contact angle on liquid-solid interfacial energy, we develop an analytic model to show the cos θ as a linear function of the adsorption energy E ads of a single water molecule over the substrate surface. This model agrees with our molecular dynamic results very well. Together with the linear dependence of E ads on biaxial strains, we can thus understand the effect of strains on the surface wettability. Thanks to the ease of reversibly applying mechanical strains in micro/nano-electromechanical systems, we believe that strain engineering can be a promising means to achieve the reversibly control of surface wettability.     

Effect of impingement angle on the outcome of single water drop impact onto a plane water surface

Experiments of single water drop impact onto a plane water surface were carried out to investigate the effect of impingement angle on the total mass of secondary drops produced during the collision. When the impingement angle (the angle between the velocity vector of primary drop and the normal vector to water surface) was less than 50°, an increase in the impingement angle led to a remarkable increase in the total mass of secondary drops; this could be attributed to a significant increase in the secondary drop size. However, no secondary drop was observed within the experimental ranges tested when the impingement angle exceeded 70°.     

Effects of oxidation and surface roughness on contact angle

Contact angle is known to be a parameter that effects boiling. This study was undertaken to measure contact angle of high and low surface tension fluids on copper and aluminum surfaces.Data were taken for polished, oxidized, and rough surfaces. A simple, yet fairly accurate method of measuring the static equilibrium contact angle of a solid/liquid interface is presented. The principles of a line light source and tilting plate were modified and then combined in the design of this apparatus. The angles obtained and their variation with the solid surface properties were in good agreement with previously published data. The contact angle of distilled water o of the organic fluids and refrigerants tested were in the range of 2–5°. Roughness and oxidation reduce the contact angle. If the depth of the roughness is less than 0.5 μm contact angle. The apparatus is fairly simple in construction, is inexpensive, and has good reproductibity. The measured angles were then compared to those measured with the sessile drop method.     

Numerical and experimental studies of natural convective heat transfer from vertical and inclined narrow isothermal flat plates

Natural convective heat transfer from an isothermal narrow flat plate embedded in a plane adiabatic surface and inclined at moderate positive and negative angles to the vertical has been numerically and experimentally studied. The solution has the Rayleigh number, the dimensionless plate width, the angle of inclination, and the Prandtl number as parameters. Attention was restricted to a Prandtl number of 0.7. The numerical results have been obtained for Rayleigh numbers between 10³ and 10⁷ for dimensionless plate widths of between 0.3 and 1.2 and for angles of inclination between +45° and −45°. In the experimental study, results have been obtained for Rayleigh numbers between 4 × 10² and 10⁵ for dimensionless plate widths of 0.4 and 2.5 and for angles of inclination between +45° and −45° to the vertical. Empirical equations for the heat transfer rate have been derived.     

RUPTURE OF THIN METAL TUBES BY NORMAL AND OBLIQUE IMPACT OF BLUNT CONICALNOSED MISSILES: EXPERIMENTS

Impact tests at both normal and oblique angles of incidence were conducted on thin mild tubes using a moderate size of 90° conical-nosed missiles. The minimum impact speed that generated cracks through the thickness of the wall, termed the speed for rupture, was measured, and various modes of rupture were identified. For a thin tube hit by a missile at a normal angle of obliquity at the speed for rupture, the contact region spreads across the nose of the missile, and the transverse shear deformation is predominant in the final failure process. If the angle of obliquity is 30°, the missile pierces a hole through the wall of the tube. At the speed for rupture, the kinetic energy of the missile for oblique angle 30° is only about 45% that required for plugging at a normal angle of obliquity. The project sponsored by National Natural Science Foundation of China(No. 19842001, 19872048) and Scientific Research Foundation for Returned Overseas Chinese Scholars of State Education Commission and Shanxi Province of China.     

Measurements of the contact angle between R134a and both aluminum and copper surfaces

Measurements of quasi-static advancing contact angles of refrigerant R134a on copper and aluminum surfaces are reported over a temperature range from 0 °C to 80 °C. The metal surfaces tested were aluminum (alloy 3003) and copper (alloy 101) plates. Measurements were done using a direct optical observation technique where the liquid meniscus at the surface of a vertical plate was captured using a high magnification camera system. The contact angle of solid–liquid interface was deduced by enhancing and manipulating the digital image using solid modeling software by drawing a tangent line to the meniscus at the intersection location of the solid, liquid and vapor. Values of the contact angle were found to vary between 8.3° and 5.6° for aluminum and between 5.1° and 6.5° for copper when the temperature rose from 0 °C to 80 °C. Maximum standard deviation amongst the measured values of contact angles was 1.3°.     

Drag force on a free surface-piercing yawed circular cylinder in steady flow

The force distribution on a surface-piercing yawed cylinder surface differs significantly from that on a surface-piercing vertical cylinder. The established numerical model for flow past the surface-piercing yawed cylinder with yaw angles from −45° to 45° was solved by the standard large-eddy simulation (LES) methodology. Six cases at intervals of ±15° relative to the vertical were studied at the Reynolds number of 27 000 and the Froude number of 0.8 based on the cylinder diameter and free-stream velocity, among which the drag forces on four cylinders with yaw angles from −15° to 30° were tested for the validation of the LES approach. The results revealed that the time-averaged total drag coefficient for all cases increases with the increase of yaw angle compared to that of the surface-piercing vertical cylinder, even over 2.5 for the ±45°-yawed cylinders. The sectional drag coefficients for the negatively yawed cylinders are much greater than that for the vertical cylinder, and much less for the positively yawed cylinders. The unbalanced hydrostatic pressures on the inclined section are mainly responsible for those increment and decrement. Once the hydrostatic pressure was removed, the sectional drag coefficient on the mid-span of the positively yawed cylinder increases from the top section to the bottom, and decreases for the negatively yawed cylinder. The corresponding integrated total drag coefficient decreases with the increase of the yaw angle to ±15°, then increases with the further increase of the magnitude of yaw angle.