Ballistic Jumping Drops on Superhydrophobic Surfaces via Electrostatic Manipulation

The ballistic ejection of liquid drops by electrostatic manipulating has both fundamental and practical implications, from raindrops in thunderclouds to self‐cleaning, anti‐icing, condensation, and heat transfer enhancements. In this paper, the ballistic jumping behavior of liquid drops from a superhydrophobic surface is investigated. Powered by the repulsion of the same kind of charges, water drops can jump from the surface. The electrostatic acting time for the jumping of a microliter supercooled drop only takes several milliseconds, even shorter than the time for icing. In addition, one can control the ballistic jumping direction precisely by the relative position above the electrostatic field. The approach offers a facile method that can be used to manipulate the ballistic drop jumping via an electrostatic field, opening the possibility of energy efficient drop detaching techniques in various applications.     

Stability of sessile and pendant liquid drops

The solution space of axisymmetric liquid drops attached to a horizontal plane is investigated, and the stability of hydrostatic shapes is assessed by a novel numerical linear stability analysis involving discrete perturbations. For a given contact angle and Bond number, multiple interfacial shapes exist with compact, lightbulb, hourglass, and more convoluted pearly shapes. It is found that more than one solution branch can be stable, and that negative curvature at the contact line of a pendant drop is not a prerequisite for instability. Numerical simulations based on the boundary-integral method for Stokes flow illustrate the process of unstable drop detachment. Unstable drops transform into elongated threads with a spherical head whose volume is determined by a Bond number expressing the significance of surface tension. A complementary investigation of the shape and stability of two-dimensional drops attached to a horizontal or inclined plane reveals that hydrostatic shapes are least stable in the inclined configuration and most stable in the pendant or sessile configuration.     

The influence of electrostatic fields on films of liquid helium

Prompted by the recent striking experimental results reported by Babkin and Hakonen that appeared to show that liquid helium-II does not wet magnesium fluoride, we have examined the effects that an inhomogeneous electrostatic field has on thin films of liquid helium at temperatures below 0.5K. Our model includes the influence of gravity, surface tension, the electric field and the van der Waals interaction between the helium and its supporting substrate. We show that, an inhomogeneous charge on the substrate can produce effects that mimic the surface profiles between wetted and non-wetted areas. The calculations also indicate that some special precautions may be necessary when studying films of liquid or solid helium on insulators.     

Influence of Bond Number on Behaviors of Liquid Drops Deposited onto Solid Substrates

The problem of spreading behaviors of pendant and sessile drops was studied experimentally and numerically under the action of gravity force and surface tension. Bond number was considered to be a main factor of the influence on shape behaviors of liquid drops. This study was performed in the framework of an experimental investigation of drop behaviors in microgravity onboard a Chinese satellite in future. The experiments were carried out in the Drop Tower of Beijing, which could supply about 3.6?s of microgravity (free-fall) time. The surface shape change of liquid drops was investigated and the contact angle variety in sessile and pendant drops were measured from normal gravity to microgravity. A sharp decrease and oscillatory variation of the contact angle for both sessile and pendant drops were found with the sudden decrease of Bond number. The succedent comparison between experimental and numerical results suggests that Bond number has a significant influence on the drop contact angle. Additionally, the drop shapes and the bulk flows inside sessile and pendant drops were analyzed numerically, and it was found that the bulk flows could affect the free-surface shape of liquid drops apparently. Comparison of the moving velocity of contact line between sessile and pendant drops indicated that the pendant drops had a faster response to Bond number.     

The surface tension of liquid aluminium-based alloys

In a systematic study, the surface tensions of the binary alloys Al–Fe and Al–Ni were investigated over a wide temperature and concentration range using electromagnetic levitation and the oscillating drop technique. Surface tensions were derived from the oscillation frequencies applying the formalism of Cummings and Blackburn. Temperature was measured by single-color pyrometry. Of particular interest in these alloys are melts corresponding to compositions of intermetallic phases, because potential ordering phenomena may influence all thermophysical properties. In both systems, an increase of the surface tension is observed at such concentrations. On the basis of partial excess Gibbs enthalpies, surface tensions can be calculated via the Butler equation and compared with experimental results. The agreement with our experimental data depends crucially on the quality of the thermodynamic potentials used. In addition, phenomenological models are also discussed, which describe the general trend correctly.     

Surface Tension Measurements of Liquid Metals by the Quasi-Containerless Pendant Drop Method

The surface tensions of liquid metals, Zr, Ni, Ti, Mo, and Nb, have been measured at their melting points using the quasi-containerless pendant drop method. This method involves melting the end of a high-purity metal rod by bombardment with an electron beam to form a pendant drop under ultrahigh-vacuum conditions to minimize surface contamination. The magnified image of the drop is captured from a high-resolution CCD camera and digitized using a frame-grabber. The digital image is analyzed by reading the pixel intensities from a graphics file. The edge coordinates of the drop along rows and columns of pixels are searched by a computer program and stored in an array. An optimized theoretical drop shape is computed from the edge coordinates by solving the Young–Laplace differential equation to deduce the surface tension. The measured surface tensions are compared with available experimental results and theoretical calculations.     

