Numerical Simulation of Cone Formation in Electrospraying Process

2010 ◽  
Author(s):  
Mohammad Passandideh-Fard ◽  
Mortaza Rahimzadeh ◽  
Sajad Pooyan
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Electric Field ◽  
Capillary Tube ◽  
Surface Profile ◽  
Surface Tension Force ◽  
Transient Behavior ◽  
Perfect Conductor ◽  
Electric Force ◽  
Liquid Free Surface

A numerical model is developed to study the transient behavior of a liquid jet leaving a capillary tube under an electrostatic field. The surface profile of the deforming jet is defined using the Volume-of-Fluid (VOF) scheme and the advection of the liquid free-surface is performed using Youngs’ algorithm. Surface tension force is treated as a body force acting on the free-surface using continuum surface force (CSF) method. To calculate the effect of the electric field on the shape of the free-surface, the electrostatic potential is solved first. Next, the surface density of the electric charge and the electric field intensity are computed, and then the electric force is calculated. Liquid is assumed to be a perfect conductor, thus the electric force only acts on the liquid free-surface and is treated similar to that of surface tension using the CSF method. The developed model is validated by a comparison between the calculated results and measurements for an electrowetting scenario for which experimental results are available in the literature.

Numerical Simulation of Electrostatic Atomization in Spindle Mode

2010 ◽  
Author(s):  
Mohammad Passandideh Fard ◽  
Mohammad Reza Mahpeykar ◽  
Sajad Pooyan ◽  
Mortaza Rahimzadeh
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Electric Field ◽  
Stable State ◽  
Surface Shape ◽  
Liquid Jet ◽  
Perfect Conductor ◽  
Electric Force ◽  
Electrostatic Atomization ◽  
Liquid Free Surface

The behavior of a liquid jet in an electrostatic field is numerically simulated. The simulations performed correspond to a transient liquid jet leaving a capillary tube maintained at a high electric potential. The surface profile of the deforming jet is defined using the VOF scheme and the advection of the liquid free surface is performed using Youngs’ algorithm. Surface tension force is treated as a body force acting on the free surface using continuum surface force (CSF) method. To calculate the effect of the electric field on the shape of the free surface, the electrostatic potential is solved first. Next, the surface density of the electric charge and the electric field intensity are computed, and then the electric force is calculated. Liquid is assumed to be a perfect conductor, thus the electric force only acts on the liquid free surface and is treated similar to surface tension using the CSF method. To verify the simulation results, a simplified case of electrowetting phenomenon is simulated and free surface shape in stable state is compared with experimental results. Then the electrostatic atomization in spindle mode is simulated and the ability of the developed code to simulate this process is demonstrated.

Surface Deformation and Convection in Electrostatically-Positioned Droplets of Immiscible Liquids Under Microgravity

2005 ◽  
Vol 128 (6) ◽  
pp. 520-529 ◽  
Author(s):  
Y. Huo ◽  
B. Q. Li
Keyword(s):  
Surface Tension ◽  
Fluid Flow ◽  
Free Surface ◽  
Electric Field ◽  
Outer Layer ◽  
Thermal Gradient ◽  
Surface Deformation ◽  
Inertia Force ◽  
Weighted Residuals ◽  
Inertia Forces

