Frictionless Liquid Research Articles

Hierarchical ‘rose-petal’ ZnO/Si surfaces with reversible wettability reaching complete water repellence without chemical modification

Smart surfaces with externally controlled wettability patterns are ubiquitous building blocks for micro-/nanofluidic and lab-on-chip devices, among others. We develop hierarchical surfaces of ZnO nanorods grown on laser-microstructured silicon with reversible photo-induced and heat-induced wettability. The as-prepared surfaces are superhydrophilic, with very low water contact angles (~ 10°), and transition to a wetting state with high water contact angles (~ 150°) when annealed in vacuum. As the annealing temperature increases to 400 °C, the surfaces become completely water-repellent. Even though the annealed surfaces present high water contact angles, at the same time, they are very adhesive for water droplets, which do not roll off even when tilted at 90° or 180o (rose-petal effect), unlike standard hydrophobic surfaces which typically combine high water contact angles with low roll-off angles. The surfaces return to the superhydrophilic state when irradiated with UV light, which indicates a reversible wettability with external stimuli. Based on this transition, we demonstrate local modification of the wetting state of the surfaces by UV irradiation through a mask, which results in directed liquid motion, useful for microfluidic applications. The high contact angles obtained in this work are usually obtained only after chemical modification of the ZnO surface with organic coatings, which was not necessary for the hierarchical surfaces developed here, reducing the cost and processing steps of the fabrication route. These rose-petal surfaces can be used as “mechanical hands” in several applications, such as no-loss transport of small liquid volumes, precision coatings, spectroscopy, and others. Furthermore, the completely water-repellent surfaces, rarely reported elsewhere, may find important applications in frictionless liquid transport for microfluidic and other devices.

Viscous oscillations in a circular cylindrical tank with elastic surface cover

In order to shift the frequencies of a liquid with a free surface away from dangerous system frequencies, the surface of the liquid may be covered with a flexible membrane or a thin elastic plate. The magnitude of such a frequency shift depends on the parameters of the liquid and those of the structural system and should be known for the design of an aerospace vehicle. For that reason, we treat a rigid circular cylindrical large aspect ratio container filled with incompressible and viscous liquid, being covered by an elastic structure. The coupled frequencies and the decay magnitudes are determined for the lower vibration modes. The fact that we deal with a large aspect ratio tank, where the liquid close to the bottom of the container exhibits only small velocities, suggests that the adhesive bottom conditions may be deleted, while those at the side wall of the container are mainly contributing to the damping and are for that reason considered in the analysis. We determine the complex frequencies of the hydroelastic system. The results show that the coupled frequencies increase with increasing liquid height ratio and reach soon a nearly constant value, which is being reached much earlier for higher modes. The decay magnitude also reaches quickly a constant value. Higher modes are damped out fast. In addition, it was found that the coupled oscillation frequencies are always larger than those of the frictionless liquid, and that the difference between them decrease considerably with increasing mode numbers.

Axisymmetric Surface Oscillations in a Cylindrical Container with Compensated Gravity

In this study the first mode of axisymmetric surface oscillations of a free liquid interface in a partly filled right circular cylinder under compensated gravity is investigated numerically. The situation is similar to a spacecraft that enters a ballistic flight at the end of thrust. A reorientation of the liquid of the free liquid surface toward the new equilibrium position takes place. The characteristics of this flow, such as the frequency and the damping, are governed by the behavior of the contact line. The investigations focus on the dependence on the contact line boundary condition, including contact angle variation, and on viscous effects. The effect on the natural frequency and the damping is considered. An analytical approximation for the frequency behavior for a frictionless liquid for a free and a fixed contact line condition is given. Further analytical approximations for the damping behavior in dependence on the contact angle and the Ohnesorge number are determined. The numerical results show very good agreement with experimental data.

Oscillations of captured spherical drop of viscous liquid

The complex frequencies of a viscous spherical drop where part of the free surface is embedded in a rigid spherical cap of the same radius have been determined as a function of the cap angle and the free surface tension parameter. With increasing cap angle α , the oscillation frequencies and decay magnitudes increase. This is also true for liquid drops of larger surface tension parameters. It also could be found, as has been found previously for a free floating sphere of viscous liquid, that the oscillations may cease to exist for certain diameters and low surface tension parameters, a fact not present in the treatment of frictionless liquid. In such cases, the captured liquid globule performs just an aperiodic motion. Three different liquid systems have been considered. In addition, the response of a captured spherical drop due to harmonically forced vertical translational excitation of the cap has been determined. Only a liquid sphere embedded in a spherical cap of the same radius has been evaluated numerically. The results reveal that for the mode n = 1 the geometry of a liquid sphere in a spherical cap of equal radius represents—depending on the magnitude α of the cap—for small surface tension parameters σ * ≡ σ a ρ / η 2 , a stable configuration, while for large σ * -values the spherical geometry is unstable, indicating that for those large cases the free liquid surface assumes a different geometry.

