Electrohydrodynamic Models

The key link between ELS experiments and particle electrostatic properties is the theoretical model of colloidal electrohydrodynamics. The required model is considerably more complicated than the one needed in the interpretation of DLS data. DLS relies upon a relatively simple colloidal hydrodynamic model to relate the measured particle diffusivity to particle radius via the Stokes-Einstein Eq. (39). The colloidal electrohydrodynamic model for ELS must account for the complex physical/chemical/electrical structure of the particle surface as well as the distortion of the diffuse part of the electrostatic double layer due to the motion of the particle through the medium. 

Vlahovska, P.M., Gracia, R.S., Aranda-Espinoza, S., and Dimova, R. (2009) Electrohydrodynamic model of vesicle deformation in alternating electric fields. Biophysical Journal, 96 (12), 4789-4803. 

In the nemato-electrohydrodynamic model nematics are treated as ohmic conductors. To describe the dynamics of the charge density p = V D, which... 

A general electrohydrodynamic model of a weakly conductive viscous jet accelerated by an external electric field was also derived, by considering inertial, hydrostatic, viscous, electric, and surface tension forces. Nonlinear rheologic constitutive equation for the jet radius was derived,... 

Reneker and Yarin model Refs 35, 65, 71, 275 Electrohydrodynamic models Refs 46, 48, 57, 58 Feng Refs 283, 290 Carroll and Joo Refs 291-293 Straight jets and bending instabilities Straight jets and whipping instabilities Straight jets Linear viscoelasticity (Maxwellian) Newtonian N on-Newtonian X ... 

FIGURE 3 Scheme of the cylindrical fluid element used in electrohydrodynamic modeling [9]. 

Models of colloidal electrohydrodynamics relate the electrophoretic mobility /t to the zeta potential , the particle radius / , the composition of the solution via the Debye length /k, and the solvent viscosity and permittivity, // and f. Dimensional analysis shows that these variables must be related by... 

The synthesis of a model library of 100 amides from anhydrides on microchips has been described with quality control indicating excellent yields of pure amides and no cross-contamination of the wells (199). This test validated the chip structure, the seals of the system, and the electrohydrodynamic pumping system in the presence of solvents such as DMF and methanol and reagents such as the anhydrides, piperidine, and DIPEA. More challenging chemistries and larger libraries have also been presented. 

In the ion-evaporation model of Iribame and Thomson [11-14], the seqnence of solvent evaporation and electrohydrodynamic droplet disintegration also leads to the production of microdroplets. Gas-phase ions can be generated from the highly-charged microdroplets, at which the local field strength is sufficiently high to allow preformed ions in solution to be emitted into the gas phase (lEV). 

Vervoort, N., Gzil, R, Baron, G. V, and Desmet, G, Model column structure for the analysis of the flow and band-broadening characteristics of silica monoliths, J. Chromatogr. A, 1030, 177, 2004. Nischang, I., Chen, G, and Tallarek, U., Electrohydrodynamics in hierarchically structured monohthic and particulate fixed beds, J. Chromatogr. A, 1109, 32, 2006. 

FIGURE 22.5 Forces acting on the Taylor cone in EHDA process. (Reprinted from J. Aerosol ScL, 30(7), Hartman, R.P.A., Bruimer, D.J., Camelot, D.M.A., Marijnissen, J.C.M., and Scarlett, B., Electrohydrodynamic atomization in the cone-jet mode physical modeling of the liquid cone and jet, 823-849. Copyright 1999, with permission from Elsevier.)... 

The other model for the ionic friction concerns the dielectric response of solvent to the solute perturbation. When an ion is fixed in polar solvent, the solvent is polarized according to the electrostatic field from the ion. If the ion is displaced, the solvent polarization is not in equilibrium with a new position of the ion, and the relaxation of the polarization should take place in the solvent. The energy dissipation associated with this relaxation process may be identified as an extra friction. The extra friction, called the dielectric friction, decreases with increasing ionic radius, thereby, with decreasing electrostatic field from the ion. The dielectric friction model developed by Born [66], Fuoss [67], Boyd [68] and Zwanzig [69, 70] has taken a complete theoretical form due to the work by Hubbard and Onsager [71, 72] who proposed a set of continuum electrohydrodynamic equations in which the electrostatic as well as hydrodynamic strains are incorporated. 

The canonical example is that of a Janus particle with one metallic and one insulating hemisphere [9], using the standard low-voltage model for electrokinetic motion of polarizable particles. In response to an applied electric field, the Janus particle rotates to align the interface between the two hemispheres with the field axis, due to both ICEP (electrohydrodynamics) and DEP (electrostatics). At the same time, for any orientation, the particle translates in the direction of its insulating end, propelled by ICEO flow on the metallic end, with a velocity... 

The early work on modeling electrohydrodynamic instabilities performed a linear stability analysis of the electric and fluid interfacial boundary conditions using the transfer relations developed by Melcher [1]. Melcher developed... 

Electrokinetic and electrohydrodynamic instability mixing in microsystems is a complex phenomenon which researchers are only beginning to exploit and understand. Future work requires a further development of experimental models and expansion of computational simulations to better understand how the instabilities form and grow. Specific applications of electrokinetic and electrohydrodynamic instabilities are still limited. The application of these instabilities to improve mixing between components should be explored. One example is through the use of multiphase systems where electrohydrodynamic instabilities are utilized to improve component partitioning for liquid extraction devices. 

Saville DA (1997) Electrohydrodynamics the Taylor-Melcher leaky dielectric model. Annu Rev Fluid Mech 29 27-64... 

The modeling of electrohydrodynamic droplet generation from a microchannel within a microchip via an applied electric field has been studied by Kim et al. [96]. They modeled the droplet formation using a Level Set method coupled with a Poisson solver for the electric field. The model was used to determine the role of the surface properties of the microtube. They demonstrated that the system could generate mono-sized droplets at a regular frequency with no satellite droplets. The... 

A theoretical investigation of the stability of nematic liquid crystals with homeotropic orientation requires a three-dimensional approach. Helfrich s one-dimensional theory predicts the dependence of the threshold of the instability on the magnitude of Ae, as shown by curve 2 in Fig. 5.8, according to which the electrohydrodynamic instability should be observed when either Ae < 0 (and consequently the bend Frederiks effect reorientation will not take place), or when small Ae > 0. In Helfirich s model the destabilizing torque as dvzjdx is responsible for this instability, which replaces the destabilizing torque a dvzjdx in the equation for the director rotations (5.27). Although the torque is small ( a3 -C o 2 ) it is not compensated for (e.g., when Ae = 0) by anything else apart from the elastic torque. 

FIGURE 5.8. Experimental dependences on Ae of (1) the threshold for the (bend) Prederiks effect Ub (4) the threshold of an electrohydrodynamic instabihty with a homeotropic initial orientation (3) the threshold of the Kapustin-Williams domains with planar initial orientation. The calculation of Uthr using the Helfrich s one-dimensional model for a homeotropic orientation (5.30) is shown in curve 2 [31]. 

---