A numerical study is presented of the free surface deformation and Marangoni convection in immiscible droplets positioned by an electrostatic field and heated by laser beams under microgravity. The boundary element and the weighted residuals methods are applied to iteratively solve for the electric field distribution and for the unknown free surface shapes, while the Galerkin finite element method for the thermal and fluid flow field in both the transient and steady states. Results show that the inner interface demarking the two immiscible fluids in an electrically conducting droplet maintains its sphericity in microgravity. The free surface of the droplet, however, deforms into an oval shape in an electric field, owing to the pulling action of the normal component of the Maxwell stress. The thermal and fluid flow distributions are rather complex in an immiscible droplet, with conduction being the main mechanism for the thermal transport. The non-uniform temperature along the free surface induces the flow in the outer layer, whereas the competition between the interfacial surface tension gradient and the inertia force in the outer layer is responsible for the flows in the inner core and near the immiscible interface. As the droplet cools into an undercooled state, surface radiation causes a reversal of the surface temperature gradients along the free surface, which in turn reverses the surface tension driven flow in the outer layer. The flow near the interfacial region, on the other hand, is driven by a complimentary mechanism between the interfacial and the inertia forces during the time when the thermal gradient on the free surface has been reversed while that on the interface has not yet. After the completion of the interfacial thermal gradient reversal, however, the interfacial flows are largely driven by the inertia forces of the outer layer fluid.

scholarly journals Modelling nonlinear electrohydrodynamic surface waves over three-dimensional conducting fluids

2017 ◽  
Vol 473 (2200) ◽  
pp. 20160817 ◽  
Author(s):  
Zhan Wang
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Electric Field ◽  
Nonlinear Models ◽  
Three Dimensional ◽  
Separation Distance ◽  
Nls Equation ◽  
Fully Nonlinear ◽  
Special Cases ◽  
Kp Equations

The evolution of the free surface of a three-dimensional conducting fluid in the presence of gravity, surface tension and vertical electric field due to parallel electrodes, is considered. Based on the analysis of the Dirichlet–Neumann operators, a series of fully nonlinear models is derived systematically from the Euler equations in the Hamiltonian framework without assumptions on competing length scales can therefore be applied to systems of arbitrary fluid depth and to disturbances with arbitrary wavelength. For special cases, well-known weakly nonlinear models in shallow and deep fluids can be generalized via introducing extra electric terms. It is shown that the electric field has a great impact on the physical system and can change the qualitative nature of the free surface: (i) when the separation distance between two electrodes is small compared with typical wavelength, the Boussinesq, Benney–Luke (BL) and Kadomtsev–Petviashvili (KP) equations with modified coefficients are obtained, and electric forces can turn KP-I to KP-II and vice versa; (ii) as the parallel electrodes are of large separation distance but the thickness of the liquid is much smaller than typical wavelength, we generalize the BL and KP equations by adding pseudo-differential operators resulting from the electric field; (iii) for a quasi-monochromatic plane wave in deep fluid, we derive the cubic nonlinear Schrödinger (NLS) equation, but its type (focusing or defocusing) is strongly influenced by the value of the electric parameter. For sufficient surface tension, numerical studies reveal that lump-type solutions exist in the aforementioned three regimes. Particularly, even when the associated NLS equation is defocusing for a wave train, lumps can exist in fully nonlinear models.

Large-Wave Simulation of Surface Tension Effect on Weak Spilling Breakers

2005 ◽  
Author(s):  
Athanassios A. Dimas
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Wave Height ◽  
Weber Number ◽  
Surface Profile ◽  
Surface Flow ◽  
Surface Tension Effect ◽  
Time Step ◽  
Large Wave ◽  
Spilling Breakers

The effect of surface tension on the evolution of weak spilling breakers is studied by performing large-wave simulations (LWS) of the free-surface flow developing by the interaction of a gravity free-surface wave and a surface shear-layer current. The flow models the evolution of gravity waves under the influence of wind shear. The surface tension modifies the dynamic free-surface condition and its effect depends on the dimensionless Weber number. The Euler equations are filtered according to the LWS formulation and solved numerically by a spectral method and a fractional-time-step scheme. The results indicate a stronger surface tension effect with decreasing Weber number values and increasing initial wave height. Specifically, decreasing the Weber number alters the size and shape of the characteristic bulge of spilling breakers and the toe position resulting in sharper slopes and angles of the free surface profile. The spiller wave height is reduced with decreasing Weber number.

