Electrokinetic Mixing and Displacement of Charged Droplets in Hydrogels

Mixing in droplets is an essential task in a variety of microfluidic systems. Inspired by electrokinetic mixing, electric field-induced hydrodynamic flow inside a charged droplet embedded in an unbounded polyelectrolyte hydrogel is investigated theoretically. In this study, the polyelectrolyte hydrogel is modeled as a soft, and electrically charged porous solid saturated with a salted Newtonian fluid, and the droplet is considered an incompressible Newtonian fluid. The droplet-hydrogel interface is modeled as a surface, which is located at the plane of shear, with the electrostatic potential \(\zeta \) . The fluid inside the droplet attains a finite velocity owing to hydrodynamic coupling with the electroosmotic flow arising from the droplet and polymer charge. The fluid velocity inside the droplet is linearly proportional to the electroosmotic flow velocity in the charged gel and the electroosmotic flow velocity beyond the electrical double layer of a charged interface. It is found that the polymer boundary condition at the droplet surface and the viscosities of the fluids inside and outside the droplet significantly modulate the interior fluid flow. The ionic strength and the permeability of the polymer network impact the flow differently depending on whether the flow arises from the droplet or polymer charge. Finally, the displacement of a charged droplet embedded in a gel under the influence of an external electric field is undertaken. This work is motivated by experimental attempts, which can register sub-nanometer-scale inclusion displacements in hydrogels, to advance electrical microrheology as a diagnostic tool for probing inclusion-hydrogel interfaces. In the absence of polymer charge, a close connection is found between the electrical response of a charged droplet when it is immobilized in an uncharged incompressible gel and when it is dispersed in a Newtonian electrolyte.     

液滴撞击超疏水壁面反弹及破碎行为研究

液滴撞击壁面时,壁面亲水性对液滴撞击壁面后的变化历程具有重要的影响。利用相界面追踪的复合Level Set-VOF方法对液滴撞击超疏水壁面的运动进行了研究。研究结果表明,撞击速度较小时,液滴撞壁后发生反弹;撞击速度较大时,液滴撞壁后会发生破碎现象;初始粒径的增大和表面张力的减小,有利于液滴撞壁后产生铺展破碎现象;撞击角度对撞壁后的液滴行为具有较大的影响。通过数值模拟,给出了一定条件下液滴垂直及倾斜撞击超疏水壁面反弹及破碎的临界条件。     

A numerical study of droplet motion/departure on condensation of mixture vapor using lattice Boltzmann method

Droplet motion/departure, which is governed by external force acceleration coefficient, droplet radius and surface wettability on solid surfaces under external forces such as gravitational force, play a significant role in characterizing condensation heat transfer, especially when high fractional non-condensable gases (NCG) present. However, due to the challenge in visualizing the vapor/steam velocity field imposed by droplet motion/departure, the detailed mechanism of droplet motion/departure on condensing surfaces has not been completely investigated experimentally. In this study, droplet motion/departures on solid surfaces under external forces and their interactions with steam flow are simulated using two dimensional (2D) multiphase lattice Boltzmann method (LBM). Large external force acceleration coefficient, droplet radius and contact angle, lead to large droplet deformation and high motion/departure velocity, which significantly shortens the droplet residual time on the solid surface. Our simulation shows that steam vortices (lateral velocity) induced by droplet motion/departure can greatly disturb the vapor flow and would be intensified by increasing external force acceleration coefficient, droplet radius, and contact angle. In addition, the location of vortex center shifts in the ascending direction with increase of these factors. The average lateral velocities induced by droplet motion/departure at various conditions are obtained. The mass transfer resistance is substantially reduced owing to the droplet motion/departure, leading to an enhanced heat flux. The experimental results are compared to validate the influence of droplet motion/departure on condensation heat transfer performance, especially for steam–air mixture with the presence of high fractional NCG.     

Dynamic behaviors of droplet impact and spreading: A universal relationship study of dimensionless wetting diameter and droplet height

A notable universal relationship has been proposed in the literature for the evolution of dimensionless droplet height and wetting diameter during the initial spreading stage of droplet impingement. In this study, this universal relationship was investigated by employing three sets of measurements. Sequential images were recorded, and the whole droplet profile ensembles were plotted to facilitate this study. These sets of experiments were designed by changing impact velocity, surface hydrophobicity, or solution property. The experimental results illustrate that the importance of parameters causing the data variation is in the order of surface hydrophobicity > initial impact velocity > surfactant on wetting diameter, and surface hydrophobicity ≈ initial impact velocity > surfactant on droplet height. No universal relationship was observed for dimensionless droplet height and wetting diameter.     

