The viscous collapse of radial nonsymmetric composite tubes

Collapsing of glass tubes: analytic approaches in a hydrodynamic problem with free boundaries

“…This analysis will be denoted in the following as the 1D collapsing theory. A first extension toward a 2D analysis to study azimuthal collapsing instabilities of thick-walled tubes under stationary heat sources has been reported in [5,7]. Another 2D extension outlined in [6] takes into account the axial heat conduction to specify the axial and radial temperature and viscosity distribution for moving heat sources.…”

“…The known hydrodynamic approaches of collapsing [1][2][3][4][5][6][7][8] assume throughout a governing radial viscous flow, so that the collapsing kinematics is understood to result from a radial movement of the tube boundaries, driven by external forces in radial direction. Then the hydrodynamics reduce to the radial viscous flow and radial normal stress, both depending upon the radial coordinate only.…”

“…Such an elementary process is called collapsing (see, e.g., [1][2][3][4][5][6][7][8]). We will exclusively focus on collapsing with a uniformly moving heat source, where an observer comoving with the heat source becomes aware of a steady-state collapsing profile narrowed against the direction of motion [2][3][4][5][6][7]. Of course, this only occurs if the comoving observer measures, at the same time, an accompanying steady-state temperature field.…”

“…There is a large series of papers on analytic approaches of the drawing problem since the 1970s (e.g., [9,10,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]), but only fewer papers involve an analytic treatment of collapsing [1][2][3][4][5][6][7][8] since the 1980s. The approaches on drawing (axial symmetry assumed) favor a perturbation analysis with the prerequisite of a dominating axial viscous flow and axial viscous flow gradient, small axial viscosity dependence, and small inclination of the rod boundary (or tube boundaries) against the rotation axis, as typical for capillary geometries.…”

“…This paper is motivated by the concern to have a well-founded analytical base for data evaluation, if systematic and contactless measurements of viscosity and surface tension of molten glasses are carried out through collapsing with a moving heat source [3,4]. In addition, both collapsing and drawing are fundamental technological steps in manufacturing of optical fibers (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12]). Always for reasons of economy in time, conditions should be predicted to assure the fabrication of optical fibers where, at least, the desired properties are approached (see, e. g. [12,13]).…”