====== Phenomenology======

===== Phenomenology =====

The feet material is held in underneath the opening by the screw-elements and is transported in the screws as a solid in the direction of the screw-tips. Through contact with the heated cylinder wall, the particles in the proximity of the cylinder wall begin to sinter and melt on until finally a broad standing connected molten film over the solid tailback in the intermeshing area is formed. This procedure is supported through in the practice conventionally carried-out reductions of the short pitch of the screw elements. These are found in front of the geometric plastification zone, through which an extra compression of the solids occurs and thus a better contact with the heated cylinder wall can be achieved. At the same time, granule particles lying on the underside of this layer are heated through convection.

Through the formation of the molten film, the friction conditions in the mesh area and in the solid tailback change behind the intermeshing area. Through this process, the forced conveying of solids in a intermeshing region breaks down, and material is forced through the nip region. As a result of the 3-dimensional speed profile in the intermeshing area, an intensive mixture of the materials occurs. If the proportion of ready-fused materials is sufficient, a dispersion from the existing granules is formed from the solid phase and from the existing viscous phase polymer melt.

If the melted share for a completely formed dispersion is not yet sufficient an agglomeration of granule particles occurs. These are then further fused through the dissipation of the already existing melt, and through heat conduction of the surrounding walls. Also the agglomerates are further more molten and trans-ported during their transportation through convection and through passing of further intermeshing areas in the already stated condition of dispersion.

After the achievement of this condition, the further melting of the not yet molten Polymer particles can only be successful through the heat conduction from the hot melt to the solid granule particles. This is because the granule particles no longer have direct contact with the heated cylinder walls, i.e. they are longer touching the heated screw surface.

A condition for the described melting behavior is a sufficiently long solids-conveying section. In practice, inserted screw configurations point out that with a short conveying section, combinations of plastic elements with subsequent dust particles, results in only a partial filling in the plastification zone.

If the available length of conveying section to the molten film over the solid tail-back does not suffice, so the forced conveying of the solids remains up to the location where the first filling with melt took place. Principally, if the solid that holds a significantly larger speed component in the axial direction than the melt, reaches the melt filled area, and melt can penetrate in the cavities of the granules, then the forced conveying will collapse. In front of the location of the first filling up with melt, through a sufficiently large mass throughput, originates one with a granule filled screw area, in which, the granules rotate around the screw like in the figure.

{{ :en:grundlagenhandbuch:aufschmelzberechnung:en_sigma150_dlg_grundlagenhandbuch_aufschmelzberechnung_001.png?nolink |}}

**Figure:** Melting behavior in a co-rotating twin screw extruder

The speed component in the axial direction is substantially lower in this area than in that of the solid-forced conveying area. Between that in the fully filled solid area emerging friction and the from the extrusion flow resulting force an equilibrium attunes.

The necessary pressure for wetting of particles can be worked out by:

$$p = \frac{2K(T_m)d_p}{a_f - d_p}\left(\frac{2F(1 + 2n)}{n(a_f - d_p)}\right)^n \tag{1}$$

When assuming quadratic gap areas.

Where $\bar{v}$ is the average flow velocity of the melt that arises through the evaluation of the continuity equation:

$$\bar{v} = \frac{\dot{m}}{A_{channel} \cdot \rho_s}\left(\frac{1}{1 - \frac{1}{F_0 \rho_m + (1 - F_0)\rho_m}}\right) \tag{2}$$

With equations (1) and (2) it is possible to calculate the length of the solid tailback.

In the solid filled area, through the heated cylinder walls, as well as with the hot screws, it can likewise lead to a molten film formation. A noticeable melt, however, sets in when solid particles enter the melt filled area. Here you will find that the particles are dispersed in the melt area. The further melting is then again successful through the heat conduction of the hot melt to the solid particles, whereby the particles diameter in the cross section are reduced.

After the achievement of this condition, the distribution of the not yet melted solid particles in the polymer melt is shown in the figure in the illustration of the thinly sliced samples. The cut direction runs parallel to the screw axis.

At the point of the first filling with melt, the solids rate is just over 50%. In this area, small air holes are still observable. What this points out is that not all cavities in this area have been completely filled with melt. In further progressions of melting these air holes should disappear. At the same time the size of the solid particles will reduce until they are non-existent. A preferred distribution of the solid particles in the polymer melt during the melting process is not perceivable.