A CFD model of frost formation based on dynamic meshes technique via secondary development of ANSYS fluent

To simulate the non-uniform frost growth in flow direction for humid air flowing through a freezing channel, a 2D numerical frosting model based on dynamic meshes technique is developed in the current work via the secondary development of commercial ANSYS Fluent. The computation domain consists of both frost layer and humid air regions, and the local heat and vapor fluxes at the surface of frost layer are determined by numerical temperature and vapor fraction fields in the humid air region rather than by empirical correlations. The frost layer is treated as a growing packed bed with heat and mass transfer dominated by molecular diffusion, where local absorption coefficient of vapor desublimation and local vapor fraction are both determined by solving the pseudo steady vapor diffusion equation with a source term theoretically. The interface of frost layer and humid air regions is treated as two walls for the iteration of its temperature, of which the humid air side is specified with the temperature equal to the frost-side counterpart and the frost side takes the heat flux including the extra latent heat caused by vapor deposit. User-defined functions are compiled to implement the above treatments to ANSYS Fluent. Frosting experiments in the literature are simulated with the current model for validation. How the profile of frost layer evolves with time in the frosting process is explored. The contours and profiles of velocity, temperature and vapor fraction are presented to discuss the effects of heat and mass transfer on frost formation. Numerical results demonstrate that the proposed CFD model can predict the frost growth and densification with a relative deviation less than 5% compared with experiments. Besides, the computation load of current model is small due to no solution of complex multiphase flow. In addition, dynamic meshes help current model to capture the interface of frost layer and humid air regions accurately.     

A multi‐component lattice Boltzmann model with non‐uniform interfacial tension module for the study of blood flow in the microvasculature

This study aims at analyzing the red blood cell (RBC) deformation and velocity while streaming through venules and through capillaries whose diameters are smaller than the RBC size. The characteristics of the RBC shape change and velocity can potentially help in diagnosing diseases. In this work, the RBC is considered as a surfactant‐covered droplet. This is justified by the fact that the cell membrane liquefies under pressure in the capillaries, and this allows the marginalization of its mechanical properties. The RBC membrane is in fact a macro‐colloid containing lipid surfactant. When liquefied, it can be considered as a droplet of immiscible hemoglobin covered with lipid surfactant in a plasma surrounding. The local gradient in the surface tension due to non‐uniform local interface surfactant distribution is neglected here, and a non‐uniform zonal‐averaged value of surface tension representative of the surfactant bulk zonal concentration is rather implemented. The interplay between the surface tension geometry and the hydrodynamic conditions determines the droplet shape by affecting a change in its Weber number, and influences its velocity. The Gunstensen lattice Boltzmann model for immiscible fluids is used here since it provides independent adjustment of the local surface tension, and allows the use of fluids with viscosity contrast. The proposed concept was used to investigate the dynamic shape change of the RBC while flowing through the microvasculature, and to explore the Fahraeus and the Fahraeus–Lindqvist effects. Copyright © 2010 John Wiley & Sons, Ltd.     

Detailed Cloud Microphysics Simulation for Investigation into the Impact of Sea Spray on Air-Sea Heat Flux

This paper reports on the development of a numerical weather simulation model combined with a detailed spectral-bin cloud microphysics model that can explicitly consider the droplet motion and droplet-atmosphere interactions of sea spray. Sea spray is composed of liquid droplets ejected from the sea surface into the evaporation layer, where it enhances heat as well as momentum exchanges between the atmosphere and the sea. In our study, we analyzed the results of idealized 3D simulations to investigate the impact of sea spray on latent heat exchanges and their consequent impact on boundary layer cloud development. The results show that sea spray enhances the latent heat flux by up to 62 % for the surveyed 10m-height velocities, which ranged from 12 to 42 m/s. They also show that sea spray moistening significantly enhances boundary layer cloud development.     

