Drop Motion Research Articles

A Contact Line Dynamic Model for a Conducting Water Drop on an Electrowetting Device

AbstractThe static shape of drop under electrowetting actuation is well studied and recent electrowetting theory and experiments confirm that the local contact angle (microscopic angle) is unaffected while the apparent contact angle (macroscopic angle) is characterized by the Lippmann-Young equation. On the other hand, the evolution of the drop motion under electrowetting actuation has received less attention. In this paper, we investigate the motion of a conducting water drop on an electrowetting device (EWD) using the level set method. We derive a contact line two-phase flow model under electrowetting actuation using energy dissipation by generalizing an existing contact line model without the electric field. Our model is consistent with the static electrowetting theory as the dynamic contact angle satisfies the static Young's equation under equilibrium conditions. Our steady state results show that the apparent contact angle predicted by our model satisfies the Lippmann-Young's relation. Our numerical results based on the drop maximum deformation agree with experimental observations and static electrowetting theory. Finally, we show that for drop motion our results are not as good due to the difficulty of computing singular electric field accurately. Nonetheless, they provide useful insights and ameaningful first step towards the understanding of the drop dynamics under electrowetting actuation.

Wave-Based Turing Machine: Time Reversal and Information Erasing.

The investigation of dynamical systems has revealed a deep-rooted difference between waves and objects regarding temporal reversibility and particlelike objects. In nondissipative chaos, the dynamic of waves always remains time reversible, unlike that of particles. Here, we explore the dynamics of a wave-particle entity. It consists in a drop bouncing on a vibrated liquid bath, self-propelled and piloted by the surface waves it generates. This walker, in which there is an information exchange between the particle and the wave, can be analyzed in terms of a Turing machine with waves as the information repository. The experiments reveal that in this system, the drop can read information backwards while erasing it. The drop can thus backtrack on its previous trajectory. A transient temporal reversibility, restricted to the drop motion, is obtained in spite of the system being both dissipative and chaotic.

A multi-objective intelligent water drop algorithm to minimise cost Of goods sold and time to market in logistics networks

The Intelligent Water Drop (IWD) algorithm is inspired by the movement of natural water drops (WD) in a river. A stream can find an optimum path considering the conditions of its surroundings to reach its ultimate goal, which is often a sea. In the process of reaching such destination, the WD and the environment interact with each other as the WD moves through the river bed. Similarly, the supply chain problem can be modelled as a flow of stages that must be completed and optimised to obtain a finished product that is delivered to the end user. Every stage may have one or more options to be satisfied such as suppliers, manufacturing or delivery options. Each option is characterised by its time and cost. Within this context, multi–objective optimisation approaches are particularly well suited to provide optimal solutions. This problem has been classified as NP hard; thus, this paper proposes an approach aiming to solve the logistics network problem using a modified multi–objective extension of the IWD which returns a Pareto set.Artificial WD, flowing through the supply chain, will simultaneously minimise the cost of goods sold and the lead time of every product involved by using the concept of Pareto optimality. The proposed approach has been tested over instances widely used in literature yielding promising results which are supported by the performance measurements taken by comparison to the ant colony meta-heuristic as well as the true fronts obtained by exhaustive enumeration. The Pareto set returned by IWD is computed in 4 s and the generational distance, spacing, and hyper–area metrics are very close to those computed by exhaustive enumeration. Therefore, our main contribution is the design of a new algorithm that overcomes the algorithm proposed by Moncayo-Martínez and Zhang (2011).This paper contributes to enhance the current body of knowledge of expert and intelligent systems by providing a new, effective and efficient IWD-based optimisation method for the design and configuration of supply chain and logistics networks taking into account multiple objectives simultaneously.

Predicting flows from the Dynamic Ergun Equation

Positron Emission Particle Tracking observations of charge and slurry flow have shown that the pressure drop is effectively described by an Euler equation modified by a Darcy-like term. Here we consider the inverse problem: constructing and testing approximate solutions to the new Dynamic Ergun Equation. These solutions allow the prediction of transport in tumbling mills and other systems given information on the pressure drop and charge motion.

