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Droplet oscillations driven by an electric field
... Many modern studies in the field of physics and chemistry are based on the analysis of shape oscillations of liquid droplets and bubbles (Milne et al., 2014;Zografov et al., 2014). The main applications of these studies are in the field of surface tension measurements, in examining viscoelastic properties of liquids (Meier et all, 2000;Zografov et al., 2013) and in fundamental studies (Noblin et al., 2005). ...
... The oscillating drop technique, for measuring properties of liquids and studying the interface of a droplet, has been analyzed and reviewed widely in literature (Milne et al. 2014;Zografov et al 2014;Meier et al. 2000;Mettu et al. 2012). Most of the theoretical analyses are based on the pioneering work of Rayleigh, considering resonant modes of an ideal liquid sphere (Rayleigh, 1882). ...
... oscillation frequencies) are detected by an optical system comprising of a weak laser beam and a photodiode. Detailed description of the technique has been published elsewhere (Zografov et al., 2014;Тankovsky et al., 2011;Tankovsky et al., 2013). With the help of the proposed stroboscopic technique, images of droplet shapes in resonant modes 2 n and 3 n were observed. ...
A simple and affordable stroboscopic imaging technique for studying liquid droplet shape oscillations is proposed. It's based on regular PC sound card I/O capabilities, a standard web camera, used as an imaging device, and free software. The sound card is used as a functional generator sending wave-form signals to the light source and is simultaneously used as an oscilloscope. The webcam captures images or videos that can be obtained and either analyzed in real time or saved for further analysis. In the present work, we describe the theoretical bases, technical details, the capabilities and limitations of the developed stroboscopic technique. Experimental results of study on shape oscillations up to 300 Hz of millimeter-sized pendant or sessile water droplets are reported.
... The solution for the lowest resonant mode n = 1 yields ω 01 = 4.415. This result coincide with our previous experiments with hemispherical pendant droplet [12,13]. Let's remind, this consideration is applicable only for small oscillation amplitudes and small bond numbers of hemispherical, pendant or sessile droplets with an anchored edge. ...
... Resonant droplet tensiometry [2,12,13] is an experimental technique for studying resonant frequencies of pendant droplets with very small Bond numbers - Fig 2a. The oscillations are driven by a modulated dielectrophoretic force exerted directly on the droplet's interface [17] - Fig. 2c. ...
An experimental study of the lowest resonant mode of spherical and hemispherical pendant droplets with low
Bond numbers (less than 0.1) is proposed. The resonant frequency was determined by Resonant Droplet Tensiometry
(RDT), where the forced oscillations are driven by an electric field. The main aim of the study is to demonstrate the
influence of the supporting surface radius as well as the droplet radius on the resonant frequencies of small pendant
droplets. For that purpose, precisely crafted and polished metal and PTFE surfaces, different in radius, were used to
support spherical or hemispherical droplets of deionized water driven in oscillations by a frequency modulated
dielectrophoretic force. Experimentally obtained resonant frequencies of the lowest resonant mode were used to calculate
the dimensionless eigenfrequencies with respect to the droplet radius. The results are compared with other theoretical
studies.
... These droplets are difficult, or even impossible to study with the widely used axisymmetric drop shape analysis (ADSA) techniques because small droplets are not deformed noticeably by the gravity [6]. The "Resonant Droplet Tensiometry" (RDT) is capable of determining the surface tension and to studying surface and other properties of very small droplets since it doesn't rely on the shape analysis, it uses the droplet resonant frequency instead [7,8]. The proposed RDT driven by an electric field, uses a combination of AC and DC electric field in order to generate frequency modulated dielectrophoretic force and to drive the droplets in to axisymmetric resonant oscillations [9]. ...
... Details about the implementation of RDT can be found in details in our previous works. In tensiometric mode RDT was successfully used for surface tension measurements of small droplets of aqueous solutions with accuracy of 2% [5,7]. The viscosity of glycerol mixtures with different concentrations were studied using Q-factor approach [8]. ...