MOVEMENT AND SPLASHING OF A DROPLET IMPACTING ON A WET WALL

壁面液体层的存在对液滴撞击壁面的运动具有重要的影响。采用气液两相流动相界面追踪的水平集和流体体积复合方法和壁面润湿模型，实现了液滴撞击湿润壁面运动的数值求解；在此基础上，开展了液滴撞击湿润壁面运动的研究。研究结果表明：液滴以不同速度撞击湿润壁面时，会呈现出黏附铺展、波动运动、皇冠几何体运动以及飞溅运动等几种不同的运动形态，液滴撞击湿润壁面后的压力分布是不同运动形态形成的主要原因；飞溅运动是一定条件下皇冠几何体运动的一种特殊形态，液滴从皇冠几何体侧壁顶端的飞溅分离满足毛细破碎理论；撞击速度对分离液滴的运动方向影响较小，而对壁面液体层厚度的影响则较大；撞击速度和壁面液体层厚度对分离液滴形态、飞溅分离位置、飞溅速度以及飞溅发生时刻等都具有一定的影响。     

Numerical simulation of droplet ejection of thermal inkjet printheads

In this study, we present a method to predict the droplet ejection in thermal inkjet printheads including the growth and collapse of a vapor bubble and refill of the firing chamber. The three‐dimensional Navier–Stokes equations are solved using a finite‐volume approach with a fixed Cartesian mesh. The piecewise‐linear interface calculation‐based volume‐of‐fluid method is employed to track and reconstruct the ink–air interface. A geometrical computation based on Lagrangian advection is used to compute the mass flux and advance the interface. A simple and efficient model for the bubble dynamics is employed to model the effect of ink vapor on the adjacent ink liquid. To solve the surface tension‐dominated flow accurately, a hierarchical curvature‐estimation method is proposed to adapt to the local grid resolution. The numerical methods mentioned earlier have been implemented in an internal simulation code, CFD3. The numerical examples presented in the study show good performance of CFD3 in prediction of surface tension‐dominated free‐surface flows, for example, droplet ejection in thermal inkjet printing. Currently, CFD3 is used extensively for printhead development within Hewlett‐Packard. Copyright © 2015 John Wiley & Sons, Ltd.     

航空发动机轴承腔中油滴运动与沉积的特性分析

本文在获得轴承腔中气相介质流场的基础上,采用Lagrangian方法建立油滴在气相介质流场中运动的分析模型,通过瞬时步进法数值模拟油滴的运动过程,获得了油滴直径和旋转轴转速对油滴运动过程中的速度和轨迹影响的规律.基于获得的油滴与腔壁碰撞前的运动状态,以及结合油滴与腔壁的碰撞模型,实现了油滴直径和旋转轴转速对碰撞后油滴沉积率和动量转移率影响规律的分析.结果表明:油滴直径和旋转轴转速对油滴速度及轨迹,以及油滴沉积率及动量转移率都有很大影响,而且前者的影响更为明显.与国外同等条件下的试验结果对比表明,本文提出的油滴运动与沉积特性分析方法具有较好的可靠性和精度.碰撞前后油滴运动状态和沉积率及动量转移率的计算,为下一步油膜厚度和速度的计算,继而为轴承腔润滑设计和换热分析提供了初始条件.     

Boundary layer and heat transfer in a two-phase gas-evaporating droplet medium

An asymptotic model of the flow in the laminar boundary layer of a gas-evaporating droplet mixture is constructed within the framework of the two-continuum approximation. The case of evaporation of the droplets into an atmosphere of their own vapor is examined in detail with reference to the example of longitudinal flow over a hot flat plate. Numerical and asymptotic solutions of the boundary layer equations constructed are found for a number of limiting situations (low droplet concentration, no droplet deposition, significant droplet deposition). The development of the flow with respect to the longitudinal coordinate is studied and it is shown that in the absence of droplet deposition a region of pure vapor may be formed near the surface. Similarity criteria are established and the mechanism of surface heat transfer enhancement is studied for a low evaporating droplet concentration in the boundary layer. In the inertial deposition regime the results of calculating the integral heat transfer coefficient are found to correspond with the experimental data [1].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 42–50, May–June, 1992.     

