Once the electric field overcomes surface tension at the nozzle, the polymer solution erupts from a Taylor cone as a thin, uniformly charged jet. This is the classic Reneker–Yarin bead model: the jet is discretised into charged beads linked by viscoelastic elements, and Newton's second law is integrated for every bead:
F_Coulomb(i,j) = k_e · q² · (r_i − r_j) / |r_i − r_j|³
F_field(i) = q · E (axial, toward collector)
F_visco(seg) = k·(ℓ − ℓ₀) + c·(dℓ/dt) (Maxwell spring-dashpot)
F_tension(i) ∝ γ · curvature (straightens the path)
m·(dv_i/dt) = ΣF − drag·v_i
A perfectly straight jet is only an equilibrium in principle. Any lateral perturbation displaces neighbouring charged elements sideways, and because like charges repel, the Coulomb force then has a component that grows the displacement further — a positive feedback loop. Viscoelastic tension and surface tension resist this bending, but once the electric field stretches the jet thin enough, the destabilising Coulomb torque wins and the path buckles into the characteristic 3D whipping (bending) instability, often cascading into smaller secondary loops. This chaotic stretching — not simple axial elongation — is what reduces the jet from a micrometre-scale filament to a nanometre-scale fibre before it lands on the collector.
- Electric field — the axial driving force; higher fields pull the jet taut and speed up transit.
- Charge density — sets the strength of the destabilising Coulomb repulsion; raise it to trigger a wider, faster whip.
- Elastic modulus — solution stiffness/viscosity resisting bending; raise it to suppress the instability and keep the jet straighter.
- Flow rate — how fast new jet material is fed from the nozzle and the starting jet radius.
Real-world relevance: this instability is why industrial electrospinning can turn a millimetre-wide polymer drop into kilometres of continuous nanofiber a few hundred nanometres across, used in filtration membranes, wound dressings and tissue-engineering scaffolds.