Investigation of Fog Collection on Cactus-inspired Structures

We demonstrate the application of cactus-inspired structures for fog collection. The drop-on-cone system is modeled to analyze Gibbs free-energy gradients, equilibrium positions and motion of drops. Normalized free energy and free energy gradient are presented to characterize barrel and clam-shell drops, revealing the relations of the driving force and wettability to the half-apex angle of the cones. Small half-apex angle results in long collecting length and weak driving force. Thus it is important for fog collection to balance the driving force and collecting length with a suitable half-apex angle. Fog collection experiments on cactus-inspired structures are conducted for verification. Inflection points around 1.1° are observed, where the fog collection ability is mainly limited by the weak driving force when below the inflection points, while increases with the collecting length when above the inflection points. These indicate that the half-apex angle at the inflection point is a compromise between the driving force and collecting length, agreeing with the normalized functions. The results also prove that the hydrophilic cones are more suitable for fog collection with regard to condensation and driving force. Our research offers design guidance for efficient fog collection structure.

Water drop movement on woven fiber mat surfaces due to flow of diesel fuel

Abstract Fuel contamination by water is one of the major factors of engine failures. Separation of water from diesel fuel is often achieved by coalescing or depth filter media. The separation performance is strongly related to the motion of drops on the surface and in the depth of a filter medium. The dynamics of the motions of drops on a filter surface are influenced by many factors such as the wetting properties of the media. Direct observations of drop movements on fiber surfaces are not well documented. Of particular interest in this work are the dynamics of drops on surfaces of hydrophobic mats that resist drop movement into the interior of the mat, forcing the drops to move on the surface of the mat. Such materials function as barriers to the dispersed phase and allow the continuous phase to move through the mat. In this paper, the motions of water drops were studied on surfaces of mats woven of polypropylene, nylon and Teflon™ (ie, polytetrafluoroethylene) fibers. Pore sizes of the mats ranged from 100 to 1000 μm and drop sizes ranged from 200 to 6000 μm. The flow of ultra low sulfur diesel fuel parallel to the mat surface provided a drag force that induced the movement of the drops. The effects of surface wettability, flow velocity, drop size, fiber size, fiber mat pore size, fiber mat orientation were considered. A correlation for a drag coefficient to estimate the average velocity of drops moving on the woven mats surfaces was derived from the flow and the material’s characteristics. In addition, another correlation was obtained for estimating the minimum velocity, or minimum Reynolds number, required to initiate the drop motion on the woven mat surfaces.

New Drop Fluidics Enabled by Magnetic-Field-Mediated Elastocapillary Transduction.

This research introduces a new drop fluidics that uses a deformable and stretchable elastomeric film as the platform instead of the commonly used rigid supports. Such a soft film impregnated with magnetic particles can be modulated with an external electromagnetic field that produces a vast array of topographical landscapes with varying surface curvature, which, in conjunction with capillarity, can direct and control the motion of water droplets efficiently and accurately. When a thin layer of oil is present on this film that is deformed locally, a centrosymmetric wedge is formed. A water droplet placed on this oil-laden film becomes asymmetrically deformed, thus producing a gradient of Laplace pressure within the droplet and setting it in motion. A simple theory is presented that accounts for the droplet speed in terms of such geometric variables as the volume of the droplet and the thickness of the oil film covering the soft elastomeric film as well as material variables such as the viscosity of the oil and the interfacial tension of the oil-water interfaces. Following the verification of the theoretical result using well-controlled model systems, we demonstrate how the electromagnetically controlled elastocapillary force can be used to manipulate the motion of single and/or multiple droplets on the surface of the elastomeric film and how elementary operations such as drop fusion and thermally addressed chemical transformation can be carried out in aqueous droplets. It is expected that the resulting drop fluidics would be suitable for the digital control of drop motion by simply switching on and off the electromagnetic fields applied at different positions underneath the elastomeric film in a Boolean sequence. We anticipate that this method of directing and manipulating water droplets is poised for application in various biochemical reaction engineering situations, an example of which is the polymerase chain reaction (PCR).