On the calculation of wall temperatures in the post dryout heat transfer region

A non-equilibrium post dryout heat transfer model for calculating the wall temperature distribution in vertical upflows is presented in this study. The model is based upon the three path heat transfer formulation developed by MIT researchers (Laverty & Rohsenow 1964, Forslund & Rohsenow 1968, Hynek et al. 1969 and Plummer et al. 1974) that involves heat transfer from wall to vapor, from wall to droplets in contact with the wall and from vapor to liquid droplets in the vapor core. Downstream gradients for the bulk vapor temperature, vapor quality, droplet size and vapor velocities are identical to those used by Hynek et al. (1969) and Plummer et al. (1974). Conditions at the dryout location are calculated using a modified version of a technique developed by Hynek et al. (1969).A procedure for determining an average droplet diameter based on a size distribution is introduced. Migration of droplets through the boundary layer and droplet deposition flux are predicted with the model of Gani? & Rohsenow (1979). Heat transfer from the wall to the impinging liquid droplets is calculated with a correlation by Holman & McGinnis (1969). Mechanisms contributing to wall to droplet heat transfer are identified as (a) droplet-wall contact, (b) intensive droplet evaporation inside the boundary layer, and (c) destruction of the boundary layer due to droplet migration to, and rebound from, the hot surface. The significance of the average droplet size and size distribution is demonstrated through its control over the free stream evaporation and droplet deposition rates.Predicted uniform heat flux wall temperature profiles for water, nitrogen and freon 12 are in good agreement with the data of Era et al. (1966), Bennett et al. (1967), Forslund & Rohsenow (1968), Ling et al. (1971), Groeneveld (1972) and Janssen & Kervinen (1975).     

Pure steam condensation model with laminar film in a vertical tube

A new physical model for calculating the liquid film thickness and condensation heat transfer coefficient in a vertical condenser tube is proposed by considering the effects of gravity, liquid viscosity, and vapor flow in the core region of the flow. To estimate the velocity profile in the liquid film, the liquid film was assumed to be in Couette flow forced by the interfacial velocity at the liquid–vapor interface. For simplifying the calculation procedures, the interfacial velocity was estimated by introducing an empirical power-law velocity profile. The resulting film thickness and heat transfer coefficient from the model were compared with the experimental data and the results obtained from the other condensation models. The results demonstrated that the proposed model described the liquid film thinning effect by the vapor shear flow and predicted the condensation heat transfer coefficient from experiments reasonably well.     

Nonlinear vibrations of a vapor film in the presence of intense heat fluxes

Waves propagating along the interface between a thin vapor film and a liquid layer in the presence of a heat flux are investigated. The boundary conditions on the vapor-liquid phase surface take into account the temperature dependence of the pressure and the possibilities of formation of the metastable state of the superheated liquid and mass flow. Variations in the saturation pressure as functions of the temperature and mass flux lead to generation of weakly damped periodic waves of low amplitude whose velocity can be much higher than the velocity of the gravity waves. The waves ensure stability of the vapor film beneath the liquid layer in the gravity field. The finite-amplitude waves on the surface of the vapor film differ from the Stokes surface waves on the free surface of isothermal fluid. Instability regimes related with superheating of the liquid ant its explosive boiling when the amplitude of an initially small wave increases to infinity in a finite time can develop in a certain working-parameter regime.     

Combustion of a Powder Layer of Methane Hydrate: The Influence of Layer Height and Air Velocity Above the Layer

The paper studies the dissociation and combustion of a layer of methane hydrate powder at a forced air flow over the upper surface of the layer (the air velocity is directed parallel to the upper surface of the layer). The influence of the layer thickness and air velocity on the combustion of gas hydrate is investigated. The calculated curves for the effect of the heat transfer coefficient, external convection and vapor concentration on the combustion temperature are obtained. The layer thickness and the air velocity significantly affect the dissociation rate of methane hydrate.

     

The fate of soluble and insoluble surfactant monolayers subjected to drop impacts

Surfactant monolayers were formed on a water surface and subjected to water drops falling from a nozzle. Surface tension was measured during these experiments to determine the effect of the drop impacts on the surfactant monolayer. The purpose of this work was to determine whether monolayers can be altered by drop impacts without the formation of a splash. Accordingly, a small fall height was used to avoid drop splashes and concomitant surfactant loss by droplet ejection. The relevance of this work pertains to the fate of surfactant monolayers during rain events. Results are presented for a soluble and insoluble surfactant. The results show that the insoluble monolayer is virtually unaffected by the drops, indicating that the monolayer immediately reforms after the drop impact. The soluble monolayer shows significant changes in measured surface tension during droplet impact when the surfactant concentration is high.     

