Electrospinning Jet: Force-Balance Thinning & Whip Model (2D)

The 3D version of this simulator drives the whipping instability by simulating real pairwise Coulomb repulsion, spring tension and drag across a chain of jet beads — the bending emerges from the N-body force sum. This 2D counterpart takes a genuinely different route to the same physics: each jet element's axial velocity comes from the exact analytic solution of a first-order force-balance ODE (electric driving force against viscous drag), its shrinking cross-section follows directly from mass conservation once that velocity history is known, and the whipping wavelength and growth rate are predicted up front from a linear-stability dispersion relation of the kind used in the electrospinning literature, rather than left to emerge from particle-particle forces. Tune voltage, flow rate, tip-to-collector distance and solution viscosity and watch the fiber diameter, whip wavelength and growth rate respond to the closed-form physics in real time.