电场作用下液态金属表面锥尖的形成

Topological structures of velocity and electric field in the vicinity of a cusp-type magnetic null point

Topological characteristics reveal important physical properties of plasma structures and astrophysical processes. Physical parameters and constraints are linked with topological invariants, which are important for describing magnetic reconnection scenarios. We analyze stationary non-ideal Ohm's law concerning the Poincare classes of all involved physical fields in 2D by calculating the corresponding topological invariants of their Jacobian (here: particularly the eigenvalues) or Hessian matrices. The magnetic field is assumed to have a cusp structure, and the stagnation point of the plasma fl…

Unmasking of Novel Conic Modes in Electrically Stressed Perfectly Conducting Liquids

Liquid metal ion sources (LMIS) are widely used in applications ranging from local ion implantation in semiconductors, to focused ion beam systems for milling and nanolithography, to space micropropulsion devices being developed by NASA. Above a critically large field strength, an electrically stressed liquid metal develops one or more cuspidal protrusions which undergo accelerated conic tip sharpening with runaway field self-enhancement. Zubarev (2001) first predicted from an inviscid model that the electric stresses at the liquid apex undergo self-similar divergent growth in finite time. The…

Self-Similar Cusp Formation in Thin Liquid Films By Runaway Thermocapillary Forces

Many physical systems give rise to dynamical behavior leading to cuspidal shapes which represent a singularity of the governing equation. The cusp tip often exhibits self-similarity as well, indicative of scaling symmetry invariant in time up to a change of scale. Cusp formation can even occur in liquid systems when the driving force for fluid elongation is sufficiently strong to overcome leveling by capillarity. In almost all cases reported in the literature, however, the moving interface is assumed to be \textit{shear-free} and the operable forces orient exclusively in the direction normal t…

Electrified Cone Formation in Perfectly Conducting Viscous Liquids: Self-Similar Growth Irrespective of Reynolds Number

Above a critical field strength, the free surface of an electrified, perfectly conducting viscous liquid, such as a liquid metal, is known to develop an accelerating protrusion resembling a cusp with a conic tip. Field self-enhancement from tip sharpening is reported to generate divergent power law growth in finite time of the forces acting in that region. Previous studies have established that tip sharpening proceeds via a self-similar process in two distinct limits - the Stokes regime at $\textsf{Re}=0$ and the inviscid regime $\textsf{Re} \to \infty$. Using finite element simulations to tra…

电场中悬浮肥皂泡的形变与不稳定性

Deformation and instability of sessile soap bubbles in an electric field

研究电场中悬浮肥皂泡的形变与不稳定性，通过实验观察其稳定变形阶段和锥形不稳定性，揭示电场作用下肥皂泡的变形机制与动态行为。

介电流体中的动态点形成

Dynamic Point-Formation in Dielectric Fluids

本文用边界积分方法计算了在均匀电场E作用下，一滴电介质液浸入另一种电介质液中时变变形。稳态理论预言，当介电常数比β足够大时，在两个锥角上可以存在一个锥形界面，其中θ <（β）是稳定的，θ>（β）是不稳定的。相反，我们的数值证据表明，当E和β超过临界值时，会产生一个锥形成和一个瞬态有限时间奇异性的动力学过程。基于电应力和流体运动的标度分析，我们能够应用近似边界条件来计算尖端区域的演化。我们发现，在电应力远大于表面张力的非平衡情况下，新生长锥区的电应力与表面张力之比可以收敛到一个依赖于β的值，α_c（β）>1，而锥角收敛到θ_<（β）。这个新的动力学解是自相似的。