Dynamics of a disturbed sessile drop measured by atomic force microscopy (AFM)

A new method for studying the dynamics of a sessile drop by atomic force microscopy (AFM) is demonstrated. A hydrophobic microsphere (radius, r ～ 20-30 μm) is brought into contact with a small sessile water drop resting on a polytetrafluoroethylene (PTFE) surface. When the microsphere touches the liquid surface, the meniscus rises onto it because of capillary forces. Although the microsphere volume is 6 orders of magnitude smaller than the drop, it excites the normal resonance modes of the liquid interface. The sphere is pinned at the interface, whose small (<100 nm) oscillations are readily measured with AFM. Resonance oscillation frequencies were measured for drop volumes between 5 and 200 μL. The results for the two lowest normal modes are quantitatively consistent with continuum calculations for the natural frequency of hemispherical drops with no adjustable parameters. The method may enable sensitive measurements of volume, surface tension, and viscosity of small drops.     

Total Gaussian curvature,drop shapes and the range of applicability of drop shape techniques

Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The new definition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.     

Size-selective sliding of sessile drops on a slightly inclined plane using low-frequency AC electrowetting

When placed on an inclined solid plane, drops often stick to the solid surface due to pinning forces caused by contact angle hysteresis. When the drop size or the plane's incline angle is small, the drop is difficult to slide due to a decrease in gravitational force. Here we demonstrate that small drops (0.4-9 μL) on a slightly inclined plane (~12°, Teflon and parylene-C surface) can be mobilized through patterned electrodes by applying low-frequency ac electrowetting under 400 Hz (110-180 V(rms)), which has a mechanism different from that of the high-frequency ac method that induces sliding by reducing contact angle hysteresis. We attribute the sliding motion of our method to a combination of contact angle hysteresis and interfacial oscillation driven by ac electrowetting instead of the minimization of contact angle hysteresis at a high frequency. We investigated the effects of ac frequency on the sliding motion and terminal sliding of drops; the terminal sliding velocity is greatest at resonance frequency. Varying the electrowetting number (0.21-0.56) at a fixed frequency (40 Hz) for 5 μL drops, we found an empirical relationship between the electrowetting number and the terminal sliding velocity. Using the relationship between the drop size and ac frequency, we can selectively slide drops of a specific size or merge two drops along an inclined plane. This simple method will help with constructing microfluidic platforms with sorting, merging, transporting, and mixing of drops without a programmable control of electrical signals. Also, this method has a potential in heat transfer applications because heat removal capacity can be enhanced significantly through drop oscillation.     

New interferometric technique to evaluate the electric charge of gas bubbles in liquids

We report a new interferometric technique to measure the electric charge at the gas-liquid interface of a bubble in a liquid. The bubble rests by buoyancy against an electrode, and an alternating electric field excites its capillary oscillations. The oscillation amplitude of the quadrupolar mode frequency is measured by the interferometer, and it is used to evaluate the electric charge. The mode frequency scales with the square root of the interfacial tension and with a -(3)/(2) power law as a function of the bubble radius. For bubbles in the millimeter diameter range in pure water, the measured negative charge scales with the square of the radius, hence, giving a constant surface charge density on the order of 1.8 × 10(-5) C m(-2), which is rather consistent with the electrophoretic values reported in the literature.     

Vibration-actuated drop motion on surfaces for batch microfluidic processes

When a liquid drop is subjected to an asymmetric lateral vibration on a nonwettable surface, a net inertial force acting on the drop causes it to move. The direction and velocity of the drop motion are related to the shape, frequency, and amplitude of vibration, as well as the natural harmonics of the drop oscillation. Aqueous drops can be propelled through fluidic networks connecting various unit operations in order to carry out batch processing at the miniature scale. We illustrate the integration of several unit operations on a chip: drop transport, mixing, and thermal cycling, which are precursor steps to carrying out advanced biological processes at microscale, including cell sorting, polymerase chain reaction, and DNA hybridization.     

