Nonlinear electrohydrodynamics of slightly deformed oblate drops

2015 ◽  
Vol 774 ◽  
pp. 245-266 ◽  
Author(s):  
Javier A. Lanauze ◽  
Lynn M. Walker ◽  
Aditya S. Khair
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Surface Charge ◽  
Time Scale ◽  
Applied Field ◽  
Major Axis ◽  
Boundary Integral ◽  
Numerical Results ◽  
Transient Deformation ◽  
Leaky Dielectric

The transient deformation of a weakly conducting (‘leaky dielectric’) drop under a uniform DC electric field is computed via an axisymmetric boundary integral method, which accounts for surface charge convection and a finite relaxation time scale over which the drop interface charges. We focus on drops that attain an ultimate oblate (major axis normal to the applied field) steady-state configuration. The computations predict that as the time scale for interfacial charging increases, a shape transition from prolate deformation (major axis parallel to the applied field) to oblate deformation occurs at intermediate times due to the slow buildup of charge at the surface of the drop. Convection of surface charge towards the equator of the drop is shown to weaken the steady-state oblate deformation. Additionally, convection results in sharp shock-like variations in surface charge density near the equator of the drop. Our numerical results are then compared with an experimental system consisting of a millimetre-sized silicone oil drop suspended in castor oil. Agreement in the transient deformation is observed between our numerical results and experimental measurements for moderate electric field strengths. This suggests that both charge relaxation and charge convection are required, in general, to quantify the time-dependent deformation of leaky dielectric drops. Importantly, accurate prediction of the observed modest deformation requires a nonlinear model. Discrepancies between our numerical calculations and experimental results arise as the field strength is increased. We believe that this is due to the observed onset of rotation and three-dimensional flow at such high electric fields in the experiments, which an axisymmetric boundary integral formulation naturally cannot capture.

Surprising consequences of ion conservation in electro-osmosis over a surface charge discontinuity

2008 ◽  
Vol 615 ◽  
pp. 323-334 ◽  
Author(s):  
ADITYA S. KHAIR ◽  
TODD M. SQUIRES
Keyword(s):  
Electric Field ◽  
Surface Charge ◽  
Applied Field ◽  
Surface Current ◽  
Diffuse Layer ◽  
Debye Screening Length ◽  
Ion Distribution ◽  
Electro Osmosis ◽  
Field Lines ◽  
Surface Conduction

A variety of microfluidic technologies utilise electrokinetic transport over rigid surfaces possessing rapid variations in charge. Here, as a paradigmatic model system for such situations, we consider electro-osmosis past a flat plate possessing a discontinuous jump in surface charge. Although the problem is relatively simple to pose, our analysis highlights a number of interesting and somewhat surprising features. Notably, the standard assumption that the electric field outside the diffuse screening layer is equal to the uniform applied field leads to a violation of ion conservation, since the applied field drives an ionic surface current along the diffuse layer downstream of the jump, whereas there is zero surface current upstream. Instead, at the surface charge discontinuity, field lines are drawn into the diffuse layer to supply ions from the bulk electrolyte, thereby ensuring ion conservation. A simple charge conservation argument reveals that the length-scale over which this process occurs is of the order of the ratio of surface-to-bulk electrolyte conductivities, LH=σs/σb. For a highly charged surface, LH can be several orders of magnitude greater than the Debye screening length λD, which is typically nanometres in size. Remarkably, therefore, nano-scale surface conduction may cause micrometre-scale gradients in the bulk electric field. After a distance O(LH) downstream, the bulk field ‘heals’ and is once again equal to the applied field. Scaling all distances with the ‘healing length’ LH yields a universal set of equations for the bulk field and fluid flow, which are solved numerically. Finally, we discuss the role of surface conduction in driving a non-uniform ion distribution, or concentration polarization, in the bulk electrolyte.