On dual-grid level-set method for contact line modeling during impact of a droplet on hydrophobic and superhydrophobic surfaces

In this paper, a numerical methodology for modeling contact line motion in a dual-grid level-set method (DGLSM) – solved on a uniform grid for interface which is twice that for the flow equations – is presented. A quasi-dynamic contact angle model – based on experimental inputs – is implemented to model the dynamic wetting of a droplet, impacting on a hydrophobic or a superhydrophobic surface. High-speed visualization experiments are also presented for the impact of a water droplet on hydrophobic surfaces, with non-bouncing at smaller and bouncing at larger impact velocity. The experimental results for temporal variation of the droplet shapes, wetted-diameter and maximum height of the droplet match very well with the DGLSM based numerical results. The validation of the numerical results is also presented with already published experimental results, for the non-bouncing on a hydrophobic and bouncing on a superhydrophobic surface, at a constant impact velocity. Finally, a qualitative as well as quantitative performance of the DGLSM as compared to the traditional level set method (LSM) is presented by considering our experimental results. The accuracy of the partially refined DGLSM is close to that of the fine-grid based LSM, at a computation cost which is close to that of the coarse-grid based LSM. The DGLSM is demonstrated as an improved LSM for the computational multi-fluid dynamics (CMFD) simulations involving contact line motion.     

Effect of wall friction and vortex generation on the radial distribution of different phases

Arguments are presented to prove the existence of rolling vortices in single-phase and two-phase flow. In the liquid phase, they appear in a boundary layer near a wall while in the continuous vapor phase they occur near the interface with a liquid film. The intensity and size of these vortices depend on the local velocity gradients normal to the wall. The interaction between the rotational field associated with such vortices and bubbles in liquid flow or droplets in vapor flow is discussed. This interaction may be called the wall-vortex effect. It appears that several, apparently unrelated, phenomena observed in two-phase flow systems may be interpreted in terms of this mechanism. Among these are: (i) radial void peaking near the walls (ii) vapor velocities less than liquid velocity observed also in vertical upward flow (iii) reduced droplet diffusion near the liquid film and (iv) reduced vapor mixing between subchannels at low steam qualities. The cause of secondary flows in non-circular channels may also be explained in terms of rolling vortices near the walls. Finally, a comparison is made with the well known Magnus effect.     

Evaporation phenomenon past a rotating hydrocarbon droplet of ternary components

A numerical study of heat and mass transfer from an evaporating fuel droplet rotating around its vertical axis was performed in forced convection only on the side opposite to the flow. The flow was assumed to be laminar, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on the abovementioned assumption, the conservation equations in a general curvilinear coordinate were solved numerically. The behavior of rotating droplet evaporation in the forced convection flow can be investigated by analyzing the effects of the rotation of the droplet on the evaporation process of multi-component hydrocarbons droplet. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method. Thomas algorithm is used to solve the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hydrocarbon droplet were determined. The thickness of the boundary layer is unknown for this model and therefore, it was determined in function of time. Additionally, the study concerns “Dgheim dimensionless number” which is the ratio of the rotation forces over the viscosity forces. Dgheim dimensionless number is correlated to Nusselt and Sherwood numbers for multi-component hydrocarbon droplets in evaporation by taking into account the effect of heat and mass Spalding, Prandtl and Schmidt numbers respectively. Also, correlations for Nusselt and Sherwood numbers in terms of Reynolds, Prandtl and Schmidt numbers are proposed. These correlations consider the rotation phenomenon and advance the variation of the thermophysical and transport properties in the vapor phase of multi-component blends.     

Atomized non-equilibrium two-phase flow in mesochannels: Momentum analysis

Two-phase pressure drop measurements are very difficult to make while the fluid is in non-equilibrium condition, i.e. while phase change is taking place. This is further complicated when an atomized liquid is introduced in the system at much higher velocity than other components such as liquid layer, vapor core, and entrained droplets. The purpose of this paper is to develop a model to predict the two-phase pressure characteristics in a mesochannel under various heat flux and liquid atomization conditions. This model includes the momentum effects of liquid droplets from entrainment and atomization. To verify the model, an in-house experimental setup consisting of a series of converging mesochannels, an atomization facility and a heat source was developed. The two-phase pressure of boiling PF5050 was measured along the wall of a mesochannel. The one-dimensional model shows good agreement with the experimental data. The effects of channel wall angle, droplet velocity and spray mass fraction on two-phase pressure characteristics are predicted. Numerical results show that an optimal spray cooling unit can be designed by optimizing channel wall angle and droplet velocity.