Bubble entrainment with drops

The study reported here was undertaken because recent research on nucleate boiling has implicated vapor entrainment by drops as a mechanism for vapor bubble nucleation. The mechanism has been called secondary nucleation. The purpose of this research was to determine the behavior of entrained air bubbles when a drop of liquid strikes a liquid surface. A liquid drop striking the surface of a pool of the same liquid was found usually to entrain large numbers of small air bubbles. Some of these bubbles are frequently carried rapidly deep into the pool by a vortex ring but many can be deposited in a trail or left floating on the surface. Air bubble entrainment was observed with water and several organic liquids and some differences were noted. Drops with diameters from 200 μm to 4 mm were studied. Sometimes hundreds of bubbles were entrained some with diameters up to 100 μm. These results lend support to the secondary nucleation hypothesis and indicate further research on vapor bubble entrainment under conditions more typical of boiling would be appropriate.     

Detachment force of particles from air-liquid interfaces of films and bubbles

The detachment force required to pull a microparticle from an air-liquid interface is measured using atomic force microscopy (AFM) and the colloidal probe technique. Water, solutions of sodium dodecyl sulfate (SDS), and silicone oils are tested in order to study the effects of surface tension and viscosity. Two different liquid geometries are considered: the air-liquid interface of a bubble and a liquid film on a solid substrate. It was shown that detaching particles from liquid films is fundamentally different than from bubbles or drops due to the restricted flow of the liquid phase. Additional force is required to detach a particle from a film, and the maximum force during detachment is not necessarily at the position where the particle breaks away from the interface (as seen in bubble or drop systems). This is due to the dynamics of meniscus formation and viscous effects, which must be considered if the liquid is constrained in a film. The magnitude of these effects is related to the liquid viscosity, film thickness, and detachment speed.     

Asymmetric deformation of bubble shape: cause or effect of vortex-shedding?

Two perpendicular projections of rising bubbles were observed in counter-current downstream diverging flow. Evidently, the bubbles did not enter the boundary layer at the channel wall and a plug liquid flow assumption was acceptable in our experimental equipment. This confirmed that the experiment was appropriate for simulation of bubble rises in a quiescent liquid column. Recent data obtained by a high-speed camera permitted recording over a period of 60 s. Image analysis by a tailor-made program provided a time-series of quantities related to the position, size, and shape of bubbles. In addition to determination of the aspect ratio of the equivalent oblate ellipsoid, deviation from this shape was investigated in respect of the difference between the bubble’s centre of mass and the geometrical centre of bubble projection. Autocorrelation of the data indicated that the bubble inclination oscillated harmonically with a frequency of 5–10 Hz; cross correlation showed that the horizontal shift of the centre of mass, as well as the horizontal velocity, increased with increasing bubble inclination, and the vertical shift of the centre of mass increased with an increases in the absolute value of the bubble inclination. There is no significant phase shift in the oscillation of these quantities. The bulky bottom side of the bubbles is in accordance with the model of bubble oscillation induced by instability of the equilibrium of gravity and surface tension forces. The oscillation frequency dependence on surface forces (Eötvös number) is evident, while viscosity does not play a significant role in low-viscosity liquids. Therefore, vortex-shedding is more likely to be an effect of the oscillation and not its cause.     

A novel method to study particle–air/liquid surface interactions

A novel method to study the dynamics of hydrophilic solid particle interactions with the gas/aqueous surface has been developed; the gas/liquid surface oscillation was monitored using light reflection microscopy. Two modes of gas/liquid surface oscillation are observed: a high mode of oscillation during the first 0.1 s and a low mode of oscillation during the last 0.4 s. It has been shown that the two modes of oscillation are related with the two-stage process of particle–gas/liquid interactions; during the first stage, the particle and gas/liquid surface interact via a long-range hydrodynamic interaction. The liquid film between the particle and the gas/liquid surface decreases its thickness. During the second stage, the particle is adhered (via liquid film) to the air/aqueous surface, and the air/aqueous surface oscillates with the particle. Effects of particle size and surface tension on the frequency of oscillation of the gas/liquid surface were also studied. Two theoretical models are used to predict the high frequency and low frequency of the air/aqueous surface oscillation.     

