Separation-driven coalescence of droplets: an analytical criterion for the approach to contact

2009 ◽  
Vol 632 ◽  
pp. 97-107 ◽  
Author(s):  
ANN LAI ◽  
NICOLAS BREMOND ◽  
HOWARD A. STONE
Keyword(s):  
Viscosity Ratio ◽  
Continuous Phase ◽  
Separation Distance ◽  
Dimensional Model ◽  
Droplet Deformation ◽  
Dimensional Parameter ◽  
Domain Perturbation ◽  
Microfluidic Flow ◽  
Analytical Criterion ◽  
Good Agreement

Recent microfluidic experiments by Bremond, Thiam & Bibette (Phys. Rev. Lett., vol. 100, 2008, paper no. 024501), along with simulations by Yoon et al. (Phys. Fluid, vol. 19, 2007, paper no. 102102) and near-contact experiments and simulations by Manica et al. (Langmuir, vol. 24, 2008, pp. 1381–1390), have demonstrated that two droplets can coalesce as they are separating rather than upon their collision. We analyse the experimental microfluidic flow configuration for the approach to contact with a two-dimensional model: we apply a lubrication analysis followed by the method of domain perturbation to determine the droplet deformation as a function of time. We find the approximate shape for the deformed droplet at the time of contact. In particular, for droplets of radius R, moving apart according to h0(t) = h0(0) + αt2, where 2h0(t) is the separation distance, we define a non-dimensional parameter A=4CμR2α1/2/πγ[h0(0)]3/2, where μ is the viscosity of the continuous phase; γ is the interfacial tension; and C depends on the viscosity ratio between the droplets and the continuous phase. Our model suggests that there exists a critical value Acrit = 16/33/2 ≈ 3.0792, below which separation is unlikely to facilitate the coalescence of the droplets. The predictions are in good agreement with available experimental data.

scholarly journals Comparison of Experimental and Numerical Transient Drop Deformation during Transition through Orifices in High-Pressure Homogenizers

2021 ◽  
Vol 5 (3) ◽  
pp. 32
Author(s):  
Benedikt Mutsch ◽  
Peter Walzel ◽  
Christian J. Kähler
Keyword(s):  
High Pressure ◽  
Visual Analysis ◽  
Imaging Technique ◽  
Extensional Flow ◽  
Droplet Breakup ◽  
Experimental Results ◽  
Drop Deformation ◽  
Droplet Deformation ◽  
Shadow Imaging ◽  
Good Agreement

The droplet deformation in dispersing units of high-pressure homogenizers (HPH) is examined experimentally and numerically. Due to the small size of common homogenizer nozzles, the visual analysis of the transient droplet generation is usually not possible. Therefore, a scaled setup was used. The droplet deformation was determined quantitatively by using a shadow imaging technique. It is shown that the influence of transient stresses on the droplets caused by laminar extensional flow upstream the orifice is highly relevant for the droplet breakup behind the nozzle. Classical approaches based on an equilibrium assumption on the other side are not adequate to explain the observed droplet distributions. Based on the experimental results, a relationship from the literature with numerical simulations adopting different models are used to determine the transient droplet deformation during transition through orifices. It is shown that numerical and experimental results are in fairly good agreement at limited settings. It can be concluded that a scaled apparatus is well suited to estimate the transient droplet formation up to the outlet of the orifice.

Use of a three-dimensional model to predict heavy metal (copper) fluxes in the Oujiang estuary

2014 ◽  
Vol 69 (6) ◽  
pp. 1334-1343 ◽  
Author(s):  
Shasha Lu ◽  
Ruijie Li ◽  
Xiaoming Xia ◽  
Jun Zheng
Keyword(s):  
River Discharge ◽  
Water Surface ◽  
Three Dimensional ◽  
Measured Data ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Pollutant Concentrations ◽  
Suspended Sediment Concentrations ◽  
Adsorption Desorption ◽  
Good Agreement

