Wilder

Description

Wilder (1960) introduced a rate-dependent parameter to the Campbell-Ingmason relationship (Ingmanson and Whitney, 1954; Campbell, 1947).

Application

The Wilder relationship has a similar applicability region to the Campbell-Ingmanson relationship, besides the fact that the former can also take into account rate-dependent effects.

The Wilder relationship describes well the stress-strain behaviour of fibre network for individual compression or relaxation, but not for cycles of compression and relaxation. Regarding concentration, it is applicable up to fibre concentrations at where water flows out of the fibre walls (i.e. at approximately 20 percent dryness).

It is therefore suitable in the forming and vacuum sections.

Background

The Wilder relationship introduces a rate-dependent parameter to the Campbell-Ingmanson relationship:

$\displaystyle c = c_0 + \left[M_1 + M_2 \mathrm{log} \left( t \right) \right] \left(\frac{\sigma}{\sigma_r}\right)^N,$    

where $ c$ is the concentration, $ sigma$ and $ \sigma_r$ are the applied a reference stress and $ M_1$ , $ M_2$ and $ N$ are fitting constants. $ \sigma_r$ is introduced just to avoid complex units in $ M_1$and $ M_2$. $ t$is the time.

Bibliography

Campbell, W. B., 1947, Pulp and Paper Magazine of Canada 48(3), 103.

Ingmanson, W. L., and R. P. Whitney, 1954, Tappi Journal 37(11), 523.

Wilder, H. D., 1960, Tappi Journal 43(8), 715.

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