Interfacial dilational behaviour of adsorbed β-lactoglobulin layers at the different fluid interfaces

β-Lactoglobulin adsorption layers at the interfaces solution/air, /tetradecan and /sunflower oil were characterised by dynamic interfacial tension measurements and harmonic drop oscillation experiments in a time scale of some seconds. Axialsymmetric drop shape analysis (ADSA) was used to calculate drop volume, area and interfacial tension. Within a definite range of drop volume amplitude, the oscillation of the surface tension is harmonic and interfacial dilation parameters can be determined. Dependence of the dilational parameters on the amplitude and frequency of drop volume oscillation were determined and methodical demands are given for this special kind of ADSA application. The concentration of interfacial saturation is minimal at the interface with sunflower oil. Interfacial dilational elasticities, and viscosities are maximal at the saturation concentration of all systems investigated. The dilational viscosities are maximal in the frequency range 0.007–0.011 Hz and characterise molecular rearrangement processes in the adsorption layer. Interfacial dilational elasticity and viscosity are the largest at the interface with air. They are the smallest at the interface with sunflower oil. Similarities and differences of the systems investigated are discussed by taking into account the adsorption behaviour and the solvatation of different apolar and polar parts of the protein molecules in the neighbouring phase.     

Ratcheting motion of liquid drops on gradient surfaces

The motions of liquid drops of various surface tensions and viscosities were investigated on a solid substrate possessing a gradient of wettability. A drop of any size moves spontaneously on such a surface when the contact angle hysteresis is negligible; but it has to be larger than a critical size in order to move on a hysteretic surface. The hysteresis can, however, be reduced or eliminated with vibration that allows the drop to sample various metastable states, thereby setting it to the path of global energy minima. Significant amplification of velocity is observed with the frequency of forcing vibration matching the natural harmonics of drop oscillation. It is suggested that the main cause for velocity amplification is related to resonant shape fluctuation, which can be illustrated by periodically deforming and relaxing the drop at low frequencies.     

Oscillating drop/bubble tensiometry: effect of viscous forces on the measurement of interfacial tension

The oscillating drop/bubble technique is increasingly popular for measuring the interfacial dilatational properties of surfactant/polymer-laden fluid/fluid interfaces. A caveat of this technique, however, is that viscous forces are important at higher oscillation frequencies or fluid viscosities; these can affect determination of the interfacial tension. Here, we experimentally quantify the effect of viscous forces on the interfacial-tension measurement by oscillating 100 and 200 cSt poly(dimethylsiloxane) (PDMS) droplets in water at small amplitudes and frequencies ranging between 0.01 and 1 Hz. Due to viscous forces, the measured interfacial tension oscillates sinusoidally with the same frequency as the oscillation of the drop volume. The tension oscillation precedes that of the drop volume, and the amplitude varies linearly with Capillary number, Ca=DeltamuomegaDeltaV/gammaa(2), where Deltamu=mu(D)-mu is the difference between the bulk Newtonian viscosities of the drop and surrounding continuous fluid, omega is the oscillation frequency of the drop, DeltaV is the amplitude of volume oscillation, gamma is the equilibrium interfacial tension between the PDMS drop and water, and a is the radius of the capillary. A simplified model of a freely suspended spherical oscillating-drop well explains these observations. Viscous forces distort the drop shape at Ca>0.002, although this criterion is apparatus dependent.     

Continuous flow structuring of anisotropic biopolymer particles

We review concepts and provide examples for the controlled structuring of biopolymer particles in hydrodynamic flow fields. The structuring concepts are grouped by the physical mechanisms governing drop deformation and shaping: (i) capillary structuring, (ii) shear and elongational structuring and (iii) confined flow methods. Non-spherical drops can be permanently structured if a solidification process, such as gelation or glass formation in the bulk or at the interface, is superimposed to the flow field. The physical and engineering properties of these processes critically depend on an elaborate balance between capillary phenomena, rheology, gel or glass formation kinetics, and bulk heat, mass and momentum transfer in multiphase fluids. This overview is motivated by the potential of non-spherical suspension particles, in particular those formed from ‘natural’ and ‘sustainable’ biopolymers, as rheology modifiers in food materials, consumer products, cosmetics or pharmaceuticals.     

