Stokes flow near the contact line of an evaporating drop

The evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below $90^\circ$, the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the description of the flow inside an evaporating drop has remained a challenge. Here, we focus on the asymptotic behaviour near the pinned contact line, by analytically solving the Stokes equations in a wedge geometry of arbitrary contact angle. The flow field is described by similarity solutions, with exponents that match the singular boundary condition due to evaporation. We demonstrate that there are three contributions to the flow in a wedge: the evaporative flux, the downward motion of the liquid-air interface and the eigenmode solution which fulfils the homogeneous boundary conditions. Below a critical contact angle of $133.4^\circ$, the evaporative flux solution will dominate, while above this angle the eigenmode solution dominates. We demonstrate that for small contact angles, the velocity field is very accurately described by the lubrication approximation. For larger contact angles, the flow separates into regions where the flow is reversing towards the drop centre.Comment: Journal of Fluid Mechanics 709 (2012

Stokes flow in a drop evaporating from a liquid subphase

The evaporation of a drop from a liquid subphase is investigated. The two liquids are immiscible, and the contact angles between them are given by the Neumann construction. The evaporation of the drop gives rise to flows in both liquids, which are coupled by the continuity of velocity and shear-stress conditions. We derive self-similar solutions to the velocity fields in both liquids close to the three-phase contact line, where the drop geometry can be approximated by a wedge. We focus on the case where Marangoni stresses are negligible, for which the flow field consists of three contributions: flow driven by the evaporative flux from the drop surface, flow induced by the receding motion of the contact line, and an eigenmode flow that satisfies the homogeneous boundary conditions. The eigenmode flow is asymptotically subdominant for all contact angles. The moving contact-line flow dominates when the angle between the liquid drop and the horizontal surface of the liquid subphase is smaller than $90^\circ$, while the evaporative-flux driven flow dominates for larger angles. A parametric study is performed to show how the velocity fields in the two liquids depend on the contact angles between the liquids and their viscosity ratio.Comment: submitted to Physics of Fluid

Droplet deformation by short laser-induced pressure pulses

When a free-falling liquid droplet is hit by a laser it experiences a strong ablation driven pressure pulse. Here we study the resulting droplet deformation in the regime where the ablation pressure duration is short, i.e. comparable to the time scale on which pressure waves travel through the droplet. To this end an acoustic analytic model for the pressure-, pressure impulse- and velocity fields inside the droplet is developed in the limit of small density fluctuations. This model is used to examine how the droplet deformation depends on the pressure pulse duration while the total momentum to the droplet is kept constant. Within the limits of this analytic model, we demonstrate that when the total momentum transferred to the droplet is small the droplet shape-evolution is indistinguishable from an incompressible droplet deformation. However, when the momentum transfer is increased the droplet response is strongly affected by the pulse duration. In this later regime, compressed flow regimes alter the droplet shape evolution considerably.Comment: Submitted to JF

Avalanche of particles in evaporating coffee drops

The pioneering work of Deegan et al. [Nature 389, (1997)] showed how a drying sessile droplet suspension of particles presents a maximum evaporating flux at its contact line which drags liquid and particles creating the well known coffee stain ring. In this Fluid Dynamics Video, measurements using micro Particle Image Velocimetry and Particle Tracking clearly show an avalanche of particles being dragged in the last moments, for vanishing contact angles and droplet height. This explains the different characteristic packing of the particles in the layers of the ring: the outer one resembles a crystalline array, while the inner one looks more like a jammed granular fluid. Using the basic hydrodynamic model used by Deegan et al. [Phys. Rev. E 62, (2000)] it will be shown how the liquid radial velocity diverges as the droplet life comes to an end, yielding a good comparison with the experimental data.Comment: This entry contains a Fluid Dynamics Video candidate for the Gallery of Fluid Motion 2011 and a brief article with informatio

iLIF: illumination by Laser-Induced Fluorescence for single flash imaging on a nanoseconds timescale \ud