Oscillations of Charged Helium II Drops

We report on an experimental study of the shape oscillations of charged helium drops levitated with a magnetic field. Shape oscillations are excited with an AC electric field. Many different modes of oscillation of the drop are observable. The resonant frequencies of the drops are found to be a function of amplitude. Quantitative measurements of the damping of shape oscillations are made by using a laser beam focused through the drop. The observed damping of shape oscillations is found to be greater than the damping due to the viscosities of the liquid and the surrounding vapor. Other mechanisms possibly responsible for this damping are discussed. We also report experiments on drops with angular momentum.     

Multidimensional analysis of poly(ethylene glycols) by size exclusion chromatography and dynamic surface tension detection

Substantial improvements in a multidimensional dynamic surface tension detector (DSTD) are presented. Rapid, online calibration and measurement of the dynamic surface tension for high-performance liquid chromatography separations is achieved. Dynamic surface tension is determined by measuring the differential pressure across the liquid-air interface of repeatedly growing and detaching drops. Continuous surface tension measurement throughout the entire drop growth (50 ms to 2 s) is achieved, for each eluting drop, providing insight into the kinetic behavior of molecular orientation processes at the liquid-air interface. Three-dimensional data are obtained, with surface tension first converted to surface pressure, which is plotted as a function of elution time axis versus drop time axis. Two key innovations will be reported. First, a novel calibration procedure is described and implemented. Differential pressure signals from three drops (mobile phase, standard in mobile phase, and analyte in mobile phase) are utilized to make the dynamic surface tension measurement, thereby eliminating the need for optical imaging, and viscosity and hydrostatic pressure corrections, as required by other methods. Only pressure signals from one mobile-phase drop and one standard drop pressure signal are required, while the analyte drop pressure signal is measured along the chromatographic time axis. Second, corrections for drop elongation are not required, because the drops are precisely detached by an air burst actuation method in a regime were the surface tension forces significantly dominate gravitational forces. Drops that would fall with a volume of approximately 10 microL due to gravity are precisely and repeatedly detached earlier at a volume of 2 microL. The sensitivity and unique selectivity of the DSTD opens up new possibilities in the analysis of small molecular weight polymers of varying degrees of surface activity, as illustrated for the size-exclusion chromatography analyses of complex poly(ethylene glycol) (PEG) samples. Using partial least squares for data analysis, polydispersity of complex PEG samples is determined at a relative precision of approximately 1%.     

Surface tension of mercury on glass,molybdenum and tungsten substrates

The surface tension of mercury on a glass substrate has been determined by the sessile drop technique. It was found that the uncorrected value of surface tension varied with changes in the drop diameter in the range from 0.60 to 4.10 cm. From the Worthington equation for curvature a corrected surface tension of 456 dyn/cm was obtained for the 4.1 cm diameter drop, a value which is in reasonable agreement with previous investigations. However, application of a curve fitting procedure to the results from the smaller drops gave a corrected surface tension which was approximately independent of diameter but at a smaller average value of 413 dyn/cm. The surface tension of a 1.20 cm diameter drop was also measured on tungsten and molybdenum substrates and, in general, corrected values larger than on glass were derived. It is suggested that the small corrected values obtained for drops ⩽2.06 cm in diameter are due to adsorption of impurity from the glass substrate.     

Breakup and deformation of a falling droplet under high voltage electric field

In this paper the lattice Boltzmann method (LBM) is employed to simulate deformation and breakup of a falling drop under gravity and electric field. First the two-phase LBM is applied to verify the Laplace law for static drops. Then relaxation of a square droplet is conducted. Furthermore a comparison is made with Taylor theoretical results for different electrical capillary number, permittivity and conductivity ratio. It is seen that with permittivity ratio larger than conductivity, droplet takes an oblate and for lower ratio takes prolate shape. It is seen that for relatively low Eotvos number where the surface tension is a dominant factor and for high Ohnesorge number where the viscosity plays an important role shear breakup occurs. On the other hand it is also found that by increasing the Eotvos number and decreasing Ohnesorge number drop distorts more and back breakup happens in addition to shear breakup.     

An automatic technique for measuring the surface tension of liquid metals

A methodology for automatic measurement of surface tension of liquid metals is presented. The procedure involves the digitization of a television image of a drop of the liquid metal, image processing to obtain the real coordinates of the drop profile, and a final computation of the drop surface tension by a nonlinear regression technique. The method is faster and more reliable than other classical methods, and yields results that are reproducible and as precise as those obtainable by non-automatic procedures. An important feature of this approach is that it can be used for metallurgical tests to check the quality of an alloy during its production, or to provide surface tension data in non-equilibrium processes.     

