equilibrium condition(A21), and that the transition to some other potential distribution capable of matching the real electrode shape takes place far enough from the liquid to be of little consequence. We should expect, however, that the Taylor cone solution will be disturbed to some extent by non-ideal conditions, and will eventually disappear In one respect at least, the Taylor cone cannot be an exact solution: the infinite electric field predicted at the apex(r=o) will produce various physical absurdities. Something must yield before that point, and that is explored next A3. CURRENT AND FLOW FROM TAYLOR CONES As the photograph in Fig. 6 shows, a jet is seen to issue from the cone's tip, implying the need for a flow rate, say Q (m/s). Since the surface being ejected is charged, this also implies a net current, I. It will be seen that these flows and currents are (in the regime of interest)extremely small: 0=10-m/s, =10 A per needle. The tip jet is likewise extremely thin(of the order of 20-50 nm) Not very near the cone s tip the current is mostly carried by ionic conduction in the electrolytic solution. In a good, highly polar solvent (i.e, one with 8>>1), the salt in solution is highly dissociated, at least at low concentration. For example, Lice in Formamide dissociates into L, and Ce, and each of these ions, probably "solvated"(i.e with several molecules of formamide attached), will drift at some terminal velocity (in opposite directions) in response to an electric field. At high concentrations(several molar)the degree of dissociation decreases. Following are the measured electrical conductivities K, of solutions of LiCe in Formamide((E=100) NOTE: Use is made of 912() -2E where K and e are the complete elliptic integrals of the Is and 2 kind, respectively. It is also noteworthy that Pn2(x)==/2(x),so Rr[cos(180'-9)] could equivalently be used as the angular part in(A23) 16.522, Space Propulsion Lecture 23-25 Prof. Manuel Martinez-Sanchez Page 16 of 36equilibrium condition (A21), and that the transition to some other potential distribution capable of matching the real electrode shape takes place far enough from the liquid to be of little consequence. We should expect, however, that the Taylor cone solution will be disturbed to some extent by non-ideal conditions, and will eventually disappear. In one respect at least, the Taylor cone cannot be an exact solution: the infinite electric field predicted at the apex (r=o) will produce various physical absurdities. Something must yield before that point, and that is explored next. A3. CURRENT AND FLOW FROM TAYLOR CONES As the photograph in Fig. 6 shows, a jet is seen to issue from the cone’s tip, implying the need for a flow rate, say Q (m3 /s). Since the surface being ejected is charged, this also implies a net current, I. It will be seen that these flows and currents are (in the regime of interest) extremely small: Q ≈10 −13 m−13 /s, ≈ 10−8 A per needle. The tip jet is likewise extremely thin (of the order of 20-50 nm). Not very near the cone’s tip, the current is mostly carried by ionic conduction in the electrolytic solution. In a good, highly polar solvent (i.e., one with ε >> 1), the salt in solution is highly dissociated, at least at low concentration. For example, LiCl in Formamide dissociates into L and i + Cl− , and each of these ions, probably “solvated” (i.e., with several molecules of formamide attached), will drift at some terminal velocity (in opposite directions) in response to an electric field. At high concentrations (several molar) the degree of dissociation decreases. Following are the measured electrical conductivities K, of solutions of LiCl in Formamide ((ε ≅ 100) 1/ 2( )x = K 1 + x 2 ⎛ ⎝ ⎞ ⎠ − 2E 1 + x 2 ⎛ ⎝ ⎞ ⎠ P 1/2( )x = 2 • NOTE: Use is made of Q , where K and E are the complete elliptic integrals of the 1st and 2nd kind, respectively. It is also noteworthy that π Q1/2(−x) P1 / 2 cos 180o [ ( − ϑ) , so ] could equivalently be used as the angular part in (A23). 16.522, Space Propulsion Lecture 23-25 Prof. Manuel Martinez-Sanchez Page 16 of 36