Session L6: Drops VIII: Complex Phenomena

Foliar disease transmission: insights from fluid dynamics

Rainfalls are suspected to trigger the spread of a multitude of foliar diseases that could be devastating for agricultural and forestry outputs and balance. A wealth of key fluid mechanics phenomena arise from the impact of drops on plant leaves. We present the results of a combined experimental and modelling investigation shading light on the modes of precipitation-induced foliar disease transmission.   

Sliding motion of an oscillating drop driven by ac electrowetting on inclined plane

When a drop is placed on an inclined solid plane, the drop can stick to or slide along the solid surface due to an opposition between the gravitational force and the pinning force from contact angle hysteresis. Here we demonstrate that sessile drops of sizes below the capillary length can be mobilized through drop oscillation induced by ac electrowetting at low frequency on a low inclined solid plane. The effects of ac frequency on the sliding condition and terminal sliding velocity are investigated. At resonant frequency, drops reach maximum terminal sliding velocities. Varying the applied voltage at a fixed frequency, we find the threshold voltage for a sliding drop and the empirical relationship between the applied voltage and terminal sliding velocity. Using the relationship between drop size and frequency, we can selectively slide drops of a specific size along an inclined plane.   

Droplet dynamics in microfluidic stratifications

We experimentally study the dynamic response of viscous droplets to external microflows. A segmented flow of droplets is injected into a stratified flow of miscible fluids using a square microchannel with two focusing sections. This method enables us to locally manipulate the capillary number of the continuous phase and examine the hydrodynamic coupling between droplets and a variety of flow fields in confined geometries. Focus is on the behavior of droplets entering a region with parallel streams having different interfacial tensions and viscosities. A general phase-diagram is proposed and droplet behavior is investigated in relation with dynamic wetting properties. This study shows methods for modifying the physicochemical environment of microfluidic droplets.   

Scaling laws for electrospraying

When stressed by strong electric fields, fluid menisci develop conical structures called Taylor cones which emit from their tips fine jets that in turn break up to form a mist of charged droplets. This phenomenon, known as electrohydrodynamic tip-streaming, cone-jetting, or electrospraying finds application in a number of industrially and scientifically important processes, including mass spectrometry, particle synthesis, and cloud physics. Here, this phenomenon is analyzed using the leaky-dielectric model developed by Taylor and Melcher for the situation in which an initially spherical free drop of an incompressible Newtonian fluid surrounded by a gas is subjected to an electric field. The resulting initial-boundary-value-problem is solved using the finite element method with elliptic mesh generation and adaptive, implicit time integration. The simulation results and simple scaling arguments are then used to infer the universal scaling laws governing the sizes and charges of the small electrospray drops.   

Transient Reduction of the Drag Coefficient of Charged Droplets via the Convective Reversal of Stagnant Caps

Droplets are frequently observed to move as if they were solid rather than liquid, i.e. with no slip at the liquid-liquid interface. This behavior is usually explained in terms of the so-called ``stagnant cap'' model, in which surfactants accumulate at the trailing edge of the droplet, immobilizing the surface and increasing the observed drag coefficient. Here we show that the drag coefficient for charged droplets is temporarily reduced by reversing the direction of an electric driving force. Using high speed video we simultaneously track the velocity and relative interfacial velocity of individual aqueous droplets moving electrophoretically through oil. The observed surface behavior is highly sensitive to the surfactant concentration. For sufficiently low or sufficiently high surfactant concentrations, upon reversal of the electric field the droplet rapidly accelerates in the opposite direction but then decelerates, concurrent with a transient rearrangement of tracer particles on the droplet surface. In contrast, droplets with intermediate surfactant concentrations exhibit no deceleration nor tracer particle rearrangement. We interpret these observations in terms of convectively dominated rearrangement of the stagnant cap, and we discuss the implications for precise electrophoretic control of droplet motion in lab-on-a-chip devices as well as droplet charge estimation through velocimetry.   

Electromagnetic liquid pistons for capillarity-based pumping

Two adjoining ferrofluid droplets can behave as an electronically-controlled oscillator or switch by an appropriate balance of magnetic, capillary, and inertial forces. Their motion can be exploited to displace a surrounding liquid, forming electromagnetic liquid pistons. Such ferrofluid pistons can pump a precise volume of liquid via finely tunable amplitudes or resonant frequencies with no solid moving parts. Here we demonstrate the use of these liquid pistons in capillarity-dominated systems for variable focal distance liquid lenses with nearly perfect spherical interfaces. These liquid/liquid lenses feature many promising qualities not previously realized together in a liquid lens, including large apertures, immunity to evaporation, invariance to orientation relative to gravity, and low driving voltages. The dynamics of these liquid pistons is examined, with experimental measurements showing good agreement with a spherical cap model. A centimeter-scale lens was shown to respond in excess of 30 Hz, with resonant frequencies over 1 kHz predicted for scaled down systems.   