A submillimeter sized pendant spherical droplet is placed in a nonuniform electric field. Combination of AC
and DC electric field generates a frequency modulated dielectrophoretic force. Caused by the dielectric permittivity jump
over the liquid-air interface, the force acts directly upon the interface. Thus the droplet is set in to forced axisymmetric
oscillations. An optical laser system is used to measure the amplitude and the frequency of the surface oscillations in real
time. The droplet radius is measured with a highly accurate imaging system and shape analysis software. The resonant
frequency determined from the obtained resonant curves is used to estimate the surface tension of the liquid. Analysis of
the resonant curves gives additional information about the viscosity and the supporting surface influence on the droplet’s
behavior. Our technique operates in two modes: “tensiometric mode” for surface tension measurements and
“manipulation mode” for studying and manipulating liquid interfaces via an electric field. In the present work the
principles, applications and capabilities of Resonant Droplet Tensiometry driven by an electric field, have being reviewed
as well as the latest results and challenges.
... In the present work the surface tension change due to solute adsorption is measured in real time by using a resonant hemispherical droplet tensiometry. The method is based on registering the resonant frequency of electrically driven small spherical or hemispherical droplets with small Bond numbers (B 0 r0.1), for which the surface tension is dominant (Tankovsky and Zografov, 2011;Tankovsky et al., 2013;Zografov et al., 2014). The examined gas vapors are introduced into a closed transparent jar by evaporation of deposited by injection small liquid droplets. ...
... These correction terms can be eliminated if a hemispherical droplet is used and Eq. (2) can be applied for defining the surface tension, as described in (Tankovsky et al., 2013;Zografov et al., 2014). The droplet is also illuminated by a lamp and observed by a video camera, which allows a precise measurement and control of the droplet radius R and height H with the help of appropriate software. ...
A resonant hemispherical pendant droplet tensiometry has been used to register in real time the change of surface tension of low Bond number water droplets due to evaporation of simple volatile liquids, acetone and chloroform, in a closed vessel. The contributions of the gas vapor pressure and of the gas molecules adsorption to the surface tension changes are distinguished and evaluated in time. After the initial increase of gas adsorption, a negative adsorption has been found in later time, which may be informative for the dynamics of the adsorption and desorption processes in the interface layer. The observed desorption processes are stimulated by the mechanical oscillations of the interface layer, as far as the droplet is in resonance during the measurements.
... Investigations regarding the behavior of pendant and sessile drops in response to external forcing are relatively limited. The dynamics of pendant and sessile drops have been induced by vibrating rods, 28 electric fields, [29][30][31][32] and acoustics. [33][34][35] In the presence of an acoustic field, pendant drops exhibit longitudinal, lateral, and rotational modes, the lowest of which is drop rotation about the gravitational axis similar to a conical pendulum. ...
When exposed to an ascending flow, pendant drops oscillate at magnitudes determined by windspeed, drop diameter, and needle diameter. In this study, we investigate the retention stability and oscillations of pendant drops in a vertical wind tunnel. Oscillation is captured by a high-speed camera for a drop Reynolds number Re = 200–3000. Drops at Re ≲ 1000 oscillate up to 12 times the frequency of drops with high Re. Increasing windspeed enables larger volume drops to remain attached to the needles above Re = 500. We categorize drop dynamics into seven behavioral modes according to the plane of rotation and deformation of shape. Video frame aggregation permits the determination of a static, characteristic shape of our highly dynamic drops. Such a shape provides a hydraulic diameter and the evaluation of the volume swept by the oscillating drops with time. The maximum swept volume per unit drop volume occurs at Re = 600, corresponding to the peak in angular velocity.
... In dimension 2, the mean curvature is simply called the curvature. The right-hand-sides f + and f − are given volume forces, representing for example the effect of an electric field [71], or some density contribution like in the case gravity Stokes flows [32], leading to the so-called Stokes-transport system [40,43]. The function g is a surface tension type force, acting on the interface Γ(t). ...
