Article pubs.acs.org/Langmuir
Impact of the Imaginary Part of the Surface Dilatational Modulus on the Splashing Behavior of Drops Matthias J. Hofmann,† Robert Weikl,† Hubert Motschmann,*,† and Ger J. M. Koper‡ †
Institute of Physical and Theoretical Chemistry, University of Regensburg, D-93040 Regensburg, Germany Department of Chemical Engineering, TU Delft, 2600GA Delft, The Netherlands
‡
ABSTRACT: The relation between the complex surface dilatational modulus E of aqueous surfactant solutions and the splashing behavior of their drops on liquid surfaces was investigated. The surface dilatational modulus E of selected surfactant systems has been determined in the frequency range of 3 to 500 Hz by means of the oscillating bubble technique. According to the functional dependence of the phase ϕ of the complex modulus E(ω, c)exp[iϕ(ω, c)] at higher frequencies, adsorption layers can be classified as surface elastic or surface viscoelastic. Each behavior shows pronounced differences in drop splashing experiments. The impact of a drop on the liquid was monitored with a high-speed camera. The splash of a drop is a rather complex phenomenon, so the focus of this article is to establish a relationship between the imaginary part of the surface dilatational modulus E and the height of the drop rebound. These findings may be of importance for formulations in crop protection, introducing a chemical way to influence the impact of drops on solid and liquid interfaces.
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presenting an attractive strategy to fine tune the surface properties by chemical means7 and deliberately control the surface tension and surface rheology.8,9 The difference in surface tension between a water surface covered with an adsorption layer of amphiphiles σfilm and a neat water surface σH2O can be interpreted as a surface pressure Π (physical units [mN m−1]):10
INTRODUCTION We all expect to have fresh, high-quality food at our disposal, serving our nutritional needs at an affordable price. Chemical crop protection is a crucial element in controlling the diseases threatening our food supply.1 Nevertheless, pesticides jeopardize the environment, and there is a trade-off between the benefits and environmental cost.2 On the one hand, waiving pesticides and herbicides will cause harvesting to decrease, but on the other hand, misuse or overuse can lead to severe damage.3 Great care should be taken to target solely the foliage and avoid spray drifting or off-target contamination. In this article, we demonstrate that a careful adjustment of the surface rheological properties of the applied pesticide formulations may help to minimize these undesired side effects, introducing a chemical way to fine tune the spraying process. A plant protection formulation gets nebulized and sprayed on a leaf. The first interaction between the contact area and drop involves a deformation of its surface. The drop impact on a fluid or solid surface is a rather complex phenomenon. The underlying physics is described in an extended review article by Rein.4 A crucial element determining the height of drop rebound is the dynamic surface tension within the neck formed between the drop and the bulk liquid and the energy dissipation that occurs during its rupture.5 The impact of the drop may also lead to the generation of surface waves, satellite drops, and other accompanying processes.6 The focus of this article is the elucidation of the impact of the imaginary part of the surface dilatational modulus E on this process. The modulus can be controlled by adsorption layers of soluble amphiphiles, © 2015 American Chemical Society
Π = σH2O − σfilm
(1)
The surface elastic dilatational modulus E is defined by analogy to the corresponding bulk quantity as the change in surface pressure ΔΠ upon a relative change in area ΔA/A.11 E = −A
∂Π = |E(ω , c)|exp[iϕ(ω , c)] ∂A
(2)
The modulus depends on the bulk concentration c of the amphiphile and the frequency ω of the harmonic compression and expansion cycles. The magnitude and phase of this complex quantity can be measured with the oscillating bubble technique.12 According to the functional dependence of the phase ϕ of the complex modulus E at higher frequencies, adsorption layers can be classified as either surface elastic or surface viscoelastic.13 The expansion or compression of the surface creates a nonequilibrium state. As a result, the surface coverage deviates from the equilibrium value. In an instant of Received: May 20, 2014 Revised: January 23, 2015 Published: January 24, 2015 1874
DOI: 10.1021/la5050128 Langmuir 2015, 31, 1874−1878
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Langmuir
The amplitude of the pressure response and the phase shift between the piezo driving oscillation and pressure signal were evaluated via a phase-sensitive lock-in detection scheme.18 The amplitude of the pressure response is proportional to the magnitude of the complex surface dilatational modulus |E|, while the phase shift gives access to the imaginary part of the modulus and the intrinsic surface dilatational viscosity κ. A detailed description of the oscillating bubble technique can be found in publications by Ravera et al.19 and Koelsch and coworkers.20 The latter describes the impact of hydrodynamic contributions to the recorded pressure and ways to eliminate this unwanted effect in data treatment. In order to improve the reproducibility and precision of the measurements, a high-speed camera was synchronized with the piezo driver capturing images of the oscillating bubble in a stroboscopic fashion. The evaluation of the images yields the relative changes in area ΔA/A upon oscillation. The system was calibrated using decanoic acid at a concentration of 0.2 mM as a well-defined standard. The frequency dependence of the magnitude of the surface dilatational modulus |E| and its corresponding phase ϕ has been measured with the oscillating bubble technique from 3 to 500 Hz. Two strikingly different shapes of the functional dependence |E(ω)| and ϕ(ω) were observed; the surface elastic and the surface viscoelastic behavior. The characteristics of both quantities |E(ω)| and ϕ(ω) are shown in Figures 2 and 3 as a function of frequency.
