Charged Species Flow

The motion of the liquids or the solutes in many lab-on-a-chip applications are controlled electrically. Therefore, it is highly relevant to study electrohydrodynamics, that is, the coupling of electromagnetism and hydrodynamics. Electrohydrodynamics comprises a wide range of phenomena in addition to hydrodynamics such as electrochemistry and electrokinetics, which involves electrical properties of liquids. 

We will deal with electromagnetic phenomena in the electrostatic regime, that is, we disregard any magnetic and radiative effects. In accordance with the continuum hypothesis, the governing equations for continuous media are Maxwell equation. Here, the eleetric field E, the electric displacement field D, the magnetic field B, the polarization field P, the electrical current density and the electrical potential (p are averaged locally over their microscopic counterparts. The fundamental equations are 

Transport Phenomena in Microfluidic Systems, First Edition. Pradipta Kumar Panigrahi. 

Assuming the permittivity of a material, e to be a constant, the equation (6.1b) can be written as 

This equation is known as the Poisson equation for electrostatics. The knowledge of charge density distribution pg) is required for obtaining potential distribution. If the charge density is zero, we get Laplace equation. These equations will be used in the electrohydrodynamic analysis of microfluidics. 

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