Investigations of liquid surface rheology of surfactant solutions by droplet shape oscillations: Theory

Tian, Yuren; Holt, R. Glynn; Apfel, Robert E.

doi:10.1063/1.868671

Cited by 52 publications

(38 citation statements)

References 25 publications

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“…The resulting surface tension gradient gives rise to a redistribution of surfactant molecules over the droplet interface, which counteracts the droplet deformation. This additional resistance to deformation of the droplet increases the decay rate of the oscillation amplitude (Lu and Apfel 1991;Tian et al 1995). This effect of surfactants is usually called the Gibbs elasticity, and its influence on the oscillation frequency and damping rate has been reported before for oscillating mm-sized droplets of surfactant solutions .…”

Section: Resultsmentioning

confidence: 99%

Ultrafast imaging method to measure surface tension and viscosity of inkjet-printed droplets in flight

Staat

Bos²,

Berg³

et al. 2016

Exp Fluids

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(Wijshoff 2010). The solvents carry the pigment particles to the medium and evaporate, solidify or crystallize, while the surfactants prevent wetting of the nozzle plate and promote spreading of the droplet after it impacts the underlying medium. In order to accurately control the droplet formation process, its in-flight dynamics, and subsequent interaction with the substrate, it is key to quantify the liquid properties of the droplet during the entire inkjet-printing process.The surface tension of a surfactant solution is determined by the concentration of adsorbed surfactant molecules at the liquid-air interface. When a fresh interface is formed, the surface tension equals that of the solvent (Ohl et al. 2003) and it decreases while surfactants adsorb at the interface, until reaching an equilibrium surfactant concentration. The associated timescales of the adsorption process are governed by the diffusion time of the surfactant molecules to diffuse from the so-called adsorption depth h to the interface (Ferri and Stebe 2000). This depth depends on the bulk surfactant concentration, the critical micelle concentration and the surface concentration of surfactants at equilibrium surface tension (Ferri and Stebe 2000). The typical diffusion time then scales with the surfactant diffusion coefficient D as τ D ∼ h 2 /D and ranges from milliseconds to days, depending on the surfactant type and surfactant concentration (Chang and Franses 1995;Eastoe and Dalton 2000). As the surfactants in inkjet printing must act before the ink dries, it is required that they adsorb as fast as possible. Droplet formation, however, is an extremely fast process that takes in the order of 10 µs, which is shorter than the approximately 100 µs that a droplet is typically in flight and much shorter than the time a droplet needs to evaporate, which is several seconds (Staat et al. 2016). A surfactant with a typical adsorption time scale of the order of milliseconds is considered a fast-adsorbing surfactant Abstract In modern drop-on-demand inkjet printing, the jetted droplets contain a mixture of solvents, pigments and surfactants. In order to accurately control the droplet formation process, its in-flight dynamics, and deposition characteristics upon impact at the underlying substrate, it is key to quantify the instantaneous liquid properties of the droplets during the entire inkjet-printing process. An analysis of shape oscillation dynamics is known to give direct information of the local liquid properties of millimeter-sized droplets and bubbles. Here, we apply this technique to measure the surface tension and viscosity of micrometer-sized inkjet droplets in flight by recording the droplet shape oscillations microseconds after pinch-off from the nozzle. From the damped oscillation amplitude and frequency we deduce the viscosity and surface tension, respectively. With this ultrafast imaging method, we study the role of surfactants in freshly made inkjet droplets in flight and compare to complementary techniques for dynamic surface tension me...