Resonance Behavior of Oscillating Bubbles

A convolution-type equation has been derived to describe the behavior of a bubble under periodical pressure oscillations. This equation holds for a diffusion-controlled adsorption mechanism and small disturbances of the equilibrium state, and it describes both the established and transition regimes of bubble oscillation. Systems free of any surfactant and in the presence of a surfactant are considered. The results obtained allow all aspects of surfactant influence on the bubble oscillation resonance to be analyzed. The sharp increase in the bubble oscillation amplitude may result in bubble detachments, even at rather low harmonic pressure oscillations. The presence of surfactant can result in a depression of the resonance amplitudes. Copyright 2000 Academic Press.     

Experimental investigation of bubble and drop formation at submerged orifices

The aim of this study was to investigate bubble/drop formation at a single submerged orifice in stagnant Newtonian fluids and to gain qualitative understanding of the formation mechanism. The effects of various governing parameters were studied. Formation behavior of bubbles and drops in Newtonian aqueous solutions were investigated experimentally under different operating conditions with various orifices. The results show that the volume of the detached dispersed phase (bubble or drop) increases with the viscosity of the continuous phase (or dispersion medium), surface tension, orifice diameter, and dispersed phase flow rate. A PIV system was employed to measure the velocity flow field quantitatively during the bubble/drop formation, giving interesting information useful for the elucidation of the fundamental formation process at the orifice. It was revealed that the orifice shape strongly influences the size of the bubble formed. Furthermore, based on a simple mass balance, a general correlation successfully predicting both bubble and drop sizes has been proposed.     

Dynamic surface and interfacial tensions of surfactant and polymer solutions

Dynamic surface and interfacial tensions are the most frequently measured non-equilibrium properties of adsorption layers at liquid interfaces. The review presents the theoretical basis of adsorption kinetics, taking into consideration different adsorption mechanisms, and specific experimental conditions, such as liquid flow and interfacial area changes. Analytical solutions, if available, approximations as well as numerical procedures for direct solution of the physical models are presented.Several experimental techniques are discussed frequently used in studies of the dynamic adsorption behaviour of surfactants and polymers at liquid interfaces: drop volume, maximum bubble pressure, and pendent drop technique, drop pressure tensiometry, pulsating bubble and elastic ring method. Experimental results, most of all obtained with different technique on one and the same surfactant system, are then discussed on the basis of current theories.Finally, the role of dynamic interfacial properties in several practical applications is discussed: foam and emulsion film formation and stabilisation, rising of bubbles and drops in a surfactant solution.     

A reformulation of the fundamental thermodynamics of surface tension for spherical bubbles and drops

The surface energy term is revised in classical thermodynamic theory of surface tension for drops and bubbles. This simplifies the resulting analysis and leads immediately to Kelvin’s formula for the over-pressure The reformulation turns on interpreting the area element dA not as an element of a fixed area but as the increase due to a growth in bubble or drop size.     

Experimental observation of oscillatory effects on the relaxation of a sheared liquid drop

This work deals with the experimental observation of the shape oscillations followed by a viscous liquid drop immersed in another viscous fluid matrix when retracting from a deformed state into the spherical shape under the action of interfacial forces. The droplet is firstly deformed into an ellipsoidal shape by a shear flow and later allowed to recover the equilibrium shape after cessation of the flow. It is observed that such an oscillatory process occurs for a wide range of viscosity ratios and it may be described by a dampened oscillation. Viscous components dominate the drop retraction, just allowing few oscillations. The dampening factor, frequency and amplitude of the oscillations are affected by the drop viscosity. Frequencies and amplitudes are also influenced by the initial drop deformation.     

