A numerical investigation of the fluid mechanical sewing machine

Abstract

A thin thread of viscous fluid falling onto a moving belt generates a surprising variety of patterns depending on the belt speed, fall height, flow rate, and fluid properties. Here we simulate this experiment numerically using the Discrete Viscous Threads method that can predict the non-steady dynamics of thin viscous filaments, capturing the combined effects of inertia, stretching, bending and twisting. Our simulations successfully reproduce nine out of ten different patterns previously seen in the laboratory, and agree closely with the experimental phase diagram of Morris et al.\ (2008). We propose a new classification of the patterns based on the Fourier spectra of the longitudinal and transverse motion of the point of contact of the thread with the belt. These frequencies appear to be locked in most cases to simple ratios of the frequency ${\Omega }_c$ of steady coiling obtained in the limit of zero belt speed. In particular the intriguing `alternating loops' pattern is produced by combining the first five multiples of ${\Omega }_c/3$.

References in corpus (2)

• The meandering instability of a viscous thread
• Frequency structure of the nonlinear instability of a dragged viscous thread

Cited by in corpus (8)

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• A discrete geometric approach for simulating the dynamics of thin viscous threads
• Frequency structure of the nonlinear instability of a dragged viscous thread
• Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets
• Some fluid mechanical aspects of artistic painting
• Simple deformation measures for Discrete elastic rods and ribbons
• Coiling instability in the kitchen
• Pattern formation in coiling of falling viscous threads: Revisiting the geometric model