Hydroelastic vibrations in a two-dimensional rectangular container filled with frictionless liquid and a partly elastically covered free surface

For a structure partially covering the free liquid surface of a two-dimensional rectangular container of infinite width, length l and a filling grade of height h hydroelastic vibrations have been treated for a frictionless liquid. It was found that with a partial covering of the free surface the lower coupled frequencies increase with structural area, yielding in addition a calmed down motion of the liquid. It also was found that the coupled frequencies stay always below those of the case of the rigid surface covering.

Oscillations of captured spherical drop of frictionless liquid

The natural frequencies and mode shapes have been investigated for a frictionless spherical liquid globule where part of the free surface is embedded in a spherical cap of the same radius. Five different liquid systems have been considered. With increasing cap angle α and higher modes n, the natural frequencies increase. The different mode shapes exhibit a drastic change of frequencies. In addition, the response of the captured spherical drop due to harmonically forced translational excitation of the rigid cap has been determined for the two major directions.

HYDROELASTIC COUPLED VIBRATIONS IN A CYLINDRICAL CONTAINER WITH A MEMBRANE BOTTOM, CONTAINING LIQUID WITH SURFACE TENSION

A linear free hydroelastic vibration analysis of a frictionless liquid with a free surface contained in a cylindrical tank with a flexible bottom has been performed. The side-wall has been treated as rigid and the effect of surface tension taken into consideration. The container bottom was treated as a membrane, while for the free liquid surface the effect of two contact line conditions has been investigated. One edge condition was that of a slipping contact line, while the other one treated the contact line as fixed, ie., an anchored edge. The vibration characteristics of a membrane–liquid coupled system have been investigated for various system parameters, i.e., membrane tension parameter T, liquid surface tension parameter σ, material density parameter ρ, liquid height ratio ℓ0 and vibration mode numbers m and n. The degree of coupling between a membrane and a liquid was represented with vibration mode diagrams as well as with frequency diagrams. For axisymmetric coupled vibrations with anchored edge condition, vibration mode exchanging of both a membrane and liquid free surface with membrane bottom tension parameter T has been investigated. An interesting phenomenon which is only observed for a flexible bottom container and an anchored edge free surface condition is presented.

Free and forced oscillations of a frictionless liquid in a long rectangular tank with structural obstructions at the free liquid surface

If a free liquid surface is partly covered with a solid wall, the natural frequencies and the response of the liquid in the container may be drastically changed. The fundamental natural frequency of a frictionless and incompressible liquid in an infinitely long rectangular container is determined for increasing structural coverage of the free surface. With increasing coverage of the surface by a rigid structural member, the natural frequencies increase drastically and reduce the sloshing motion. The response to translational excitation is evaluated also numerically.

HYDROELASTIC VISCOUS OSCILLATIONS IN A CIRCULAR CYLINDRICAL CONTAINER WITH AN ELASTIC COVER

If the surface of a viscous liquid is completely covered by an elastic structure, the hydroelastic frequencies are shifted to a larger magnitude than those obtained with a free surface. It was found that viscosity decreases the oscillation frequencies in comparison to the coupled hydroelastic frequencies of frictionless liquid and that a new phenomenon appears, exhibiting for certain liquid height ranges h/a only aperiodic motion. With increasing angular and radial mode numbers these aperiodic ranges of h/a decrease. Higher modes show larger damping. An increase in the membrane tension decreases the aperiodic region, while an increase in the mass of the membrane increases it.

VIBRATION OF A HYDROELASTIC SYSTEM CONSISTING OF A SECTOR SHELL AND VISCOUS LIQUID IN ZERO GRAVITY

For a circular sector system consisting of an elastic shell to which an incompressible and viscous liquid layer is attached, the coupled liquid-structure frequencies are determined under zero gravity conditions. The influence of the viscosity of the liquid, the flexibility of the shell, the thickness of the liquid layer and the Ohnesorge number have been determined for freely slipping and anchored contact lines. With increasing shell flexibility the oscillation frequencies decrease and exhibit a smaller magnitude for a viscous liquid than for a frictionless liquid. In addition, we observe a phenomenon not present in a system with frictionless liquid, involving regions of only aperiodic motion. In these regions, depending mainly on viscosity (Ohnesorge number) and liquid layer thickness, the hydroelastic system cannot perform any oscillatory motion. A motion identification chart is presented showing that for large Ohnesorge number Oh≡(ρν2/σa)1/2only very thick liquid layers are able to perform oscillatory motions. Increasing the flexibility of the shell results in an increased region of aperiodic motion.

Oscillations of a viscous liquid in a cylindrical container

The natural damped frequencies of a viscous liquid in a circular cylindrical container are obtained for slipping and anchored contact line at the container wall r = a. In addition the response to translational forced excitation has been determined. The results may also be applied to viscous liquid in a micro-gravity environment, as long as the contact angle of the liquid surface to the cylindrical container wall is in the vicinity of π 2 , indicating, that the free liquid surface equilibrium position remains a plane surface. It could be found that there exists in contrast to frictionless liquid a small filling range, in which the liquid performs only an aperiodic motion. The adherence condition at the side wall was replaced by the somewhat weaker condition of an anchored contact line.

