**5.1. Modelling of pressure loss**

The magnitude of final pressure that appears on the surface of skin is more relevant in the compression treatment. Compression bandage applies a total pressure on the surface of padding which causes a pressure loss. This pressure loss is attributed to the significant changes in structure of the padding during compression, which results in its permanent thickness reduction, and significant energy loss. The absorbed energy by the padding during compres‐ sive load could be a good indicator of the pressure loss or absorption during the use of padding beneath compression bandage. The thickness change during compression-load-recovery test is used to obtain this energy loss or absorption in the nonwoven structure. The thickness changes in loading can be expressed as [42, 43]:

Nonwoven Padding for Compression Management http://dx.doi.org/10.5772/61309 173

$$\frac{T}{T\_o} = 1 - a \ln\left(\frac{P}{P\_o}\right) \tag{2}$$

where *T* is the thickness at arbitrary pressure *P*, *To* is the initial thickness at pressure *Po* and *α* is the compressibility parameter. After loading to final pressure *Pf* , the thickness of the sample reduces to a lowest thickness *Tf*. . During recovery case, the thickness *T* at arbitrary lower pressure *P* (<*Pf* ) can be expressed as:

by measuring the wicking height against gravity for a hanging fabric. An in-plane wicking deals with the transport behaviour in the horizontal plane of the fabric and describes several useful parameters such as the liquid flow anisotropy, the rate of movement, and the area of wet surface with time. Figure 5 shows the photograph of the computerized wicking tester for

in-plane transport measurement [41].

172 Non-woven Fabrics

**Figure 5.** Photograph of the instrumental set-up for measuring in-plane wicking

**5. Theoretical insights into padding behaviour**

changes in loading can be expressed as [42, 43]:

The magnitude of final pressure that appears on the surface of skin is more relevant in the compression treatment. Compression bandage applies a total pressure on the surface of padding which causes a pressure loss. This pressure loss is attributed to the significant changes in structure of the padding during compression, which results in its permanent thickness reduction, and significant energy loss. The absorbed energy by the padding during compres‐ sive load could be a good indicator of the pressure loss or absorption during the use of padding beneath compression bandage. The thickness change during compression-load-recovery test is used to obtain this energy loss or absorption in the nonwoven structure. The thickness

**5.1. Modelling of pressure loss**

$$\frac{T}{T\_f} = \left(\frac{P}{P\_f}\right)^{-\mu} \tag{3}$$

where*β* is the recovery parameter. Both *α* and *β* are dimensionless constants that could be easily obtained by a simple load-recovery test. Using these parameters, it is possible to characterise the compressional and recovery behaviour of different types of nonwoven fabrics. Figure 6 shows a typical thickness-pressure curve for a nonwoven fabric during loading and unloading. The shaded area under load and recovery curve represents the energy loss during a cycle. The work done during compression (*Ec*) can be obtained using Eq. (2) as:

$$E\_c = \int\_{T\_s}^{T\_f} PAdT = P\_o A \int\_{T\_s}^{T\_f} e^{\sqrt{1 - \frac{T}{T\_s}}} dT \tag{4}$$

where *A* is the area of specimen; *To* and *Tf* are initial and final thicknesses, respectively; and *Po* is the initial pressure. The potential energy recovered during release of load (*Er*) taking into account Eq. (3), is given by:

$$E\_r = \bigcap\_{T\_f}^{T\_r} PA dT = P\_o A \bigcup\_{T\_f}^{T\_r} \left(\frac{T}{T\_o}\right)^{\frac{-1}{\rho}} dT \tag{5}$$

where *Tr* is the recovered thickness after load removal. Using these potential energies (*Er* and *Ec*), it is possible to calculate the energy loss (*EL*) of the fabric during the compression recovery cycle:

$$EL = \frac{E\_c - E\_r}{E\_c} \tag{6}$$

The lower the value of *EL* (energy loss), the poorer is the performance of padding in energy absorbance. Padding bandage lies underneath the compression bandage that applies signifi‐

**Figure 6.** A typical curve of pressure-thickness data for a nonwoven

cant amount of interface pressure in the range from 10 to 50 mmHg, depending on severity of venous disease. The applied pressure by the compression bandage on the padding has two components: first, the pressure that is transferred through padding and finally appears on the skin; second, the pressure loss in the padding structure. This pressure loss can be related to the energy loss *EL* as described in Eq. (6). So, the pressure results can be expressed as:

$$P\_f = P\_T - P\_l = P\_T - f\left(EL\right) \times P\_T = \frac{F}{r} \left(1 - f\left(EL\right)\right) \tag{7}$$

where, *Pf* is the final pressure on the surface of skin, *F* is the applied force to the compression bandage which generates total pressure *PT* on the padding, *r* is the radius of the limb and *Pl* is the pressure loss that can be related to *EL*. Using a set of experimental results, one can easily obtain the function relating pressure loss and energy loss for a given padding sample. Once expressed, it would be easy to obtain the final pressure at any given applied force (*F*). The measurement of applied force is difficult to judge during wrapping but the applied extension *ε* is easy to measure. The applied force *F* is related to the extension applied in the compression bandage during wrapping:

$$F = \tau \times \mathcal{E} \tag{8}$$

where *τ* is the tensile modulus of the compression bandage. So, using the experimental results of tensile test for the compression bandage and the load-recovery tests for padding bandage, it is possible to predict the pressure results of the multi-layer compression system. Both these experiments can be done in the laboratory and therefore provide a simple method to access multi-layer bandaging performance.