The aim of this paper is to design a feedback operator for stabilizing in infinite time horizon a system modeling the interactions between a viscous incompressible fluid and the deformation of a soap bubble. The latter is represented by an interface separating a bounded domain of R2 into two connected parts filled with viscous incompressible fluids. The interface is a smooth perturbation of the 1-sphere, and the surrounding fluids satisfy the incompressible Stokes equations in time-dependent domains. The mean curvature of the surface defines a surface tension force which induces a jump of the normal trace of the Cauchy stress tensor. The response of the fluids is a velocity trace on the interface, governing the time evolution of the latter, via the equality of velocities. The data are assumed to be sufficiently small, in particular the initial perturbation, that is the initial shape of the soap bubble is close enough to a circle. The control function is a surface tension type force on the interface. We design it as the sum of two feedback operators: one is explicit, the second one is finite-dimensional. They enable us to define a control operator that stabilizes locally the soap bubble to a circle with an arbitrary exponential decay rate, up to translations, and up to non-contact with the outer boundary.
... Oscillatory motions of droplets can show interesting effects like making a droplet move up on an inclined, vibrating plate 8,9 . As such, the opportunity to change surface properties in time has a variety of applications, e. g. it can be used in devices, which measure liquid properties like surface tension 11,12 . It can also be applied to mix liquids inside a drop 10 , which again is useful for the design of Labs-On-A-Chip 1 . ...
The development of substrates with a switchable wettability is on a fast pace. The limit of switching frequencies and contact angle differences between substrate states are steadily pushed further. We investigate the behavior of a droplet on a homogeneous substrate, which is switched between two wettabilities for a large range of switching frequencies. Here, we are particularly interested in the dependence of the wetting behavior on the switching frequency. We show, that results obtained on the particle level via molecular dynamics simulations and on the continuum level via the thin-film model are consistent. Predictions of a simple models as the molecular theory of wetting (MKT) and analytical calculations based on the MKT also show good agreement and offer analytical insights within the limits of the approximations employed.
... It has been shown recently, that a hemispherical, pendant liquid droplet can be driven into oscillations by applying an external ac electric field [14][15][16]. When the driving force frequency coincides with the main resonant mode of the droplet, the oscillations achieve essential amplitudes, which can influence the properties of the liquid-air interface and the evaporation processes. ...
An oscillating hemispherical pendant droplet has been used as an instrument to modify evaporation conditions of simple and complex liquids. The resonant droplet vibrations can influence the evaporation by different mechanisms: by induced convective flows, by periodical changes of the pressure in the vapor phase and in the liquid phase, by stretching and contraction of the interface layer etc. On the other hand the applied dc voltage can influence and manipulate the diffusion flows of charged molecules and aggregates, if present. Pure water and water-SDS surfactant mixture, with micellar concentration 10−2M, have been examined. The time dependencies of the evaporation-rate are evaluated with evaporated-volume compensation technique.
... Hence, the microwave does not change the natural frequencies of the droplet, in spite of the reduced surface tension and increased temperature. Since electrical field of microwave was alternated at 2.45 GHz, the effect of microwave on the frequency for droplet shape is smaller than electrostatic field (Zografov et al., 2014). Fig. 9 shows the rotation speed inside droplet during microwave radiation. ...
Surface tension of fluids is an important factor controlling multiphase systems and is often manipulated by surfactants during industrial processes. Previously, we have found that water surface tension was reduced under continuous microwave irradiation. The reduction was not explainable by thermal effects. The new insights can lead to important application of microwaves in multiple-phase systems. In this study, effect of various microwave irradiation modes on surface tension of water was investigated. The surface tension reduction was confirmed for pulsed microwave irradiation. The reduction varied with the applied power as well as interval between irradiations. The droplet oscillation and internal convection were also investigated during and after microwave irradiation to clarify the mechanism. It was found that the convection within the water droplet was proportional to the microwave power. In contrast, the frequency of oscillation was independent on the microwave power. These results on surface tension, oscillation and convection will provide important insights for designing microwave applications.
