Calculation of absorption properties of absorbent materials

1. IntroductionOne of major applications of disposable nonwovens is in absorbent materials, which constitute a broad range of products, ranging from baby diapers, personal hygiene & adult incontinent pads to tampons, paper towels, tissues & sponges.Fig-1 shows anatomy of a diaper where key requirement for absorbent materials at cover sheet is its ability to imbibe rapidly & hold large amount of fluid under pressure.Absorbency rate & absorbent capacity are the two most important performance parameters to be considered for absorbent applications of nonwovens. Absorbent capacity is mainly determined by interstitial space between fibres, absorbing and swelling characteristics of material & resiliency of web in wet state. Absorbency rate is governed by balance between forces exerted by capillaries & frictional drag offered by fibre surfaces. For non-swelling materials, these properties are largely controlled by capillary sorption of fluid into structure until saturation is reached [1]. Absorbency rate & absorbent capacity are affected by fibre mechanical & surface properties, structure of fabric (i.e., size & orientation of flow channels), nature of fluids imbibed, & manner in which web or product is tested or used [2-7]. Among those factors, surface wetting characteristics (contact angle) of fibres in web & structure of web, such as size, shape,orientation of capillaries, & extent of bonding, aremost important.

Fig. 1: Anatomy of Diaper [10]Polymer type of fibres in fabrics, hydrophilic or hydrophobic, influences inherent absorbent properties of fabrics. A hydrophilic fibre provides capacity to absorb liquid via fibre imbibitions, giving rise to fibre swelling. It also attracts & holds liquid external to fibre, in capillaries, & structure voids. On other hand, a hydrophobic fibre has only latter mechanism available to it normally [7]. Effect of small amount of fibre finish (generally 0.1 to 0.5% by weight) is also important since it is on fibre surface. Particular finish applied on fibre can significantly change surface wetting property of fibre.Fibre linear density and its cross-section area affect void volume, capillary dimensions & total number of capillaries per unit mass in fabrics. Fibre surface morphology, surface ruggedness, & core uniformity can influence absorbency performance to some extent. Fibre crimps influence packing density of fabrics & further affect thickness per unit mass that affects absorbency of nonwoven fabrics. Nature of crimps, whether it is two-dimensional or three-dimensional, also has some effect.Size of capillaries is affected by thickness per unit mass & resiliency of web, & size, shape & mechanical properties of fibres. Resiliency of web is influenced by nature & level of bonding of fabrics as well as size, shape, & mechanical properties of constituent fibres [6].2. Models & equationsModels have been built to characterize the two parameters, absorbent capacity (C) & absorbency rate (Q). C (cc/g fluid/g) is given by volume/mass of fluid absorbed at equilibrium divided by dry mass of specimen, while Q is given by slope of absorbency curve divided by dry mass of specimen. Model to calculate C is based on determining total interstitial space available for holding fluid per unit dry mass of fibre. Equation is shown as follow [5,6]:.........(1)Where,Ais the area of the webTis the thickness of the webWfis the mass of the dry webfis density of dry fibreVdis amount of fluid diffused into structure of fibresisthe ratio of increase in volume of a fibre upon wetting to volume of fluid diffused into fibre.In above equation, "the second term is negligible compared to the first term, & third term is nearly zero if a fibre is assumed to swell strictly by replacement of fibre volume with fluid volume" [6]. Thus, dominant factor that controls the fabric absorbent capacity is web thickness per unit mass on dry basis (T/Wf).For absorbency rate, the Washburn-Lucas's equation [8,9] is applied.........(2)Where, S is distance through which fluid penetrated in time tris mean pore radius of capillarylis surface tension of fluidiscontact angle of fibreisviscosity of fluidtis fluid penetrated timeModifications are given to Washburn-Lucas's equation when applied to nonwoven webs in which fluid spreads radially outward from a point in centre. Modified equation is shown as follow:...... (3)Where, r is mean pore radius of capillarylis surface tension of fluidiscontact angle of fibreis viscosity of fluidT is thickness of webWfis mass of dry webA is area of webfis density of dry fibreIn a given web and fluid system, only mean pore radius r and thickness per unit mass (T/Wf) in above equation are not constant. Predicted value of r by following equation based on assumption that a capillary was bound by three fibres, oriented parallel or randomly, & specific volume of capillary unit cell equalled that of parent web [3].............(4)for,Where subscripts1and2represent different fibre types andisa constant with a value of 9x105dis fibre denierisfibre density (g/cc)fis mass fraction of a fiber in blend (f1+ f2= 1)ReferencesL. F. Fryer, B. S. Gupta, Determination of Pore Size Distribution in Fibrous Webs and Its Impact on Absorbency, "Proceedings of 1996 Nonwovens Conference," 1996, pp. 321-327.Chatterjee, P. K., "Absorbency,"Elsevier,New York, 1985.Gupta, B. S., Effect of Structural Factors on Absorbent Characteristics of Nonwovens,Tappi J.71, 147-152 (1988).Gupta, B. S., and Crews, A. L., Nonwoven: An Advanced Tutorial, "The Effect of Fluid Characteristics in Nonwovens," TAPPI Press,Atlanta,GA, 1989Gupta, B. S., and Hong, C. J., Changes in Dimensions of Web During Fluid Uptake and its Impact on Absorbency,Tappi J.77, 181-188 (1994).Gupta, B. S., Whang, H. S., Capillary Absorption Behaviors of Hydroentangled and Needlepunched Webs of Cellulosic Fibers, "Proceedings of INDA-TEC 96: International nonwovens conference,"September 11-13, 1996,HyattRegencyCrystalCity, Crystal City, Virginia, USA.Gupta, B.S., and Smith, D. K., Nonwovens in Absorbent Materials,Textile Sci. and Technol.13, 349-388 (2002).Lucas, R., Kolloid Z., "Ueber das Zeitgesetz des Kapillaren Aufstiegs von Flussigkeiten," 23, 15 (1918).Washburn, E.W.,TheDynamics of Capillary Flow,Phys. Rev.17(3), 273 (1921).Gupta, B. S. and L. C. Wadsworth, "Differentially Absorbent Cotton-Surfaced Spunbond Copoplyester and Spunbond PP with Wetting Agent," Proceedings , Seventh Nonwovens Conference at 2004 Beltwide Cotton Conferences, San Antonio , TX , January 5-9, 2004