Measuring pollutant concentrations in major tributaries is the standard method for establishing pollutant fluxes to the sea. However, this method is costly and difficult, and may be subject to a great deal of uncertainty due to the presence of unknown sources. This uncertainty presents challenges to managers and scientists in reducing contaminant discharges to water bodies. As one less costly method, a three-dimensional model was developed and used to predict pollutant fluxes to the sea. The sorptive contaminant model was incorporated into hydrodynamic and sediment models. Adsorption–desorption of copper by sediments in the Oujiang estuary were described using Henry's law. The model was validated using measured data for water surface elevations, flow velocity/direction, suspended sediment concentrations, and the proportion of copper sorbed to sediment. The validated model was then applied to predict fluxes of copper. Combined with the measured data, the copper concentration in the Oujiang River discharge was calculated as 13.0 μg/L and copper fluxes were calculated as 52 t in 2010. This copper flux prediction was verified using measured dissolved copper concentrations. Comparisons between the modeled and measured results showed good agreement at most stations, demonstrating that copper flux prediction in the Oujiang estuary was reasonably accurate.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

Viscous Flows Involving a Liquid-Vapor Compound Droplet

2001 ◽  
Author(s):  
D. Palaniappan
Keyword(s):  
Exact Solutions ◽  
Viscosity Ratio ◽  
Numerical Algorithms ◽  
Flow Fields ◽  
Continuous Phase ◽  
Boundary Integral ◽  
Liquid Volume ◽  
Drag Forces ◽  
Compound Droplet ◽  
Fluid Interactions

Abstract Exact analytical solutions for steady-state axisymmetric creeping flows in and around a compound multiphase droplet are presented. The solutions given here explain the droplet fluid interactions in uniform and nonuniform flow fields. The compound droplet has a two-sphere geometry with the two spherical surfaces (of unequal radii) intersecting orthogonally. The surface tension forces are assumed to be sufficiently large so that the interfaces have uniform curvature. The singularity solutions for the uniform and paraboloidal flows in the presence of a compound droplet are derived using the method of reflections. The exact solutions for the velocity and pressure fields in the continuous and dispersed phases are given in terms of the fundamental singularities (Green’s functions) and their derivatives. It is found that flow fields and the drag forces depend on two parameters namely, the viscosity ratio and the radii ratio. In the case of paraboloidal flows, a single or a pair of eddies is noticed in the continuous phase for various values of these parameters. The eddies changes their size and shape if the size of the droplet is altered. These observations may be useful in the study of hydrodynamic interactions of compound droplets in complex situations. It is found that the Stokes resistance is greater when the liquid volume is large compared to the vapor volume in uniform flow. It is also noticed that the maximum value of the drag in paraboloidal flow depends on the viscosity ratio and significantly on the liquid volume in the dispersed phase. The exact solutions presented here may be useful for boundary integral formulations that are based on special kernels and also in validating numerical algorithms and codes on multiphase flow and droplet-fluid interactions.

Electrowetting Induced Droplet Generation in T-junctions

2021 ◽  
Author(s):  
Arshia Merdasi ◽  
Ali Moosavi
Keyword(s):  
Shear Stress ◽  
Continuous Phase ◽  
Droplet Breakup ◽  
Droplet Generation ◽  
The Finite Element Method ◽  
Fluidic Channel ◽  
Generation Frequency ◽  
Two Phases ◽  
Breakup Time ◽  
Good Agreement

Abstract In the current study, droplet generation in a T-junction fluidic channel device was studied through using electrowetting actuation with the consideration of different droplet forming regimes. For this purpose, the finite element method (FEM) was used to solve the unsteady Naiver-Stokes equation. In addition, the level set method was applied to capture the interface between two phases. It was shown that there was a good agreement between obtained data and other work during the process of droplet generation in the absence of electrowetting actuation which results in decrease in the size of droplet with increasing the velocity ratios. In shearing regime, the effectiveness of electrowetting on the droplet generation frequency as well as droplet size is visible in a T-junction fluidic channel since after applying voltages, specified with non-dimensional electrowetting numbers of ?=0.5 and 1.2, dispersed phase is pulled out into the oil phase. In fact, with applying the voltage on the top wall, the droplet breakup time was decreased and smaller droplets were produced. Finally, different important parameters such as pressure difference across the interface as well as Shear Stress exerted from the continuous phase shear stress were examined in a detail.

