Kinematics of wet forming – Part 2: Spinneret stretching in the wet forming zone

Spinneret stretching in the wet forming zone

1.     Characters of the stretched state of the spinning line in the forming zone

(1)  Spinneret stretch rate: _a(%)= (V_L-V_O)/V_O*100

(2)  Spinneret stretch ratio: i_a= V_L/V_O= _a/100+1

(3)  Average Axial Velocity Gradient: (_x)_a= (V_L-V_O)/X_e

In the above formula: V_O is the extrusion speed of the spinning stock solution; V_L is the winding speed of the newly formed fiber on the first guide roller; X_e is the solidification length, that is, the distance between the solidification point and the surface of the spinneret.

2.     Characters of the real stretched state of the spinning line in the forming zone

It can be seen that the calculations of the above formulas all take V_O as the benchmark. For the negative stretching, zero stretching or little positive stretching process used in wet spinning, the real stretching state of the filaments cannot be characterized. Therefore, the characterization of the stretched state of the spinneret should not be based on V_O, but should be based on V_f.

(1)  Real spinneret stretch rate: _f(%)= (V_L-V_f)/V_f*100

(2)  Real spinneret stretch ratio: i_a= V_L/V_f= _f/100+1

(3)  Real average Axial Velocity Gradient: (_x)_f= (V_L-V_f)/X_e

V_f can be measured directly from the length of the free-flowing thin stream per unit time, or can be obtained from the extrapolated value when the stretching stress on the spinning line is zero. In addition, it has been suggested to calculate indirectly from the diameter Dm of the free-flowing thin stream. But in doing so, the influence of the mass transfer process must be considered.

According to the continuity equation, when there is no mass transfer, the mass of the spinning thread passing through each point of the spinning process per unit time should be equal, that is:

πR²(X)v(X)p(X) = πR₀²v₀p₀

πR²(X)v(X)p(X) = K

In the formula, P is the density of spinning thread at the spinning process.

For free-flowing thin stream: R₀²v₀p_{0 =} R_f²v_fp_f

When the density of the spinning thread does not change much along the spinning process, it can be simplified as: R₀²v_{0 =} R_f²v_f

At this time, the swelling ratio of the free-flowing thin-stream has the following relationship: B₀= R_f/R₀= (p₀v₀/p_fv_f)^1/2 = (v₀/v_f)^1/2

That is to say, in the case of negligible mass transfer and density changes, V_f can be obtained from the diameter of the free-flowing thin-stream, that is: v_f = v₀/B₀² = v₀(R₀/R_f)²

In the case of general wet spinning with mass transfer process, the above formula is no longer valid.

When the apparent spinneret stretch rate φ_a is constant, if the R_f/R₀ ratio is different, the real spinneret stretch rate is also different. The values of φ_f and φ_a often differ not only in magnitude, but also in symbol.

The effect of B₀ on stretching of swollen thin-stream

It can be seen that the spinneret stretching ratio is negative apparently. If it is due to the larger swelling of the thin-stream, the elongation rates the thin-stream withstood is actually positive.