Effect of wetting difference across junction on dynamics of drops impacting on the junction of dual‐textured surfaces

The effect of wetting difference across the junction of smooth and groove‐textured portions of a dual‐textured surface on the various stages in the dynamics of liquid drops impacting on the junction is reported. Two dual‐textured surfaces with substantially different wetting difference across their junction, Δθe = 65° and 25°, made of intrinsically hydrophilic stainless steel and intrinsically hydrophobic poly‐di‐methyl‐siloxane (PDMS) are considered. The effect of wetting difference across the junction is dominantly seen on the net drop drift velocity and subsequent bulk drop movement, ξ. ξ on the PDMS dual‐textured surface is less than that on the stainless dual‐textured surface due to the lower wetting difference across the junction of the former. The variation of ξ with impact velocity shows a contrasting trend between the stainless steel and PDMS dual‐textured surfaces due to the difference in critical impact velocity corresponding to drop impregnation on their groove‐textured portions. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4109–4118, 2016

Thermocapillary migration of an isolated droplet and interaction of two droplets in zero gravity

Fluid transfer within a stagnant liquid presents a significant challenge in zero-gravity conditions due to the lack of buoyancy effects. This challenge can be overcome by the utilisation of the Marangoni effect, or more specifically thermocapillary migration. The thermocapillary migration of droplets is driven by temperature gradients within the multiphase system which bring about a surface tension gradient driving the flow from the cold to the hot region. The migration speed of the droplet is significantly impacted by the heat transfer both inside the droplet and in its surroundings.This paper presents the analysis of drop movement in a stagnant liquid using computational fluid dynamics (CFD). The commercial software package Ansys-Fluent v.13 [1] is used to solve the governing continuum conservation equations for two-phase flow using the Volume of Fluid (VOF) method to track the liquid/liquid interface in 2D domain. This approach has been shown to be a valuable tool for studying the phenomena of liquid–liquid interaction. A strong agreement has been found with experimental observations conducted in microgravity.The inherent velocity of drops has been found to decrease with increasing Marangoni number. This finding is in line with the previous space experiments of Xie et al. (2005) [2] and in contrast to the numerical results of Ma (1999) [3] using the same liquid for the droplet and the host liquid.Data obtained in the present numerical study has been used to derive an expression predicting the scaled droplet velocity as a function of Marangoni number. A numerical study of the interaction of two spherical droplets undergoing thermocapillary migration in microgravity is also presented. The temperature thrust from the leading droplet towards the trailing droplet was found to disturb its migration velocity, but the trailing droplet was found to have no influence on the migration of the leading droplet.

Reactive Leidenfrost droplets

We experimentally investigate the reactivity of Leidenfrost droplets with their supporting substrates. Several organic liquids are put into contact with a copper substrate heated above their Leidenfrost temperature. As the liquid evaporates, the gaseous flow cleans the superficial copper oxide formed at the substrate surface and the reaction maintains a native copper spot below the evaporating droplet. The copper spot can reach several times the droplet size for the most reactive organic compounds. This study shows an interesting coupling between the physics of the Leidenfrost effect and the mechanics of reactive flows. Different applications are proposed such as drop motion tracking and vapor flow monitoring.

Effect of surface charge convection and shape deformation on the dielectrophoretic motion of a liquid drop.

The dielectrophoretic motion and shape deformation of a Newtonian liquid drop in an otherwise quiescent Newtonian liquid medium in the presence of an axisymmetric nonuniform dc electric field consisting of uniform and quadrupole components is investigated. The theory put forward by Feng [J. Q. Feng, Phys. Rev. E 54, 4438 (1996)10.1103/PhysRevE.54.4438] is generalized by incorporating the following two nonlinear effects-surface charge convection and shape deformation-towards determining the drop velocity. This two-way coupled moving boundary problem is solved analytically by considering small values of electric Reynolds number (ratio of charge relaxation time scale to the convection time scale) and electric capillary number (ratio of electrical stress to the surface tension) under the framework of the leaky dielectric model. We focus on investigating the effects of charge convection and shape deformation for different drop-medium combinations. A perfectly conducting drop suspended in a leaky (or perfectly) dielectric medium always deforms to a prolate shape and this kind of shape deformation always augments the dielectrophoretic drop velocity. For a perfectly dielectric drop suspended in a perfectly dielectric medium, the shape deformation leads to either increase (for prolate shape) or decrease (for oblate shape) in the dielectrophoretic drop velocity. Both surface charge convection and shape deformation affect the drop motion for leaky dielectric drops. The combined effect of these can significantly increase or decrease the dielectrophoretic drop velocity depending on the electrohydrodynamic properties of both the liquids and the relative strength of the electric Reynolds number and electric capillary number. Finally, comparison with the existing experiments reveals better agreement with the present theory.