The development of substrates with a switchable wettability is proceeding and the limit of switching frequencies and contact angle differences between substrate states has developed in the past years. In this paper we investigate the behavior of a droplet on a homogeneous substrate, which is switched between two wettabilities for a large range of switching frequencies. Here, we are particularly interested in the dependence of the wetting behavior on the switching frequency. We show that results obtained on the particle level via molecular dynamics simulations and on the continuum level via the thin-film model are consistent. Predictions of simple models as the molecular theory of wetting (MKT) and analytical calculations based on the MKT also show good agreement and offer deeper insights into the underlying mechanisms.
The shape dynamics of droplets exposed to an air jet at intermediate droplet Reynolds numbers is investigated. High speed imaging and hot-wire anemometry are employed to examine the mechanism of droplet oscillation. The theory that the vortex shedding behind the droplet induces oscillation is examined. In these experiments, no particular dominant frequency is found in the wake region of the droplet. Hence the inherent free-stream disturbances prove to be driving the droplet oscillations. The modes of droplet oscillation show a band of dominant frequencies near the corresponding natural frequency, further proving that there is no particular forcing frequency involved. In the frequency spectrum of the lowest mode of oscillation for glycerol at the highest Reynolds number, no response is observed below the threshold frequency corresponding to the viscous dissipation time scale. This selective suppression of lower frequencies in the case of glycerol is corroborated by scaling arguments. The influence of surface tension on the droplet oscillation is studied using ethanol as a test fluid. Since a lower surface tension reduces the natural frequency, ethanol shows lower excited frequencies. The oscillation levels of different fluids are quantified using the droplet aspect ratio and correlated in terms of Weber number and Ohnesorge number.
Abstract. A method is proposed to excite oscillations of a liquid hanging drop by interfacial
force acting upon the surface of the droplet. The oscillations are detected with the help of a He-Ne
laser beam. Resonant frequency and resonance half-width are measured and information is retrieved
about the surface properties of the interface liquid-air.
Experimental technique is proposed to excite oscillations of a hanging liquid droplet by applying interfacial dielectric force directly upon the droplet surface. The force proved to be applicable for all kinds of liquids and solutions including non-conductive, isolating liquids. The oscillations are detected optically, with the help of a laser beam. The measured resonant frequency modes and resonance half-widths may be used to retrieve information about the surface properties of the droplet (surface tension and surface charge, in particular). The method is applicable to a wide variety of liquids and interfaces. Possible applications are analyzed and discussed.
The damping oscillation of a hanging drop on a nozzle in the air was studied theoretically and experimentally. In the experiments, an elongated drop on a brass nozzle by electrostatic force was made to oscillate by removing the electric field instantaneously and the subsequent drop motion was recorded by a high-speed camera. In the theoretical study, the time-dependent drop shape and flow inside the drop were simulated numerically by use of the finite element method. It was found that the experimental results of oscillatory behavior for a hanging drop of aqueous glycerin solution were in good agreement with the calculated ones and that the frequency of oscillation was affected by drop volume, surface tension and nozzle size.
Finite-amplitude, axially symmetric oscillations of small (0.2 mm) liquid droplets in a gaseous environment are studied, both experimentally and theoretically. When the amplitude of natural oscillations of the fundamental mode exceeds approximately 10% of the droplet radius, typical nonlinear effects like the dependence of the oscillation frequency on the amplitude, the asymmetry of the oscillation amplitude, and the interaction between modes are observed. As the amplitude decreases due to viscous damping, the oscillation frequency and the amplitude decay factor reach their asymptotical values predicted by linear theory. The initial behaviour of the droplet is described quite satisfactorily by a proposed nonlinear inviscid theoretical model.
A recently demonstrated technique of aerodynamic levitation has been used to study the resonance frequency of liquid droplets. A thin pressurized gas layer supports the droplet avoiding any contact with the environment. Due to the external gravitational field, the measured frequency is different from the one predicted by the classical models for a spherical drop. An ellipsoidal shape has been introduced to take into account the competition between surface and gravitational energies. Results of this model are in good agreement with experiments in terms of volume, as well as density and surface energy, dependence of the oscillation frequency.
