Mathematical Modeling of Viscous Fiber Drawing Processes
Summary
The drawing of viscous fibres entails heating a glass or polymer preform to a temperature at which it behaves as a highly viscous fluid, then stretching it into a continuous filament under controlled tension and thermal conditions. Mathematical modelling serves as an indispensable tool for predicting the evolution of fibre geometry, material properties and thermal profiles without the need for costly trial-and-error experiments. By exploiting the slender-body assumption, researchers reduce the full three-dimensional Navier–Stokes and energy equations to effective one-dimensional descriptions that couple mass, momentum, energy and surface-tension balances. Asymptotic and numerical methods capture the interplay between axial extension, radial contraction, free-surface flow and heat transfer, while allowing for complex cross-sectional shapes such as hollow or microstructured optical fibres. These models inform furnace design, draw-tower control and cooling strategies, and address the inverse problem of determining preform geometry and process settings required to achieve a specified final profile. Such advances underpin industrial applications ranging from high-speed telecommunications and high-power laser delivery to sensing, biomedical devices and energy-efficient manufacturing worldwide.
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Mathematical Modeling of Viscous Fiber Drawing Processes publication trend
The graph below shows the total number of articles in mathematical modeling of viscous fiber drawing processes across all publications each year (not limited to Nature Index journals).
Technical terms
Slender-body assumption: Approximation that the fibre length greatly exceeds its cross-sectional dimensions, permitting reduction to one-dimensional governing equations.
Asymptotic analysis: Mathematical technique exploiting small-parameter limits to simplify coupled mass, momentum and energy equations into tractable reduced-order models.
Free-surface Stokes flow: Low-Reynolds-number regime in which surface tension and viscous stresses govern the evolution of moving boundaries.
Draw ratio: Ratio of initial preform cross-sectional area to that of the drawn fibre, controlling the axial stretch and tensile stress.
Inverse problem: Determination of the initial preform geometry and process parameters necessary to achieve a target final fibre geometry.
References
- Asymptotic Modeling of Optical Fibres: Annular Capillaries and Microstructured Optical Fibres. Fibers (2023).
- An Asymptotic Energy Equation for Modelling Thermo Fluid Dynamics in the Optical Fibre Drawing Process. Energies (2022).
- Analytic approximation for the collapse of viscous tubes driven by surface tension and pressure difference. Archive of Applied Mechanics (2022).
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