Negative radiation forces and the asymmetry of scattered radiation: spheres in Bessel beams

The discovery that acoustical [1] and optical [2,3] radiation forces computed on spheres placed on the axis of acoustical and optical Bessel beams may be opposite the direction of beam propagation makes it appropriate to reexamine the relationship between radiation forces and the asymmetry of the scattered radiation. For all of the previously identified acoustical cases in which the force was negative and the scattering pattern was also computed, it was found that the backscattering was suppressed and the forward scattering relatively enhanced (see e.g. [1]). In the present research the acoustic radiation force on an arbitrary isotropic sphere is related to the asymmetry in the scattering and the extinction introduced by the sphere for the case of a helical Bessel beam of arbitrary order [4]. The analysis confirms that conditions are more favorable for generating negative forces when the asymmetry is such that the backscattering is suppressed relative to the forward scattering. It is also found, however, that absorption of power by the sphere gives rise to a positive force contribution, a term which has been neglected in the corresponding optical analysis [2].\\[0pt] [1] P. L. Marston, J. Acoust. Soc. Am 120, 3518 (2006). [2] J. Chen et al., Nature Photonics (2011). [3] A. Novitsky \& C.-W. Qiu, arXiv:1102.5285v1 (2011). [4] L. K. Zhang \& P. L. Marston (submitted).   

Pulsating Electrohydrodynamic Cone-Jets: from Choked Jet to Oscillating Cone

Pulsating cone-jets occur in a variety of electrostatic spraying and printing systems. We report an experimental study of the pulsation frequency to reconcile two models based on a choked jet and an oscillating cone, respectively. The two regimes are demarcated by the ratio of the supplied flow rate ($Q_s$) to the minimum flow rate ($Q_m$) required for a steady Taylor cone-jet. When $Q_s < Q_m$, the electrohydrodynamic flow is choked at the nozzle because the intermittent jet, when on, emits mass at the minimum flow rate; the pulsation frequency in the choked jet regime is proportional to $Q_s/Q_m$. When $Q_s > Q_m$, the Taylor cone anchored at the nozzle experiences a capillary oscillation analogous to the Rayleigh mode of a free drop; the pulsation frequency in the oscillating cone regime plateaus to the capillary oscillation frequency which is independent of $Q_s/Q_m$.   

Electrohydrodynamic drop deformation by a strong electric field

Using matched asymptotic expansions within the Taylor-Melcher leaky-dielectric model, we analyze the strong deformation of a drop by a strong electric field. As is common in slender-body analyses, the small drop slenderness is used as the expansion parameter. This parameter however is not a priori specified in the problem formulation, and must be found throughout the course of the asymptotic solution. Sherwood's scaling for dielectric liquids, inverse with the 6/7-power of the electric field, applied here. Slender shapes are possible only for low drop viscosities. We identify a new inequality, in terms of material-property ratios, necessary for the evolution to a slender shape, which is independent of Taylor discriminating inequality, necessary for initial deviation to prolate shapes.   

Desiccation of a Sessile Drop of Blood: Cracks Formation and Delamination

The evaporation of drops of biological fluids has been studied since few years du to several applications in medical fields such as medical tests, drug screening, biostabilization... The evaporation of a drop of whole blood leads to the formation of final typical pattern of cracks. Flow motion, adhesion, gelation and fracturation all occur during the evaporation of this complex matter. During the drying, a sol-gel transition develops [1]. The drying kinetics is explained by a simple model of evaporation taking account of the evolution of the gelation front. The system solidifies and when stresses are too important, cracks nucleate. The cracks formation and the structure of the crack pattern are investigated. The initial crack spacing is found in good agreement with the implementation in open geometry of the model of cracks formation induced by evaporation proposed by Allain and Limat [2]. Finally, the drop is still drying after the end of the formation of cracks which leads, like in the situation of colloid suspensions [3], to the observation of a delamination phenomenon.\\[0pt] [1] B. Sobac and D. Brutin, Structural and Evaporative Evolutions in Desiccating Sessile Drops of Blood, Phys. Rev. E 84, 011603, 2011. [2] C. Allain and L. Limat, Phys. Rev. Lett. 74, 2981 (1995). [3] L. Pauchard, B. Abou, K. Sekimoto, Infuence of Mechanical Properties of Nanoparticles on Macrocrack Formation, Langmuir, 25(12), 6672-6677, 2009.