Axisymmetric oscillations in a slowly rotating cyclindrical container filled with viscous liquid

For a slowly rotating cylindrical container filled with an incompressible and viscous liquid the axisymmetric damped natural frequencies are obtained for a slipping and an anchored contact line of the equilibrium free liquid surface at the container wall. It was found that there exists in contrast to frictionless liquid a range where only aperiodic motion of the liquid is possible. The influence of an increase of the speed of spin was found to be an increase of the oscillation frequency at nearly constant decay magnitude.

Axisymmetric viscous liquid oscillations in a cylindrical container

The axisymmetric natural damped frequencies (m=0) of a viscous liquid in a cylindrical container are obtained for slipping and anchored contact line at the container wall. The results may also be applied to viscous liquid in a micro gravity environment, if the contact angle of the contact line to the container wall is in the vicinity of π/2, indicating that the free liquid surface remains a plane surface in equilibrium. It was found that there exists, in contrast to frictionless liquid, a range where only aperiodic motion of the liquid is possible. This appears for small liquid height ratios h/a.

Vibrations of an infinitely long flowing liquid jet—Influence of spin and axial flow

For an infinitely long liquid column the influence of axial flow velocity and spin has been investigated. The results are exhibited for axisymmetric mode m=0 and asymmetric modes m=1 and 2. A frictionless liquid shows with the increase of axial flow an increase of the frequency in flow direction and a decrease of the oscillation frequency in the opposite flow direction for axisymmetric motion. It also means that a larger surface tension, larger diameter or larger density of the liquid column exhibit the same behavior. For asymmetric motions the effect of axial velocity w0 is the opposite. With increasing axial wave length the natural frequencies decrease. At certain axial speed magnitudes both waves move in flow direction with different magnitude. The effect of increasing spin is a decrease of natural frequencies\(\frac{\omega }{{2\Omega _0 }}\) and an instability for smaller axial wave lengths. Viscous effects show usually smaller oscillation frequencies.

Anchored edge pitching response of a spinning frictionless liquid column due to bottom and/or top excitation

The response of an anchored spinning frictionless liquid bridge to different pitching top and/or bottom excitation has been determined. The free surface displacement is obtained for synchronous, counter-excited and one-sided pitching excitation as a function of the dimensionless forcing frequency\(\bar \Omega = \Omega /\sqrt {\sigma /(\varrho \alpha ^3 )}\). The contactlines at the rim of the upper and lower discs are considered to be anchored. In synchronous pitching excitation only the even resonances show response peaks, while in a counter-excited system only odd resonances appear, which is in contrast to axial excitation modes. For one-sided excitation, all reasonances appear. Because of the different natural frequencies in direction of spin and opposite to it double peaks are present in the responses.

Coupled frequencies of a liquid in a circular cylindrical container with elastic liquid surface cover

The coupled hydroelastic frequencies of an incompressible and frictionless liquid in a circular cylindrical container, of which the free liquid surface is covered by a flexible membrane or an elastic plate, have been determined analytically. Various boundary conditions for the plate have been observed. Numerical values are presented for a membrane cover of various tension and mass per unit area and for a plate cover of different flexural rigidity.

Coupled Frequencies of a Hydroelastic System of an Elastic Two-Dimensional Sector-Shell and Frictionless Liquid in Zero Gravity

For a circular sector system consisting of an elastic shell and an incompressible frictionless liquid layer with a free surface, the coupled liquid-structure frequencies are determined and compared with the natural (uncoupled) frequencies of the shell and the liquid. The coupled frequencies always exhibit smaller values than those of liquid and shell alone. The deviation increases with decreasing thickness of the liquid layer.

Response of an anchored frictionless liquid bridge to pitching bottom and/or top excitation

The natural frequencies and response of a circular cylindrical liquid bridge consisting of incompressible and non-viscous liquid has been determined. Three cases of pitching excitations have been treated: synchronous- and counter-excitation of the end discs, as well as the pitching excitation of only one end disc. The contact lines were considered to be anchored at the end discs.

Response of a solidly rotating amphora-type liquid column to axial excitation

The response of a solidly rotating finite liquid column, which under the action of an axial gravity assumes an amphora-type equilibrium position, has been determined to axial excitation. The column consists of incompressible and frictionless liquid. The response of the free surface elevation has been obtained for the elliptic ( Ω > 2Ω 0 ) frequency range.

Coupled frequencies of a hydroelastic system of an elastic two-dimensional sector-shell and frictionless liquid in zero gravity

For a circular sector system consisting of an elastic shell and an incompressible frictionless liquid layer with a free surface, the coupled liquid-structure frequencies are determined and compared with the natural (uncoupled) frequencies of the shell and the liquid. The coupled frequencies always exhibit smaller values than those of liquid and shell alone. The deviation increases with decreasing thickness of the liquid layer.