The challenge in visualizing fast microscale fluid motion phenomena is to record high-quality images free of motion-blur. Here, we present an illumination technique based on laser-induced fluorescence which delivers high-intensity light pulses of 7 ns. The light source consists of a Q-switched Nd:YAG laser and a laser dye solution incorporated into a total internal reflection lens, resulting in a uni-directional light beam with a millimeter-sized circular aperture and 3° divergence. The laser coherence, considered undesirable for imaging purposes, is reduced while maintaining a nanoseconds pulse duration. The properties of the illumination by laser-induced fluorescence (iLIF) are quantified, and a comparison is made with other high-intensity pulsed and continuous light source

Order-to-disorder transition in ring-shaped colloidal stains

A colloidal dispersion droplet evaporating from a surface, such as a drying coffee drop, leaves a distinct ring-shaped stain. Although this mechanism is frequently used for particle self-assembly, the conditions for crystallization have remained unclear. Our experiments with monodisperse colloidal particles reveal a structural transition in the stain, from ordered crystals to disordered packings. We show that this sharp transition originates from a temporal singularity of the flow velocity inside the evaporating droplet at the end of its life. When the deposition speed is low, particles have time to arrange by Brownian motion, while at the end, high-speed particles are jammed into a disordered phase.Comment: accepted for PR

Fluid flow in drying drops

When a suspension drop evaporates, it leaves behind a drying stain. Examples of these drying stains encountered in daily life are coffee or tea stains on a table top, mineral rings on glassware that comes out of the dishwasher, or the salt deposits on the streets in winter. Drying stains are also present in industrial processes, for example in the printing and coating industry, where the non-uniform drying of drops can be a problem. Pattern formation by evaporation of colloidal suspension drops can however also be used as a tool to manufacture tiny structures on a scale where direct manipulation is not possible.\ud In order to either prevent ring-stain formation or control the type of stains that are formed, one needs to understand the basic physics of evaporating drops and their internal fluid flow. In this thesis we focused on the fundamentals of drop evaporation, evaporation-driven flow in drying drops, and the subsequent particle transport and deposition. We used a simple model system: a macroscopic sessile water drop that evaporates under atmospheric conditions and contains spherical polystyrene particles. By evaporation of these colloidal suspension drops remarkable, highly-ordered drying patterns were obtained. The particle arrangement inside these patterns originates from a competition between particle diffusion and convection and therefore depends on the evaporation rate of the drop and the particle size

Competition, Cooperation and Communication: International and Minority Student – Athletes

This exploratory qualitative research project will focus on how diverse international and minority student-athletes face communication and identity challenges at home, in classes, and on teams. Research addressed the academic and identity formation challenges of student-athletes and explained that educators’ involvement in student-athletes’ athletic world might assist them to accommodate student athletes better (Jolly, 2008). Further research states that cross-cultural interpersonal conflict affect sport-team cohesiveness (Stura & Johnson, 2017) and that student-athletes might encounter a higher degree of stress (Rodriquez, 2014). The negotiation process of the athletic culture with the non-athletic academic culture will be analyzed. Communication challenges between peer-athletes as well as with coaches will be examined. Findings will be gathered by distributing surveys to international and minority student-athletes at FIU, followed by face-to-face interviews with a subset of surveyed athletes. Additionally, secondary literature sources are being reviewed. I hope to determine how the home, athletic, and academic environment plays into the overall identity formation of international and minority student-athletes. I aspire to pose strategies to bridge the gap between diverse athletes within their teams and between the athletic and academic environment; and to aid student-athletes to form a multi-faceted identity. I anticipate that international and minority student athletes construct and understand identity through overlapping spheres of influence including language, culture and athleticism that are all manifested and apparent in classes, on teams and within families. I further anticipate that there exists a communication barrier between peer-athletes, and between athletes and coaches due to different cultures and languages, as well as between athletes and non-athletic academic individuals due to biased views of each other’s groups. The project findings might assist all stakeholders, including coaches, advisors, and educators to integrate methods within their teaching and training to better engage student athletes and assist them to establish a sense of belonging