A Numerical Method for Capillarity-Driven Free Surface Flows

2005 ◽  
Author(s):  
Albert Y. Tong ◽  
Zhaoyuan Wang
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Level Set ◽  
Surface Tension Force ◽  
Surface Force ◽  
Volume Of Fluid ◽  
Free Surface Flows ◽  
Tension Force ◽  
Navier Stokes Equation ◽  
Spurious Currents

The continuum surface force (CSF) method has been extensively employed in the volume-of-fluid (VOF), level set (LS) and front tracking methods to model surface tension force. It is a robust method requiring relatively easy implementation. However, it is known to generate spurious currents near the interface that may lead to disastrous interface instabilities and failures of grid convergence. A different surface tension implementation algorithm, referred to as the pressure boundary method (PBM), is introduced in this study. The surface tension force is incorporated into the Navier-Stokes equation via a capillary pressure gradient while the free surface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method. It has been shown that the spurious currents are greatly reduced by the present method with the sharp pressure boundary condition preserved. The numerical results of several cases have been compared with data reported in the literature and are found to be in a close agreement.

On a Numerical Model for Free Surface Flows of a Conductive Liquid Under an Electrostatic Field

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Sajad Pooyan ◽  
Mohammad Passandideh-Fard
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Electric Field ◽  
Electrostatic Field ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Computational Method ◽  
Perfect Conductor ◽  
Computational Domain ◽  
Conductive Liquid

In this paper, a numerical model is developed that can simulate the unsteady axisymmetric free-surface flow of a perfectly conductive liquid under an electrostatic field. The effect of the electrostatic field is modeled by a force distributed on the liquid free surface. Assuming the liquid as a perfect conductor makes it possible to reduce the general electromagnetic equations to electrostatic equations. The Navier–Stokes equations are solved to find the velocity and pressure fields. The free surface advection and reconstruction are performed based on the volume-of-fluid method using Youngs’ algorithm. To evaluate the effect of the electric field on the free surface, the electrostatic potential is first solved for the entire computational domain. Next, the electric field intensity and the surface density of the electric charge are calculated on the free surface after which the electric force can be determined. The computational method for treating this force is similar to that of the surface tension using the continuum surface force method. The developed model is validated by a comparison between the calculated results with those of the analytics as well as experiments for an electrowetting scenario.

scholarly journals The Instability of an Electrohydrodynamic Viscous Liquid Micro-Cylinder Buried in a Porous Medium: Effect of Thermosolutal Marangoni Convection

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Galal M. Moatimid ◽  
Mohamed A. Hassan
Keyword(s):  
Mass Transfer ◽  
Surface Tension ◽  
Free Surface ◽  
Dispersion Relation ◽  
Electric Field ◽  
Heat And Mass Transfer ◽  
Viscous Liquid ◽  
Marangoni Convection ◽  
Axial Electric Field ◽  
Stabilizing Effect

The electrohydrodynamic (EHD) thermosolutal Marangoni convection of viscous liquid, in the presence of an axial electric field through a micro cylindrical porous flow, is considered. It is assumed that the surface tension varies linearly with both temperature and concentration. The instability of the interface is investigated for the free surface of the fluid. The expression of the free surface function is derived taking into account the independence of the surface tension of the heat and mass transfer. The transcendental dispersion relation is obtained considering the dependence of the surface tension on the heat and mass transfer. Numerical estimations for the roots of the transcendental dispersion relation are obtained indicating the relation between the disturbance growth rate and the variation of the wave number. It is found that increasing both the temperature and concentration at the axial microcylinder has a destabilizing effect on the interface, according to the reduction of the surface tension. The existence of the porous structure restricts the flow and hence has a stabilizing effect. Also, the axial electric field has a stabilizing effect. Some of previous analytical and experimental results are recovered upon appropriate data choices.

Existence of a Surface Tension Discontinuity at a Liquid Free Surface

Nature ◽  
1968 ◽  
Vol 217 (5128) ◽  
pp. 536-538 ◽  
Author(s):  
R. H. J. SELLIN
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Liquid Free Surface
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