Drop movements and replacement on surface driven by shear force via hybrid atomistic–continuum simulations

The movements and replacement of a nanoscale drop on a horizontal surface driven by shear force from the other immiscible fluid have been investigated by hybrid atomistic–continuum modelling in this work. The interfacial interaction near the drop, which may not be fully covered by the continuum theories, is modelled by molecular dynamics for accurate capture of transport behaviour, while the bulk flow region is simulated by the lattice Boltzmann method for high efficiency. The momentum exchange between atomistic and continuum regions is realised in a buffer region to couple the multiscale effects, where we propose an artificial solid molecular layer at the outer edge of buffer region to ensure the continuity of shear force between different regions. The influences of moving wall velocity, drop size, surface tension on resistance are examined. Our results show that the resistances increase with the moving wall velocity. A larger drop leads to a larger resistance to drop moving on solid wall, and a larger resistance to bulk flow. A higher surface tension results in a higher resistance to drop movement and bulk flow resistance over the drop because of lower deformation of drop.

Validation of Moticon’s OpenGo sensor insoles during gait, jumps, balance and cross-country skiing specific imitation movements

ABSTRACTThe purpose of this study was the experimental validation of the OpenGo sensor insole system compared to PedarX sensor insole and AMTI force-plate systems. Sixteen healthy participants performed trials in walking, running, jumping (drop and counter movement jumps), imitation drills and balance, with simultaneous measures of all three systems. Detected ground contact and flight times with OpenGo during walking, running and jumping were similar to those of AMTI. Force–time curves revealed comparable shapes between all three systems. Force impulses were 13–34% lower with OpenGo when compared to AMTI. Despite differences in mean values in some exercise modes, correlations towards AMTI were between r = 0.8 and r = 1.0 in most situations. During fast motions, with high force and impact, OpenGo provided lower force and latency in force kinetics. During balance tasks, discrepancy in the centre of pressure was found medio-lateral, while anterio–posterior direction was closer to AMTI. With awareness of these limitations, OpenGo can be applied in both clinical and research settings to evaluate temporal, force and balance parameters during different types of motion. The fully mobile OpenGo system allows for the easy and quick system application, analysis and feedback under complex field conditions, as well.

Modeling the vertical motion of drops bouncing on a bounded fluid reservoir

We present a first-principles model of drops bouncing on a liquid reservoir. We consider a nearly inviscid liquid reservoir and track the waves that develop in a bounded domain. Bouncing drops are modeled as vertical linear springs. We obtain an expression for the contact force between drop and liquid surface and a model where the only adjustable parameter is an effective viscosity used to describe the waves on the reservoir’s surface. With no adjustable parameters associated to the drop, we recover experimental bouncing times and restitution coefficients. We use our model to describe the effect of the Bond, Ohnesorge, and Weber numbers on drops bouncing on a stationary reservoir. We also use our model to describe drops bouncing on an oscillated reservoir, describing various bouncing modes and a walking threshold.

Acoustically levitated dancing drops: Self-excited oscillation to chaotic shedding.

We experimentally demonstrate self-excited oscillation and shedding of millimeter-sized water drops, acoustically levitated in a single-node standing waves cavity, by decreasing the steady acoustic wave intensity below a threshold. The perturbation of the acoustic field by drop motion is a possible source for providing an effective negative damping for sustaining the growing amplitude of the self-excited motion. Its further interplay with surface tension, drop inertia, gravity and acoustic intensities, select various self-excited modes for different size of drops and acoustic intensity. The large drop exhibits quasiperiodic motion from a vertical mode and a zonal mode with growing coupling, as oscillation amplitudes grow, until falling on the floor. For small drops, chaotic oscillations constituted by several broadened sectorial modes and corresponding zonal modes are self-excited. The growing oscillation amplitude leads to droplet shedding from the edges of highly stretched lobes, where surface tension no longer holds the rapid expanding flow.