The oscillating drop technique---in combination with some kind of levitation---is widely used today for the measurement of the surface tension and viscosity of liquids. It is based on Rayleigh's theory for the surface tension driven oscillations of a spherical, force-free, liquid drop. Unfortunately, this ideal case is never realized in practice. Whereas the influence of the levitation field and finite viscosity on the oscillation frequencies has been discussed by several authors, more practical questions related to the observation of these oscillations have not been addressed before and are the topic of this contribution. In particular, the influence of translational or rotational sample movement, and additional effects due to signal processing are discussed. It is hoped that this paper will help to avoid the many pitfalls inherent in the oscillating drop technique and will thus lead to unambiguous and reliable results.
We describe an instrument combining the advantages of two methods, axisymmetric drop shape analysis for well-deformed drops and capillary pressure tensiometry for spherical drops, both used for measuring the interfacial tension and interfacial rheological parameters. The rheological parameters are the complex interfacial elasticity, and the surface elasticity and viscosity of Kelvin-Voigt and Maxwell rheological models. The instrument is applicable for investigation of the effect of different types of surfactants (nonionic, ionic, proteins, and polymers) on the interfacial rheological properties both of air/water and oil/water interfaces, and of interfaces between liquids with equal mass densities. A piezodriven system and a specially designed interface unit, implemented in the instrument, ensure precise control for standard periodic waveforms of surface deformation (sine, square, triangle, and sawtooth) at a fixed frequency, or produce surface deformation at constant rate. The interface unit ensures accurate synchronization between the pressure measurement and the surface control, which is used for real-time data processing and feedback control of drop area in some of the applications.
Experimental svidence of internal dc flow circulation within an electrostatically levitated, 3.4 mm diameter charged water drop oscillating in shape at different amplitude is presented. The axisymmetric shape oscillations were excited using a continuously pulsed electrostatic field at the fundamental shape mode frequency (I =2) of the drop. It was found that the speed of the internal dc flow varied quadratically with respect to the oscillation amplitude without an observable minimum threshold. The implications of the observed internal flow is discussed with respect to the microgravity research facility and environment.
Natural oscillations of a hemispherical drop on a solid substrate are considered. The Hocking condition is used to take into account the contact angle dynamics. The natural oscillations attenuate due to dissipation on the contact line and the degeneracy in the azimuthal number is eliminated. Forced oscillations of the drop are studied for tangential vibrations of the substrate. For the case of a fixed contact line, the amplitude of the forced oscillations grows without bound near the fundamental requency. In other cases, the amplitude is finite.
The oscillating drop surfactometer (ODS) measures surface tension (gamma) and energy dissipation (damping constant b) of surfactant on a 1 microl sample. gamma is obtained from the period of oscillation and b from its free decay or from the phase shift slope in resonance. After calibration with substances with different gamma, corrections were made for capillary fixation and loss of mass by evaporation. Surface active substances are delivered from liposomes in the interior (subphase) or injected from outside, with microdrops (180 pl each) of solution. As an application example, we have investigated surfactant extract and pure phospholipid. In minutes after formation of a drop containing a diluted Survanta suspension, gamma, decreases by 20 mN/m, while b increases three-fold. This effect, assigned to spontaneous adsorption from liposomes to the surface, is not seen with pure dipalmitoylphosphatidylcholine (DPPC) under our conditions. However, microdrop injection of DPPC triggers a rapid decrease of gamma and a delayed strong increase in b. The effect is modulated by DPPC in the subphase and by cholesterol. Investigations with L-alpha-lysophosphatidylcholine show the high sensitivity of the ODS technique in the determination of the energy dissipation at air-liquid boundary surfaces. Although the ODS is limited to applications with gamma > 15 mN m(-1), it offers the advantage to give, with small samples and within seconds, a simultaneous readout of both Surface tension gamma and the parameter b, as a measure of surface viscosity.