stress, the deviation of the surface tension from its equilibrium value is maximized. The surface tension returns to its equilibrium with characteristic relaxation times. Different relaxation processes such as the exchange kinetics of surfactants between the topmost layer and subsurface layer,14 the reorientation of surfactants, regions of different compressibilities,15 and the dissolution of (hemi)micelles in the case of micellar solutions may contribute to the dilatational modulus. A discussion of the prevailing molecular mechanism that gives rise to an imaginary part of the modulus is not in the scope of this article. The goal of this article is the investigation of the influence of the complex surface dilatational modulus E on drop splashing behavior. The modulus can be controlled by chemical means, and various amphiphiles are used to establish the relationship between the elasticity modulus E and the drop height in a splash experiment.
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EXPERIMENTAL SECTION
Materials. The surfactant systems were selected in collaboration with an industrial partner working in the field of plant protection. The following chemicals were used: sodium dodecyl sulfate (SDS, Merck), cerium(IV) sulfate tetrahydrate (Ce(SO4)2·4H2O, Merck), decyl dimethyl phosphine oxide (C10DMPO, Convertex), polyoxyethylene8-tridecyl ether (C13EO8, BASF), polyoxyethylene-7-decyl ether (C10EO7, BASF), polyoxyethylene-10-decyl ether (C10EO10, BASF), polyoxyethylene-14-decyl ether (C10EO14, BASF), and decanoic acid (Merck). Additionally, C10DMPO was analyzed with tributyl phosphate (TBP, Sigma-Aldrich) and SDS with Ce(SO4)2·4H2O as additives. All measurements have been carried out at room temperature and below the critical micelle concentration (cmc) with the exception of C13EO8 and C10EO10 at concentrations above 3 mM. Measurement of the Dilatational Rheology: The Oscillating Bubble Technique. The complex surface dilatational modulus E was measured by the oscillating bubble technique.12 A scheme of the crosssectional view of this technique is shown in Figure 1. A small hemispherical bubble was formed at the tip of a capillary with a diameter of about 0.3 which was immersed in the liquid. The bubble was forced into a sinusoidal oscillation by a piezoelectric translator serving as an actuator. The expansion and compression cycles lead to a harmonic modulation of the Laplace pressure16,17 within the chamber, which was recorded by another sensitive piezo crystal acting as a pressure transducer located at the bottom of the chamber.
Figure 2. Characteristics of the frequency dependence of the amplitude of the surface dilatational modulus: surface elastic tridecyl-dimethylphosphinoxid (black circles) and surface viscoelastic decyl-dimethylphosphinoxid (red circles). Adsorption layers are classified as surface elastic if the phase vanishes at higher frequencies and the magnitude of the modulus levels off to a plateau value with increasing frequency.19 This implies that the equilibrium between the surface layer and bulk is established instantaneously and all dissipative losses are located within the bulk. The surface tension is then only a function of the surface composition. Viscous effects at lower frequencies are solely caused by bulk diffusion.13 Adsorption layers are classified as surface viscoelastic if the phase does not vanish at higher frequencies and the magnitude of the dilatational modulus increases with the frequency of the bubble oscillation. The surface layer exhibits surface viscoelastic behavior at all frequencies, implying that energy is dissipated within the surface layer.21 This can be accounted for by the introduction of an intrinsic surface dilatational viscosity κ. The differences between both types of behaviors are more pronounced at higher frequencies whereas at lower frequencies (
