Charge separation in the conical meniscus of an electrospray of a very polar liquid: Its effect on the minimum flow rate

An analysis is presented of the flow and the distribution of charge in the meniscus of an electrospray of a very polar liquid which is fed with a low flow rate. The shape of the meniscus is taken to be a Taylor cone. The characteristic value of the flow rate at which the liquid ceases to be quasineutral in a certain relaxation region of the conical meniscus under the action of the applied field is estimated, and the current/flow rate characteristic of the electrospray is numerically computed in these conditions. A state of complete charge separation, in which the ions that are pushed by the electric field away from the tip of the meniscus cease to reach the jet of the electrospray, is found for a finite value of the flow rate, and no stationary solution exists below this flow rate. For very polar liquids of small viscosity, this minimum flow rate is of the order of the experimental minimum for the cone-jet regime when the flux of the electric field in the jet is taken into account. The flow induced in the meniscus by the Coulomb force in the bulk of the liquid and the electric shear stress at its surface is computed and its effect on the distribution of charge and the minimum flow rate is analyzed. Estimates of the flow and the electric current in the jet are worked out for a range of flow rates above the minimum.