Barrel shaped droplet movement at junctions of perpendicular fibers with different orientations to the air flow direction

Abstract Droplet movements on surfaces are of significant interest in a wide range of practical applications. In contrast to the widely studied motion of droplets on rough and smooth surfaces in a flat configuration, knowledge of the motion across fiber junctions is sparse, despite its significance in filters. Crossed fibers at various angles to flow are a fundamental structure within a complex fibrous medium. This work presents the experimental results of a microscopic study of liquid droplet movement on crossed fibers when subjected to air flow. The crossed fibers were positioned to create different angles, within a plane, relative to the airflow direction. Crossed fibers at various angles to flow are a fundamental structure within a complex fibrous medium. The liquid droplets were placed on the intersection point using a previous method developed by the authors for single fibers. A comparison was made between different fiber layouts in terms of Reynolds number of the gas flow. A mathematical correlation for the minimum Reynolds number of gas at which the droplets began to move was developed. This correlation predicts the gas flow conditions required to start the movement of drops at the fiber junction.

Numerical study of surfactant effects on the buoyancy-driven motion of a drop in a tube

We present results of our numerical study of the effect of surfactants on buoyancy-driven motion of drops in a tube at intermediate Reynolds numbers. The drop and bulk phases are treated as incompressible Newtonian fluids and simulated using a front-tracking method. The steady shapes and velocity–volume curves for drops ranging in drop size from 0.2 to 1.3 of tube radius are determined numerically. At small Bond numbers, the velocity–volume curve shows a maximum before the velocity plateaus for large drops. As the Bond number increases, the maximum in the velocity–volume curve disappears with elongated, more streamlined drop shapes consistent with previous experimental studies. For increasing Weber numbers, the rear of the drop shows a flattening followed by the development of a negative curvature. Surfactants are modeled using a Langmuir equation of state in the adsorption–desorption limit and the effect of surfactant mass transfer, fractional coverage of surfactants, and the interfacial Peclet number on the velocity–volume curve is determined. Marangoni stress generated due to the non-uniform distribution of surfactants at the interface reduces drop mobility. Reduced drop mobility is more prominent for drop sizes that are comparable to the tube diameter and is maximum when mass transfer to and from the interface is inhibited. As the fractional coverage of soluble surfactants, or the interfacial Peclet number increases, larger Marangoni stresses are generated along the interface that lead to greater retardation of the drop motion.

APPLICATION OF VORTEX TECHNOLOGIES OF REFRACTORY COATING FORMATION FOR CONVERTER LINING. REPORT 2. FEATURES AND MOVEMENT PARAMETERS OF SLAG DROPS

The paper is devoted to the research of application of vortex technologies of the gas jets to increase the efficiency of fire-resistant coatings on the converter lining. Using numerical simulation, the authors considered the aerodynamic pattern in the working space of the unit and the features of the converter slag drop motion when supplying neutral gas through a special lance with the elements of the vortex device. The laws of slag drop motions of different size to the converter lining have been refined, as well as the dependence among the parameters of slag drop movement and the characteristics of the vortex jet has been defined. It has been established that the trajectory of the slag drops, regardless of their size is mainly determined by the degree of twist of the vortex jet. The article also shows the principal possibility of increasing the technological flexibility of the slag skull application process on the lining converter when using vortex gas jets.

Deviation of sliding drops at a chemical step.

The motion of partially wetting liquid drops in contact with a solid surface is strongly affected by contact angle hysteresis and interfacial pinning. However, the majority of models proposed for drops sliding over chemical surface patterns consistently neglect the difference between advancing and receding contact angles. In this article, we present a joint experimental and numerical study of the interaction of gravity-driven drops with a chemical step formed at the junction between a hydrophilic and a hydrophobic region. It demonstrates the strong impact of a contact angle hysteresis contrast on the motion of drops at a linear chemical step. Surprisingly, the smallest driving force required to drag the drop across the step onto the lower hydrophobic surface is not observed at a right angle of incidence. Our model reveals that the non-monotonous response of this passive drop 'filter' is solely due to the higher advancing contact angle on the lower surface, and creates an instance where drop motion is affected by dissipation at the contact line rather than by surface energy.

ДВИЖЕНИЕ КАПЛИ ЛАТЕКСА ПО ФОРМЕ

ДВИЖЕНИЕ КАПЛИ ЛАТЕКСА ПО ФОРМЕ