Surface modification of chromatography adsorbents by low temperature low pressure plasma

In this study we show how low temperature glow discharge plasma can be used to prepare bi-layered chromatography adsorbents with non-adsorptive exteriors. The commercial strong anion exchange expanded bed chromatography matrix, Q HyperZ, was treated with plasmas in one of two general ways. Using a purpose-designed rotating reactor, plasmas were employed to either: (i) remove anion exchange ligands at or close to the exterior surface of Q HyperZ, and replace them with polar oxygen containing functions (‘plasma etching and oxidation’); or (ii) bury the same surface exposed ligands beneath thin polymer coatings (‘plasma polymerization coating’) using appropriate monomers (vinyl acetate, vinyl pyrrolidone, safrole) and argon as the carrier gas. X-ray photoelectron spectroscopy analysis (first ∼10 nm depth) of Q HyperZ before and after the various plasma treatments confirmed that substantial changes to the elemental composition of Q HyperZ's exterior had been inflicted in all cases. The atomic percent changes in carbon, nitrogen, oxygen, yttrium and zirconium observed after being exposed to air plasma etching were entirely consistent with: the removal of pendant Q (trimethylammonium) functions; increased exposure of the underlying yttrium-stabilised zirconia shell; and introduction of hydroxyl and carbonyl functions. Following plasma polymerization treatments (with all three monomers tested), the increased atomic percent levels of carbon and parallel drops in nitrogen, yttrium and zirconium provided clear evidence that thin polymer coats had been created at the exteriors of Q HyperZ adsorbent particles. No changes in adsorbent size and surface morphology, nor any evidence of plasma-induced damage could be discerned from scanning electron micrographs, light micrographs and measurements of particle size distributions following 3 h exposure to air (220 V; 35.8 W L⁻¹) or ‘vinyl acetate/argon’ (170 V; 16.5 W L⁻¹) plasmas. Losses in bulk chloride exchange capacity before and after exposure to plasmas enabled effective modification depths within hydrated Q HyperZ adsorbent particles to be calculated as 0.2–1.2 μm, depending on the conditions applied. The depth of plasma induced alteration was strongly influenced by the power input and size of the treated batch, i.e. dropping the power or increasing the batch size resulted in reduced plasma penetration and therefore shallower modification. The selectivity of ‘surface vs. core’ modification imparted to Q HyperZ by the various plasma treatments was evaluated in static and dynamic binding studies employing appropriate probes, i.e. plasmid DNA, sonicated calf thymus DNA and bovine serum albumin. In static binding studies performed with adsorbents that had been exposed to plasmas at the 5 g scale (25 g L⁻¹ of plasma reactor), the highest ‘surface/core’ modification selectivity was observed for Q HyperZ that had been subjected to 3 h of air plasma etching at 220 V (35.8 W L⁻¹). This treatment removed ∼53% of ‘surface’ DNA binding at the expense of a 9.3% loss in ‘core’ protein binding. Even more impressive results were obtained in dynamic expanded bed adsorption studies conducted with Q HyperZ adsorbents that had been treated with air (220 V, 3 h) and ‘vinyl acetate/argon’ (170 V, 3 h) plasmas at 10.5 g scale (52.5 g L⁻¹ of plasma reactor). Following both plasma treatments: the 10% breakthrough capacities of the modified Q HyperZ adsorbents towards ‘surface’ binding DNA probes dropped very significantly (30–85%); the DNA induced inter-particle cross-linking and contraction of expanded beds observed during application of sonicated DNA on native Q HyperZ was completely eradicated; but the ‘core’ protein binding performance remained unchanged cf. that of the native Q HyperZ starting material.     

Characterisation of alkyl amines at the water/air surface with the drop and bubble profile analysis tensiometry

Pendant drop and buoyant bubble methods have been used to study the surface characteristics of alkyl amines at the water/air surface. The investigated alkyl amines, triethylamine and octylamine, showed unusual changes in the surface tension as a function of time: an initially steep drop and a subsequent steady increase in the surface tension until a value close to the one of the pure water/air system was observed. This phenomenon is explained by the evaporation of the alkyl amines, for which several sets of experiments have been conducted with the pendant drop and buoyant bubble methods. Using an appropriate experimental protocol, the equilibrium adsorption behaviour of the two amines can be quantitatively measured.