Unlike melt spinning, both dry and wet spinning use solvents in which the polymer dissolves, see Fig. 4-3. The resulting solution or suspension is a viscous "spin dope." This process necessarily introduces another species, which is subsequently removed, and therefore is more expensive than conventional melt spinning processes. It is used in cases where the polymer may degrade thermally if attempts to melt it are used or in cases where certain surface characteristics of the filaments are desired-melt spinning produces filaments with smooth surfaces and dry spinning produces filaments with rough surfaces. The rougher surface may be desirable for improved dyeing steps or for special yarn characteristics.

The term "dry spinning" is a bit misleading, since the polymer is certainly wet by a solvent. Presumably, the intent here was to distinguish the two methods of solvent removal for the two cases of dry and wet spinning. The solvent in dry spinning is a volatile organic species and this solvent starts to evaporate after the filament is formed, which is immediately downstream of the spinneret. Whereas melt spinning involved solidification by cooling, dry spinning produces solidification of the polymer by solvent removal.

Several commercial fibers, including acrylic fibers such as Orlon, are
made by a dry spinning process. You may recall that these acrylic fibers
are popular as substitutes for wool fibers. In any case, the spinning step
which defines, in large part, the spinning process is that of solvent removal
from the filaments. In the case of Orlon, the polymer, polyacrylonitrile,
is dissolved to a polymer concentration of 20 to 30 wt% in a dimethylformamide
solvent. Warm gases (air? - probably not, on account of the need for solvent
recovery) are passed through the fiber bundle in the region just downstream
of the spinneret. This begins to look very much like the cooling crossflow
in melt spinning. The solvent encounters both a diffusional resistance
within the fiber and a convective resistance in moving from the surface
of the filament to the crossflow gases. Within the filament, the material
property of greatest importance is DAB, the diffusivity
of the solvent A through the filament B. Here, we can characterize the
diffusive flux of the solvent by:

(4-16)

which is your familiar Fickian Diffusion equation. We use the ordinary
derivative here because the process is steady and we have not yet begun
to use the Lagrangian perspective. One point to emphasize here is the similarity
of this equation to the Fourier heat conduction equation. If we then adopt
the Lagrangian perspective, we have:

(4-17)

Comparison with the unsteady heat conduction equation reveals the equation
to be identical with the exception that is
replaced by DAB and T by C. Both and
DAB have dimensions of length squared over time or units of cm2/s. The
initial and boundary conditions are also practically identical to the heat
transfer case, with the assumption of uniform concentration profile at
time zero, and zero concentration gradient on the filament centerline and
matching diffusive and convective flux at the filament surface:

C (r,0) = Co for r< R and q = 0 (4-18)

at r = 0 and q>0 (4-19)

and

at r = R and q>0 (4-20)

Instead of heat transfer coefficient, h, we have mass transfer coefficient,
k. Correlations for k, expressed in terms of a dimensionless mass transfer
coefficient, Sh (for Sherwood number) as a function of ReD and Sc, are
also available. Sc is the ratio of momentum diffusivity to mass diffusivity,
v/DAB, (for the cross flow fluid) and is comparable to the Prandtl number,
v/.
Note that n and DAB are the momentum diffusivity and mass diffusivity of
the gas in crossflow, and not of the polymer solution. One correlation
(__Transport and Unit Operations__, 3rd ed., by C. J. Geankoplis, Prentice
Hall, Englewood Cliffs, (1993), p 450) for k is:

Sh = 0.281 (ReD)-0.4 (4-21)

where Sh = (kD/DAB). This correlation is a bit unusual, in that normally the mass transfer coefficient is found to be proportional to the diffusivity raised to a power less than unity. The reader may want to check other correlations to check whether this form may or may not be reasonable.

Just as we dedimensionalized the heat transfer equations, we can do
the same for solvent diffusion. The resulting equations then are exactly
identical to those for unsteady heat conduction.

(4-22)

(4-23)

(4-24)

Of course, T is replaced by C, by
D_{AB}, h by k. Therefore, the same solution (graphical or analytical)
is obtained and the same charts can be used to obtain quantitative predictions
of the fiber spinning process. One can readily calculate, therefore, the
Fourier number, X, required for the solvent concentration at the filament
centerline to become less that 1% of the original value (Y < 0.01).
From this value for X, the actual time (in a Lagrangian sense, remember)
can be calculated. Finally, by multiplying this time by the yarn speed,
the length of the solvent recovery section is obtained directly. The analogy
here might be that of using a conveyor belt in a tunnel oven to bake bread.
We can calculate the length of the tunnel oven, once we know the time to
bake the bread and the speed of the conveyor belt.

**Key elements learned in this section include:**

Equivalence of fundamental equations for heat transfer and mass diffusion,

Similarity (and difference?) between convective equations for heat transfer and those for mass transfer,

Manufacture of synthetic fibers by volatilization of solvent from fibers produced as spin "dope" is extruded through small holes.