Electric Field Gradient Theory with Surface Effect for Nano-Dielectrics

The electric field gradient effect is very strong for nanoscale dielectrics. In addition, neither the surface effect nor electrostatic force can be ignored. In this paper, the electric Gibbs free energy variational principle for nanosized dielectrics is established with the strain/electric field gradient effects, as well as the effects of surface and electrostatic force. As regards the surface effects both the surface stress and surface polarization are considered. From this variational principle, the governing equations and the generalized electromechanical Young-Laplace equations, which take into account the effects of strain/electric field gradient, surface and electrostatic force, are derived. The generalized bulk and surface electrostatic stress are obtained from the variational principle naturally. The form are different from those derived from the flexoelectric theory. Based on the present theory, the size-dependent electromechanical phenomenon in nano-dielectrics can be predicted.     

The relation of steady evaporating drops fed by an influx and freely evaporating drops

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning.     

Surface tension of nickel, copper, iron and their binary alloys

The surface tension of liquid binary alloys of the Cu-Ni-Fe system is measured by using the oscillating drop technique. The samples are processed contactlessly in an electromagnetic levitation chamber and hence, considerably large undercooling can be achieved. The alloys and the pure elements copper, nickel, and iron are investigated at various temperatures above and below their melting points. In addition, the surface tensions are also investigated as a function of the concentrations at constant temperature. The values agree well with predictions from theory and an analysis of the segregational behaviour is performed.     

Three-dimensional instabilities of ferromagnetic liquid bridges

The cross section of a ferromagnetic liquid drop held in equilibrium between horizontal plates in a magnetic field loses its circular symmetry past a critical value of the applied field strength. This is caused by instabilities that give way to non-circular cross sectional shapes which, in turn, produce three-dimensional magnetic field distribution inside and outside the drop. Theoretical predictions of equilibrium non-circular shapes and their stability are drawn from the equations governing the magnetohydrostatic equilibrium of the drop. The computational problem is three-dimensional, nonlinear and free boundary and it is solved with the Galerkin/finite element method. Entire branches of circular solutions and non-circular ones are traced by continuation in multi-parameter space. Circular, elliptical and dumbbell-shaped drops have been found. The relative stability of the various shapes is computed by means of computer-implemented bifurcation theory.     

Ballistic transport and electrostatics in metallic carbon nanotubes

We calculate the current and electrostatic potential drop in metallic carbon nanotube wires self-consistently by solving the Green's function and electrostatics equations in the ballistic case. About one-tenth of the applied voltage drops across the bulk of a nanowire, independent of the lengths considered here. The remaining nine-tenths of the bias drops near the contacts, thereby creating a nonlinear potential drop. The scaling of the electric field at the center of the nanotube with length (L) is faster than 1/L (roughly 1/L/sup 1.25-1.75/). At room temperature, the low bias conductance of larger-diameter nanotubes is larger than 4e/sup 2//h due to occupation of noncrossing subbands. The physics of conductance evolution with bias due to Zener tunneling in noncrossing subbands is discussed.     

Specific Charge Measurements in Electrostatic Air Sprays

An experimental study of the effects of both nozzle parameters and fluid properties on specific charge and ratio of ion to drop current for electrostatic air sprays is reported. The specific gun used and the parameter ranges investigated are indicative of many industrial painting processes. A simple collector system that discriminates between drop and ion currents was used to measure ensemble averaged specific charge for the drops and the ratio of ion to drop current. The data exhibit a coupled dependence on applied potential, liquid flow rate, atomizing airflow rate, and fluid properties. The trends are consistent with contact charging of the liquid and ion generation during breakup of the bulk liquid into drops. Specific charges range from zero to nine μC/g and the ratios of ion to drop currents from zero to six. Analysis of the current ratios indicates that under many conditions the ion charge density near the substrate is small in comparison to the drop charge density. Consequently, the ion charge density may be neglected and only the drop charge density must be considered in simulating the electrostatic fields.     

Viscosity measurement using drop coalescence in microgravity

We present in here validation studies of a new method for application in microgravity environment which measures the viscosity of highly viscous undercooled liquids using drop coalescence. The method has the advantage of avoiding heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Homogeneous nucleation can also be avoided due to the rapidity of the measurement using this method. The technique relies on measurements from experiments conducted in near zero gravity environment as well as highly accurate analytical formulation for the coalescence process. The viscosity of the liquid is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity for two coalescing drops. Results are presented from two sets of validation experiments for the method which were conducted on board aircraft flying parabolic trajectories. In these tests the viscosity of a highly viscous liquid, namely glycerin, was determined at different temperatures using the drop coalescence method described in here. The experiments measured the free surface velocity of two glycerin drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The liquid viscosity was determined by adjusting the computed free surface velocity values to the measured experimental data. The results of these experiments were found to agree reasonably well with the known viscosity for the test liquid used.     

The Stability of the Superfluid 3He AB Interface Pinned in an Aperture

We have been measuring the surface tension of the AB interface at zero pressure, in high magnetic fields and low temperatures below 0.2 T _c. We manipulate the phase boundary by controlling a magnetic field profile. We use the latent heat released/absorbed as the phase boundary moves to infer its position and velocity. We have observed that the motion of the interface through a small aperture is dependent on the magnetic field gradient. Here we extend numerical methods first used to calculate the shapes of liquid drops in a gravitational field to show that the gradient dependence can be accounted for by the deformation of the interface.