Dent, Robin W
ABSTRACT
Of the many transient phenomena mentioned in the fabric comfort literature, two involve vapor diffusion (without liquid water transfer) from the surface of a perspiring "sweat-covered" body: the ". . . buffering effect of hygroscopic clothing" at the onset of sweating noted by Spencer-Smith and the "after-exercise chill" discussed by Woodcock. Both Woodcock and Spencer-Smith made laboratory studies with "sweating" hot plates to try to understand the significance of these phenomena. Their fabrics did not touch the wet plate, so there was no liquid water transfer.
Both effects involve the simultaneous transport of heat and moisture vapor through fabrics or fiber assemblies, and an analytic approximation is given here to explain aspects of these phenomena. We use the basic theoretical approach developed by Henry to study the conditioning of cotton bales. The theory can qualitatively explain the different responses or results obtained experimentally by Spencer-Smith and Woodcock in terms of fiber type and regain as well as fabric structure and ambient conditions. They discussed the connection between the physical lab tests and the field psychological comfort phenomena. We do not attempt quantitative agreement here because of space limitations, but present the next step necessary to confirm the validity of the approach and effects in this theoretical paper. Other transient phenomena such as the analogous buffering effect due to changing ambient conditions (both temperature and humidity) and the initial "cold feel" of fabrics, will be similarly analyzed in later papers. In all these cases, the question is, what is the role of fiber regain and are other effects equally significant?
In this paper, we discuss the two transient effects of "cooling" or "buffering" by an absorbent fabric at the onset of sweating in hot climates and the "chilling" due to the cessation of sweating after exercise in cool climates, using Henry's theory for coupled heat and moisture flows in an assembly of fibers (or a fabric) when the driving mechanism is gas phase diffusion alone. Cassie [1], in studying conditioning of wool fiber bales considered the corresponding case where there is forced air-- flow. With such a flow of air, the diffusion effects are normally negligible, although Daniels [3] discussed cases where both transport mechanisms are significant.
In the two effects due to sweating considered here, the subject is assumed to be resting so that there is no forced air flow through the fabric and Henry's theory is taken to be applicable. In this theory, we assume that there is sorption equilibrium locally between the fiber and air and that the diffusion into the fiber is rapid enough that the fiber moisture content M always approaches the equilibrium sorption value for the local air conditions in terms of RH or concentration C and temperature T. In order to obtain analytical answers, we restrict our considerations here generally to either short or long times.
Farnworth [6] used a numerical method to obtain graphic solutions that cover the entire time scale. He also assumed that diffusion into the fibers is extremely rapid. Wehner et al. [14] showed that correcting for diffusion into the fibers adds a small but significant improvement in comparison to experimental results for moderately sorptive fibers (with a diffusion coefficient of 2.5 X 10^sup -9^ cm^sup 2^/s and radius of 10 (mu)m).
An earlier numerical approach at C.S.I.R.O. has been increasingly refined over the years [4, 8, 9, 10]; it includes an empirical treatment of diffusion in the gas phase (with local depletion at the fiber surface) and uses a finite concentration-dependent diffusion into the fiber itself. This treatment is based on data given by Downes and MacKay [5] and Watt and McMahon [13]. However, their results equally show the classical two-stage uptake of regain predicted by Henry's theory as well as his predicted rapid transient temperature wave when humidity alone is changed. Hence, these results can also be explained in principle by Henry's theory. This means that gas phase diffusion (especially in a fabric of relatively tightly woven and twisted yarns) and the roles of surface depletion and details of diffusion into the fibers can potentially be ignored in many cases. The special situations where these effects should be included will depend on the experimental conditions. A clear distinction needs to be made between the processes of gas-- phase diffusion, internal fiber diffusion, and sorption.
Hence, analytical solutions for the two sweating phenomena are given here using Henry's theory, assuming first that sorption equilibrium has been achieved and second that there is only gas-phase resistance, so that for a body at rest, the transport is by gas-phase diffusion only. We hope these calculations will help resolve some of the continuing issues relative to the balances between sorption and diffusion and the comfort of hygroscopic and hydrophobic fiber assemblies.
Discussion
The mathematical analysis given here confirms that when the body is perspiring, fabric absorbency can become important and the buffering (or cooling) effect postulated by Spencer-Smith and the after-exercise chilling discussed by Woodcock from their lab experiments can be modeled to provide further understanding of the significance of these effects for absorbent and nonabsorbent fiber fabrics and the balance in the determining factors involved. Fabric density and thickness are particularly important if the fibers of the fabric are hygroscopic.
Note that two transient waves pass through the system, and very little heat is associated with the faster wave. The buffering and chilling effects are associated mainly with the slower, subsequent wave. Also, when buffering is large, so will be the chilling effect once perspiration ceases for the same fabric and atmospheric conditions. If the fabric has a low density, there may not be any extra cooling effect due to the transients, but rather an over-- heating, which will be larger for more absorbent fibers.
In Henry's theory used here, we assume that there is local sorption equilibrium between the fiber and air. Because most textile fibers essentially attain equilibrium with the atmosphere in a few seconds, whereas the phenomena discussed here may take minutes or hours, the effect of the time lag to attain sorption equilibrium should be small. This is not necessarily true for the fast wave, but because the heat flow associated with this first wave is small, the effect on the experimental data should not be too large. This effect has been discussed by David and Nordon [4] and more recently by Li and Holcombe [9].
The theory given here also assumes that a perspiring body essentially maintains an atmosphere at the body surface with a constant concentration (presumably, but not necessarily for the theory, equivalent to 100% RH). Farnworth [6] considered instead that the rate of sweat supply should be constant. With this boundary condition, his experiments gave somewhat different results. We have not considered his boundary condition here, although it might correspond more closely to real comfort situations. Our analysis is intended to correspond only to the laboratory experiments of Spencer-Smith and Woodcock.
Conclusions
We have shown here that Henry's theory can qualitatively explain the measurements intended to simulate the two comfort phenomena of buffering and after-exercise chill in terms of fiber type, fabric structure, and ambient conditions. Thus, our theory tends to confirm the conclusions from those measurements-that denser fabrics (say phi 0.8),-which may be the case with some staple yarn fabrics-the buffering may even be less than occurs with hydrophobic fiber fabrics, as shown by Woodcock. The effects should be larger for lighter, thicker, hygroscopic fiber fabrics and for drier conditions. Density may be as important as fiber regain in some of these conditions. Quantitative calculations are not given here, but are necessary to confirm the generality of our conclusions.
ACKNOWLEDGMENTS
I thank the late Professor J. J. Hermans for his help and guidance during this work, D. Andersen and R. Curry for their help, and the late Dr. R. Buchdahl for his encouragement.
Literature Cited
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Manuscript received June 15, 2000; accepted December 15, 2000.
ROBIN W. DENT
Albany International Research Co., Mansfield, Massachusetts 02048, U.S.A.
