The asymptotic structure of a slender dragged viscous thread

摘要: The behaviour of a viscous thread as it falls onto moving belt is analysed in the asymptotic limit slender thread. While bending resistance small, its effects are dynamically important near contact point with belt, where changes curvature and orientation Steady flows shown to fall into one three distinct regimes, depending on whether faster than, slower than or close same speed free-fall velocity key dynamical balances each regime explained role stresses found be qualitatively different. solutions exhibit ‘backward-facing heel’ observed experimentally for low speeds, provide leading-order corrections stretching catenary theory previously developed high speeds. stability onset meandering also analysed. It that entire thread, rather boundary layer alone, governs stability. A balance between destabilising reaction forces restoring force gravity remainder determines meandering, an analytic estimate frequency thereby obtained. At leading order, neutral occurs little more slowly not when lower part begins under compression, but horizontal at slightly against direction motion. heel ‘losing balance’.