Charge Injection Systems: Physical Principles, Experimental and Theoretical Work

C Specific heat at constant pressure p D Displacement field D Diffusion coefficient d D Orifice diameter E Electric field E Electron charge F Force G Acceleration due to gravity I Current J Current flux K Conductivity k Boltzmann constant B L Atomizer geometry: length from electrode tip to orifice plane i L Atomizer geometry : length of orifice channel o P Polarization Q Flow rate/Heat flux Q Charge r Atomizer geometry : electrode tip radius p T Time T Temperature U Velocity V Voltage W Energy X Distance Nomenclature (Greek) Thermal expansion coefficient ? Permittivity ? Permutation operator ? ijk Ion mobility ? VI Nomenclature Debye length ? D ? Dynamic viscosity ? Mass density Surface tension ? T Electrical conductivity ? ? Timescale ? Vorticity Nomenclature (Subscripts) Reference state ? o Cartesian tensor notation ? ijk Volume density (? per unit volume) ? v Surface density (? per unit area) ? s Linear density (? per unit length) ? l ¿critical¿ state ? c Bulk mean injection ? inj Nomenclature (Superscripts) Time or ensemble averaged ? Contents Contents 1 Introduction¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿. 1 1.1 Introduction and Scope¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿.. 1 1.2 Organization¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿.. 3 2 Electrostatics, Electrohydrodynamic Flow, Coupling and Instability¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿... 5 2.1 Electrostatics¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿.. 5 2.1.1 The Coulomb Force¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿ 5 2.1.2 Permittivity¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿ 6 2.1.3 Conductors, Insulators, Dielectrics and Polarization¿¿.. 6 2.1.4 Gauss¿sLaw¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿... 8 2.2 Mobility and Charge Transport¿¿¿¿¿¿¿¿¿¿¿¿¿. 10 2.2.1 Introduction¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿ 10