scholarly journals Dynamics of sheared droplets filled with non-Brownian particles

2020 ◽  
Vol 59 (12) ◽  
pp. 935-949
Author(s):  
Helene Van Ammel ◽  
Paula Moldenaers ◽  
Ruth Cardinaels
Keyword(s):  
Bulk Viscosity ◽  
Particle Concentration ◽  
Viscosity Ratio ◽  
Viscous Medium ◽  
Particle Sizes ◽  
Droplet Dynamics ◽  
Brownian Particles ◽  
Homogenous Medium ◽  
Single Droplets ◽  
Good Agreement

AbstractThe dynamics of single droplets containing non-Brownian particles are studied. The particle over droplet size ratio (r/R) is changed by using different particle sizes (r/R = 0.02–0.4). Additionally, the effect of particle concentration (5–20 vol%) is investigated. The dynamics of droplets with r/R = 0.02 show good agreement with the corresponding particle-free reference system which has a comparable viscosity ratio. Hence, this droplet phase can be considered as a homogenous medium characterized by its bulk viscosity which is governed by the particle concentration. However, droplets with r/R ≥ 0.1 show a more suppressed deformation and slower transient dynamics and, therefore, behave as a slightly more viscous medium than expected based on their bulk viscosity. These effects become more pronounced at higher particle concentrations and higher r/R. Moreover, local particle effects like asymmetric droplet shapes, oscillating droplet shapes, and tip streaming start to influence the droplet dynamics at particle concentrations around 15 vol%.

Numerical Modeling and Parametric Analysis of Multiplanar CHS KT-Joints with K-Plane Overlap and Out-of-Plane Gap

2011 ◽  
Vol 94-96 ◽  
pp. 575-582
Author(s):  
Jian Dong Sun ◽  
Jun Li Lv ◽  
Tao Du ◽  
Yang Xian Li
Keyword(s):  
Numerical Modeling ◽  
Parametric Analysis ◽  
Element Model ◽  
Ultimate Capacity ◽  
Dimensional Parameter ◽  
International Convention ◽  
Out Of Plane ◽  
Dimensional Parameters ◽  
Test Result ◽  
Good Agreement

A finite element model simulating the experiment on multiplanar unstiffened CHS KT joints with K-plane overlapped and out-of-plane not (KT-IPOv joints), with the background of Suzhou International Convention & Exhibition Center, was advanced and validated by comparing failure mode and the ultimate capacity with experimental results, which is shown to be in good agreement with the test result. Using this model, the effect of non-dimensional parameters on ultimate capacity of KT-IPOv joints were studied, and resistance comparison between multiplanar KT-IPOv joints and uniplanar overlapped K-joints was carried out. The results of FE parametric Analysis conclude that multiplanar parameter ζ t, τT and βT have not significant influence on the ultimate strength; the effect of non-dimensional parameter βK, τK, γ, Ov on the resistance of multiplanar KT-IPOv joints has the same as that of uniplanar overlapped K-joints; the strength of multiplanar KT-IPOv joints have been not significantly influenced by the configuration with the brace inside T-plane which it is not subjected to force; it is suitable and feasiable that ultimate capacities of KT-IPOv joints predicted by formula of uniplanar K-joints.

Numerical and experimental analysis of two-dimensional separated flows over a flexible sail

2002 ◽  
Vol 466 ◽  
pp. 319-341 ◽  
Author(s):  
O. LORILLU ◽  
R. WEBER ◽  
J. HUREAU
Keyword(s):  
Velocity Field ◽  
Numerical Data ◽  
Separated Flows ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model ◽  
Wake Model ◽  
Lift And Drag ◽  
Particle Imaging ◽  
Good Agreement

This paper is a numerical analysis of the flow over a exible sail with the usual two-dimensional model of ideal weightless incompressible fluid. The sail is assumed to be impervious, inelastic and weightless, and may or may not be mounted on a mast. Separated or attached flows are considered at any angle of attack. Our method is validated by numerical and experimental results, i.e. the sail shape and velocity field are determined by particle imaging velocimetry, and lift and drag by aerodynamic balance. Despite the simplicity of the wake model we use (the Helmholtz model), the computed free streamline geometry and especially the sail shape are in good agreement with the experimental and numerical data.