Operation Characteristics of Steady-State, Applied Field, Rectangular Magnetoplasmadynamics (MPD) Thruster

2015 ◽  
Vol 63 (2) ◽  
pp. 37-44 ◽  
Author(s):  
Daisuke ICHIHARA ◽  
Shota HARADA ◽  
Hisashi KATAOKA ◽  
Shigeru YOKOTA ◽  
Akihiro SASOH
Keyword(s):  
Steady State ◽  
Applied Field ◽  
Operation Characteristics

High-speed isotachophoresis. Analytical aspects of the steady-state longitudinal temperature profiles

1979 ◽  
Vol 44 (3) ◽  
pp. 841-853 ◽  
Author(s):  
Zbyněk Ryšlavý ◽  
Petr Boček ◽  
Miroslav Deml ◽  
Jaroslav Janák
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Electric Field ◽  
Field Intensity ◽  
Electric Field Intensity ◽  
Minor Component ◽  
Physical Models ◽  
Temperature Profiles ◽  
Longitudinal Temperature ◽  
Continuous Character

The problem of the longitudinal temperature distribution was solved and the bearing of the temperature profiles on the qualitative characteristics of the zones and on the interpretation of the record of the separation obtained from a universal detector was considered. Two approximative physical models were applied to the solution: in the first model, the temperature dependences of the mobilities are taken into account, the continuous character of the electric field intensity at the boundary being neglected; in the other model, the continuous character of the electric field intensity is allowed for. From a comparison of the two models it follows that in practice, the variations of the mobilities with the temperature are the principal factor affecting the shape of the temperature profiles, the assumption of a discontinuous jump of the electric field intensity at the boundary being a good approximation to the reality. It was deduced theoretically and verified experimentally that the longitudinal profiles can appreciably affect the longitudinal variation of the effective mobilities in the zone, with an infavourable influence upon the qualitative interpretation of the record. Pronounced effects can appear during the analyses of the minor components, where in the corresponding short zone a temperature distribution occurs due to the influence of the temperatures of the neighbouring zones such that the temperature in the zone of interest in fact does not attain a constant value in axial direction. The minor component does not possess the steady-state mobility throughout the zone, which makes the identification of the zone rather difficult.

scholarly journals Computational Performance of Disparate Lattice Boltzmann Scenarios under Unsteady Thermal Convection Flow and Heat Transfer Simulation

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 65
Author(s):  
Aditya Dewanto Hartono ◽  
Kyuro Sasaki ◽  
Yuichi Sugai ◽  
Ronald Nguele
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Lattice Boltzmann ◽  
Numerical Results ◽  
Convection And Heat Transfer ◽  
Steady State Condition ◽  
Physical Systems ◽  
Flow And Heat Transfer ◽  
Computational Performance

The present work highlights the capacity of disparate lattice Boltzmann strategies in simulating natural convection and heat transfer phenomena during the unsteady period of the flow. Within the framework of Bhatnagar-Gross-Krook collision operator, diverse lattice Boltzmann schemes emerged from two different embodiments of discrete Boltzmann expression and three distinct forcing models. Subsequently, computational performance of disparate lattice Boltzmann strategies was tested upon two different thermo-hydrodynamics configurations, namely the natural convection in a differentially-heated cavity and the Rayleigh-Bènard convection. For the purposes of exhibition and validation, the steady-state conditions of both physical systems were compared with the established numerical results from the classical computational techniques. Excellent agreements were observed for both thermo-hydrodynamics cases. Numerical results of both physical systems demonstrate the existence of considerable discrepancy in the computational characteristics of different lattice Boltzmann strategies during the unsteady period of the simulation. The corresponding disparity diminished gradually as the simulation proceeded towards a steady-state condition, where the computational profiles became almost equivalent. Variation in the discrete lattice Boltzmann expressions was identified as the primary factor that engenders the prevailed heterogeneity in the computational behaviour. Meanwhile, the contribution of distinct forcing models to the emergence of such diversity was found to be inconsequential. The findings of the present study contribute to the ventures to alleviate contemporary issues regarding proper selection of lattice Boltzmann schemes in modelling fluid flow and heat transfer phenomena.

