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.

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.

Interactions Between High-Viscosity Droplets Deposited on a Surface: Experiments and Simulations

2012 ◽  
Author(s):  
J. Esmaeelpanah ◽  
A. Dalili ◽  
S. Chandra ◽  
J. Mostaghimi ◽  
H. C. Fan ◽  
...  
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Surface Force ◽  
Line Length ◽  
High Viscosity ◽  
Droplet Shape ◽  
Viscous Liquids ◽  
Straight Lines

A combined numerical and experimental investigation of coalescence of droplets of highly viscous liquids dropped on a surface has been carried out. Droplets of 87 wt% glycerin-in-water solutions with viscosity 110 centistokes were deposited sequentially in straight lines onto a flat, solid steel plate and droplet impact photographed. Impacting droplets spread on the surface until liquid surface tension and viscosity overcame inertial forces and the droplets recoiled, eventually reaching equilibrium. Droplet center-to-center distance was varied and droplet line length was measured from photographs. As droplet spacing was increased there was less interaction between the droplets. A three dimensional parallel code has been developed to simulate fluid flow and free surface interaction by solving the continuity, momentum and volume-of-fluid (VOF) equations. The two-step projection method was employed to solve the governing equations for the whole domain including both liquid and air phases. The continuum-surface-force (CSF) scheme was applied to model surface tension and the piecewise-linear-interface-construction (PLIC) technique used to reconstruct the free surface. Computer generated images of impacting droplets modeled droplet shape evolution correctly and compared well with photographs taken during experiments. Accurate predictions were obtained for droplet line length during spreading and at equilibrium.

Nonlinear interactions between a free-surface flow with surface tension and a submerged cylinder

2010 ◽  
Vol 648 ◽  
pp. 485-507 ◽  
Author(s):  
R. M. MOREIRA ◽  
D. H. PEREGRINE
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Gravity Waves ◽  
Classical Method ◽  
Surface Flow ◽  
Boundary Integral ◽  
Steady Solution ◽  
Small Scale ◽  
Fully Nonlinear ◽  
Submerged Cylinder

A submerged cylinder in a uniform stream flow is approximated by a horizontal doublet, following Lamb's classical method. A linear steady solution including surface tension effects is derived, showing that under certain conditions small-scale ripples are formed ahead of the cylinder, while a train of ‘gravity-like’ waves appear downstream. Surface tension effects and a dipole are included in the fully nonlinear unsteady non-periodic boundary-integral solver described by Tanaka et al. (J. Fluid Mech., vol. 185, 1987, pp. 235–248). Nonlinear effects are modelled by considering a flat free surface or the linear stationary solution as an initial condition for the fully nonlinear irrotational flow programme. Long-run computations show that these unsteady flows approach a steady solution for some parameters after waves have radiated away. In other cases the flow does not approach a steady solution. Interesting features at the free surface such as the appearance of ‘parasitic capillaries’ near the crest of gravity waves and the formation of capillary–gravity waves upstream of the cylinder are found.

The Oscillation of Slender Elliptical Inviscid and Newtonian Jets: Effects of Surface Tension, Inertia, Viscosity, and Gravity

1989 ◽  
Vol 56 (4) ◽  
pp. 968-974 ◽  
Author(s):  
S. E. Bechtel
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Cross Section ◽  
Nonlinear Oscillator ◽  
Major Axis ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Fully Nonlinear ◽  
Single Degree ◽  
Elliptical Jet

The motion of inviscid and Newtonian jets issuing from elliptical orifices is analyzed. The analysis is not confined to small departures of the jet free surface from a circular cylindrical mean surface, but rather is fully nonlinear. Two types of behavior are predicted: (1) In the presence of surface tension the major axis of the elliptical jet cross-section alternates between perpendicular directions with distance down the jet. In this case the system is described as a single-degree-of-freedom nonlinear oscillator, conservative for the inviscid elliptical jet in the absence of gravity, and nonconservative for the Newtonian jet. (2) When surface tension is neglected, the transformation occurs only once, after which the jet flattens into a sheet perpendicular to the major axis of the orifice. The effect of gravity is discussed both for downward flowing jets and fountains.

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

2014 ◽  
Vol 92 (10) ◽  
pp. 1249-1257 ◽  
Author(s):  
M.F. El-Sayed ◽  
N.T. Eldabe ◽  
M.H. Haroun ◽  
D.M. Mostafa
Keyword(s):  
Surface Tension ◽  
Electric Field ◽  
Potential Flow ◽  
Flow Instability ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Physical Parameters ◽  
Two Dimensional ◽  
Dielectric Fluids ◽  
Fluid Velocities

The nonlinear electrohydrodynamic Kelvin–Helmholtz instability of two superposed viscoelastic Walters B′ dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg–Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of two-dimensional disturbances. While in the nonlinear analysis, for both two- and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.

Thermocapillary Instabilities of Low Prandtl Number Fluid in a Laterally Heated Vertical Cylinder

2006 ◽  
Vol 128 (6) ◽  
pp. 1228-1235 ◽  
Author(s):  
B. Xu ◽  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Matrix Structure ◽  
Various Boundary Conditions ◽  
Banded Matrix ◽  
High Order Finite Difference

Stabilities of surface-tension-driven convection in an open cylinder are investigated numerically. The cylinder is heated laterally through its sidewall and is cooled at free surface by radiation. A seeding crystal at constant temperature is in contact with the free surface. Axisymmetric base flow is solved using the high-order finite difference method. Three-dimensional perturbation is applied to the obtained base flow to determine the critical Marangoni numbers at which the axisymmetry is broken. The eigenvalue matrix equation is solved using linear fractional transformation with banded matrix structure taken into account. Critical Marangoni-Reynolds numbers are obtained at various boundary conditions.

Low Reynolds Number Film Flow Down a Three-Dimensional Bumpy Surface

2005 ◽  
Vol 127 (6) ◽  
pp. 1122-1127 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Free Surface ◽  
Film Flow ◽  
Three Dimensional ◽  
Surface Shape ◽  
Maximal Flow ◽  
Free Surface Shape ◽  
Complex Boundary ◽  
First Time

The slow film flow down a doubly periodic bumpy surface is studied for the first time. Perturbations on the primary variables and the complex boundary conditions lead to a system of successive equations. The secondary flow and the free surface shape depend on the wavelength of the bumps and a surface tension-inclination parameter. There exists an optimum aspect ratio of the protuberances for maximal flow rate.

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.

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.

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