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Section: Resultsmentioning

confidence: 99%

Ultrafast imaging method to measure surface tension and viscosity of inkjet-printed droplets in flight

Staat

Bos²,

Berg³

et al. 2016

Exp Fluids

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“…The materials were surfactant solutions, and the drops were levitated due to the microgravity conditions of the experiment. In these studies, complementary effects of the bulk and the surface viscosities were found [9] and quantified [10]. Most recently, the oscillating drop method was proposed and developed for measuring polymeric time scales [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…To date, the existing literature discusses the measurement of material parameters, such as the dynamic viscosity of the liquid and its surface tension against the ambient medium, predominantly for Newtonian liquids [5][6][7][8]. For viscoelastic systems, the oscillating drop method was used for investigating the surface rheology [9,10]. The materials were surfactant solutions, and the drops were levitated due to the microgravity conditions of the experiment.…”

Section: Introductionmentioning

confidence: 99%

Measurement of polymeric time scales from linear drop oscillations

Plohl¹,

Brenn²

2017

Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems

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The oscillating drop method allows material properties of liquids to be measured from damped drop oscillations. The literature discusses, e.g., the measurement of the liquid dynamic viscosity and the surface tension against the ambient medium, predominantly for Newtonian liquids. We use this method for measuring pairs of material properties of polymeric liquids. Pairs of properties may be measured, since the quantity measured is a complex frequency with a real and an imaginary part. For the measurements, individual drops are levitated in air by an ultrasonic levitator and imaged with a high-speed camera. Amplitude modulation of the ultrasound drives shape oscillations of the levitated drop. When the modulation is switched off, with the levitating force maintained, the drop performs free oscillations which are damped due to the liquid viscosity. The data acquired from the images recorded are the angular frequency and the damping rate which are used as an input into the characteristic equation of the oscillating drop. Our measurements intend to yield either two viscoelastic time scales with the zero-shear viscosity known, or one time scale and the zero-shear viscosity, with the other time scale known. The two time scales are the stress relaxation and the deformation retardation times. The latter is difficult to get for polymer solutions. The present contribution presents results from a large set of measurements of the deformation retardation time. Liquids studied are aqueous solutions of poly(acryl-amides) at varying concentration. The corresponding values of the zero-shear viscosity agree well with the values from shear rheometry. Values of the deformation retardation time differ substantially from the values commonly used in viscoelastic flow simulations. Furthermore, the measured values disagree with the predictions from the viscous-elastic stress splitting approach in linear viscoelasticity. With our study we will provide a consistent set of material properties for the Oldroyd-B model in linear viscoelasticity. This will be important for material modelling in viscoelastic spray simulations.

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“…This approach could be extended to describe elastic modes of surface as well as their nonlinear coupling to capillary waves. The double-periodic structure of the elliptic solutions [11] could describe the new family of normal wave modes predicted in [4].…”

mentioning

confidence: 99%

“…Besides their direct use in rheological and surfactant theory [1][2][3][4][5][6][7], such models apply to cluster physics [8], super-and hyper-deformed nuclei [1], nuclear break-up and fission [2,3,8], thin films [9], radar [4] and even stellar masses and supernova [1,10]. Theoretical approaches are usually based on numerical calculations within different NLD models, [2][3][4] and explain/predict axis-symmetric, non-linear oscillations that are in very good agreement with experiment [1,[5][6][7]. However, there are experimental results which show non-axis-symmetric modes; for example, traveling rotational shapes [5,6] that can lead to fission, cluster emission, or fusion [5][6][7].…”

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confidence: 99%

Nonlinear Modes of Liquid Drops as Solitary Waves

Ludu

Draayer

1998

Phys. Rev. Lett.

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The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such "rotons" were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to drop-like systems from cluster formation to stellar models, including hyperdeformed nuclei and fission. 47.55.Dz, 24.10.Nz, 97.60.Jd Typeset using REVT E X 1

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Investigations of liquid surface rheology of surfactant solutions by droplet shape oscillations: Theory

Cited by 52 publications

References 25 publications

Ultrafast imaging method to measure surface tension and viscosity of inkjet-printed droplets in flight

Ultrafast imaging method to measure surface tension and viscosity of inkjet-printed droplets in flight

Measurement of polymeric time scales from linear drop oscillations

Nonlinear Modes of Liquid Drops as Solitary Waves

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