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

Spin down problem of rotating stratified fluid in thermally insulated circular cylinders

1969 ◽  
Vol 37 (4) ◽  
pp. 689-699 ◽  
Author(s):  
Takeo Sakurai
Keyword(s):  
Steady State ◽  
Time Scale ◽  
Boussinesq Approximation ◽  
Circular Cylinders ◽  
Heat Conducting ◽  
Quasi Steady State ◽  
Homogeneous Fluid ◽  
Time Duration ◽  
Viscous Heat ◽  
Final Approach

A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing thermally insulated circular cylinder under the existence of stable distribution of the temperature is investigated within the framework of the Boussinesq approximation for a time duration of the order of the homogeneous-fluid spin down time in order to resolve the Holton-Pedlosky controversy. The explicit expression of the solution is obtained by the standard method and Holton's conclusion is confirmed. The secondary meridional current induced by the Ekman layers spins the fluid down to a quasi-steady state within the present time scale. However, unlike the homogeneous case, the quasi-steady state is not one of solid body rotation. The final approach to the state of rigid rotation is achieved via the viscous diffusion in the time scale of the usual diffusion time.

scholarly journals Uniform electric-field-induced lateral migration of a sedimenting drop

2016 ◽  
Vol 792 ◽  
pp. 553-589 ◽  
Author(s):  
Aditya Bandopadhyay ◽  
Shubhadeep Mandal ◽  
N. K. Kishore ◽  
Suman Chakraborty
Keyword(s):  
Electric Field ◽  
Surface Charge ◽  
Tilt Angle ◽  
Shape Deformation ◽  
Uniform Electric Field ◽  
Lateral Motion ◽  
Drop Surface ◽  
Lateral Migration ◽  
Drop Velocity ◽  
Pressure Fields

We investigate the motion of a sedimenting drop in the presence of an electric field in an arbitrary direction, otherwise uniform, in the limit of small interface deformation and low-surface-charge convection. We analytically solve the electric potential in and around the leaky dielectric drop, and solve for the Stokesian velocity and pressure fields. We obtain the correction in drop velocity due to shape deformation and surface-charge convection considering small capillary number and small electric Reynolds number which signifies the importance of charge convection at the drop surface. We show that tilt angle, which quantifies the angle of inclination of the applied electric field with respect to the direction of gravity, has a significant effect on the magnitude and direction of the drop velocity. When the electric field is tilted with respect to the direction of gravity, we obtain a non-intuitive lateral motion of the drop in addition to the buoyancy-driven sedimentation. Both the charge convection and shape deformation yield this lateral migration of the drop. Our analysis indicates that depending on the magnitude of the tilt angle, conductivity and permittivity ratios, the direction of the sedimenting drop can be controlled effectively. Our experimental investigation further confirms the presence of lateral migration of the drop in the presence of a tilted electric field, which is in support of the essential findings from the analytical formalism.

Paper-based Triboelectric Nanogenerator and Activities of Salt Ions

2021 ◽  
Author(s):  
Shatrudhan Palsaniya ◽  
Komal Nehra ◽  
Ashok Kumar Dasmahapatra
Keyword(s):  
Steady State ◽  
Kinetic Energy ◽  
Charge Transport ◽  
Surface Charge ◽  
Aluminum Foil ◽  
Electrostatic Charge ◽  
Charge Carriers ◽  
Triboelectric Nanogenerator ◽  
Steady State Condition ◽  
Salt Ions

Abstract This work presents a triboelectric nanogenerator (TENG) fabrication using polytetrafluoroethylene, aluminum foil, and cellulose paper. Mechanical interactions lead to atomic defects that stimuli the delocalized electrostatic charge carriers and kinetic energy. The addition of ionic salt’s microdroplets improved the TENG’s performance. Eventually, surface charge activities have escalated the electrical signals. Further, studied spontaneously increased charge transport performance at the steady-state condition in the presence of NaCl ionic droplets. We considered that these ionic activities actively participated in detecting salt ions.

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