Effect of Fluid Properties on Droplet Generation in a Microfluidic T-Junction

2014 ◽  
Author(s):  
Katerina Loizou ◽  
Voon-Loong Wong ◽  
Wim Thielemans ◽  
Buddhika Hewakandamby
Keyword(s):  
Interfacial Tension ◽  
Scaling Laws ◽  
Viscosity Ratio ◽  
Continuous Phase ◽  
Generation Mechanism ◽  
Droplet Generation ◽  
Dispersed Phase ◽  
Supporting Evidence ◽  
Fluid Properties ◽  
Break Up

Over the last decade, significant work has been performed in an attempt to quantify the effect of different parameters such as flowrate, geometrical and fluid characteristics on the droplet break up mechanism in microfluidic T-Junctions. This demand is dictated by the need of tight control of the size and dispersity of the droplets generated in such geometries. Even though several researchers have investigated the effect of viscosity ratio on both the droplet break up mechanism as well as on the regime transition, fluid properties have not been included in most scaling laws. It is therefore evident that the contribution of fluid properties has not been quantified thoroughly. In the present work, the effect of fluid properties on the volume of droplets generated in a microfluidic T-junction is investigated. The main aim of this work is to examine the influence of viscosity of both the dispersed and continuous phase as well as the effect of interfacial tension on the size of droplet generated along with the break up mechanism. Three different oils have been utilised as continuous phase in this work to enable investigation of the effect of viscosity of the continuous phase with experiments performed at constant Capillary numbers. Various glycerol weight percentages have been employed to vary the viscosity of the dispersed phase fluid (water). Lastly, the effect of interfacial tension has been explored using two of the oils at constant μcUc (viscous force term). High speed imaging has been utilised to visualise and measure the volume of the resulting droplets. The viscosity ratio (viscosity of dispersed phase over viscosity of continuous phase) between the two phases appears to affect the droplet generation mechanism, especially for the highest viscosity ratio employed (mineral oil-water system) where the system behaves in a noticeably different way. Influence of interfacial tension is also noticeable even though less evident. In terms of the effect of viscosity of dispersed phase on the droplet generation a small difference on the volume of the droplets generated in olive oil glycerol systems is also reported. In an attempt to enumerate the effect of fluid properties on the droplet generation mechanism in a microfluidic T-junction, this paper will present supporting evidence in detail on the above and a comparison of the findings with the existing theories.

A One-Dimensional Model of Simultaneous Hemodialysis and Ultrafiltration With Highly Permeable Membranes

1981 ◽  
Vol 103 (4) ◽  
pp. 261-266 ◽  
Author(s):  
M. Y. Jaffrin ◽  
B. B. Gupta ◽  
J. M. Malbrancq
Keyword(s):  
Protein Concentration ◽  
Flux Distribution ◽  
Transmembrane Pressure ◽  
Dimensional Model ◽  
One Dimensional ◽  
Diffusive Mass Transfer ◽  
Model Predictions ◽  
Polyacrylonitrile Membrane ◽  
Good Agreement

A one-dimensional model of combined convective and diffusive mass transfer in a hemodialyser is presented. Solutions and results are given for two regimes of ultrafiltration (UF): at low transmembrane pressures when UF flow is proportional to transmembrane pressure and in the limit of large transmembrane pressures when UF is limited by protein concentration polarization. It is found that the overall clearance is always less than the sum of dialytic and UF clearances due to interaction between convective and diffusive transfers. For a given UF flow the clearance is not sensitive to UF flux distribution along the membrane. Model predictions of urea clearance are in good agreement with measurements obtained in vitro with saline on hemodialysers equipped with a polyacrylonitrile membrane.

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