Steady state melting

George, H. H., Model of steady state melt spinning at intermediate take-up speeds, presentation given at the Joint Meeting of the US and Japanese Rheological Societies, Kona, HI, 6-9 April, 1979. 

In a one-dimensional steady-state melting column, the variation of the enrichment factor or, with depth due to melt transport is given by Spiegelman and Elliott (1993) (after correction of another typographical error in their Eq. 15)... 

Equations (5.95), (5.96) and (5.97) are suitable for constant critical melting porosity. In a one dimensional steady state melting column as a result of decompression melting, the porosity may increase from the bottom to the top of the column. If melting porosities change as a function of the spatial position, the related differential equations need to be solved numerically. More details of various melt transport models by porous flow have been given by Spiegelman and Elliott (1993), Iwamori, (1994), and Lundstrom (2000). 

Citron (C4) generalizes Landau s derivation of the steady-state melting rate of a semi-infinite solid with instantaneous removal of the melt to temperature-dependent thermal conductivity and specific heat, expressible in the form... 

Upon setting the right-hand side of Eq. (115) equal to zero, corresponding to steady-state melting, and making use of Eq. (114), one obtains after an integration... 

With the aid of Eq. (116d), the steady-state melting rate X is found to be... 

George, H. H., Model of steady state melt spinning at intermediate take-... 

Shenoy, A.V. and Saini, D.R. (1986) Wollastonite reinforced polypropylene composites dynamic and steady state melt flow bdiavior, /. Rdnf. Plastics Comp., 5, 62-73. 

Figure 8.8 Stages in the ultrasonic welding process. In Phase 1, the horn is placed in contact with the part, pressure is applied, and vibratory motion is started. Heat generation due to friction melts the energy director, and it flows into the joint interface. The weld displacement begins to increase as the distance between the parts decreases. In Phase 2, the melting rate increases, resulting in increased weld displacement, and the part surfaces meet. Steady-state melting occurs in Phase 3, as a constant melt layer thickness is maintained in the weld. In Phase 4, the holding phase, vibrations cease. Maximum di lacement is reached, and inter-molecular diffusion occurs as the weld cools and solidifies. ...

Shenoy, A. V. a Saini, D. R., WoUastonite leinfoiced polypropylene composites Dynamic and steady state melt flow behaviour, J. Reinf. Plastics Conqtos., 5, 62-73 (1986). 

Figure 14.23 Penetration vs. time curve showing the five phases of spin welding. Coulombic friction in phase I strips off surface roughness in phase II, generating wear particles. Penetration begins in phase III, reaches a steady state in phase IV, and ends in phase V, after rotational motion has ended and the weld has solidified. The penetration velocity, shown by the dotted line, increases dramatically in phase III, reaches a constant value during steady state melting, then drops off abruptly in phase V as penetration ends.

George, H. H. 1982. Model of Steady-State Melt Spinning at Intermediate Take-up Speeds. Polym. Eng. ScL, 22(5), 292-299. 

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