Singularities of ElectroHydroDynamic Equations

• Applicant: Professor Dr. Georg Sebastian Weiss
• Subject Area: Mathematics
• Term: from 2013 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 245812409

In his pioneering paper of 1964, Sir Geoffrey Taylor describes an experiment for the formation of a liquid cone by exposing a fluid jet to an electric field, and he formally derives a formula for the electric potential (referred to as Taylor-cone-solution in the sequel) of that field. At a critical voltage value, the surface of the fluid ruptures, and a fluid jet forms, which has found applications as various as electrospraying, electrospinning and, to give more concrete examples, ink jet printers, mass spectrometers and the production of lab-on-the-chips. Despite these various applications and extensive research from a physical point of view, the phenomenon of the Taylor cone remains in effect untouched by mathematical analysis, possibly due to the particular difficulty of the free boundary problem arising from the particular ElectroHydroDynamic equations (EHD equations) used as model. The free boundary problem differs in the sign of its surface tension term from previous, extensively investigated problems. This change in the sign of the surface tension term creates a similarity to the notoriously difficult Mumford-Shah problem.Main aims of the present project are-a rigorous analytic investigation of the singularities formed by the used EHD equations-construction of a branch of solutions terminating in the singular Taylor-cone-solution-a nonlinear stability study of the Taylor-cone-solution-an investigation of the regularising effect of the EHD equations used in our model

• DFG Programme: Research Grants