Shape oscillations of drops in the presence of surfactants

Lu, Hui‐Lan; Apfel, Robert E.

doi:10.1017/s0022112091001131

Cited by 44 publications

(69 citation statements)

References 16 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: 83%

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: 83%

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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“…Prosperetti (1980a) also analysed the oscillations of bubbles and drops in terms of the initial-value problem, which as already stated is not our aim here. Theoretical and experimental results on the role of surfactants were found by Lu & Apfel (1991) quency in 3D inviscid flows is…”

Section: Dropletsmentioning

confidence: 99%

“…Similar studies have been led for other deformable objects. The problem of oscillations of drops or vesicles has received substantial attention over the years (Lamb 1932;Prosperetti 1980b;Lu & Apfel 1991;Rochal et al 2005). However, most of the approaches treat three-dimensional configurations, relevant of course to practical applications.…”

Section: Introductionmentioning

confidence: 99%

On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

2014

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We propose a procedure -partly analytical and partly numerical -to find the frequency and the damping rate of the small-amplitude oscillations of a massless elastic capsule immersed in a two-dimensional viscous incompressible fluid. The unsteady Stokes equations for the stream function are decomposed onto normal modes for the angular and temporal variables, leading to a fourth-order linear ordinary differential equation in the radial variable. The forcing terms are dictated by the properties of the membrane, and result into jump conditions at the interface between the internal and external media. The equation can be solved numerically, and an excellent agreement is found with a fullycomputational approach we developed in parallel. Comparisons are also shown with the results available in the scientific literature for drops, and a model based on the concept of embarked fluid is presented, which allows for a good representation of the results and a consistent interpretation of the underlying physics.

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“…The balance of the dynamic and capillary pressure across the surface Σ1 follows by expanding up to third order in ξ the square root of the surface energy of the drop [2,3,11],…”

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confidence: 99%

“…These traveling deformations ("rotons") can range from small oscillations (normal modes), to cnoidal oscillations, and on out to solitary waves. The same approach can be applied to bubbles as well, except that the boundary condition on Σ 2 is replaced by a far-field condition [2,3] (recently important in the context of single bubble sonoluminiscence). Nonlinear phenomena can not be fully investigated with normal linear tools, e.g.…”

mentioning

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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Shape oscillations of drops in the presence of surfactants

Cited by 44 publications

References 16 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

On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

Nonlinear Modes of Liquid Drops as Solitary Waves

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