Water Transport Models of Moisture Absorption and Sweat Discharge Yarns

594Joumal of Donghua University (Eng. Ed.) Vol. 25, No.5 (2008)Water Transport Models of Moisture Absorption and Sweat DischargeYarnsWANG Fa-ming(王发明)' '，ZHOU Xiao-hong(周小红)2，WANG Shan-yuan(王善元)'!The Key Lab of Tertile Science & Technology Ministry of Education, Donghua Unitversity, Shanghai 201620, China2 The Key Lab of Adranced Textile Materials & Manufacturing Technology Minisry of Education China，Zhejiang Sci- Tech Universisy,Hangzhou 310018, ChinaAbstract: An important property of moisture absorption andinteractions of a liquid with the walls of a thin tube. Thesweat discharge yarns is their water transport property. Ircapillary effect is a function of the ability of the liquid tothe paper, two water transport models of moisturewet a particular materialblabsorption and sweat discharge yarns were developed toThe cpilary efect was usually taken place in liquids,investigate the influence factors on their wicking rate. Insuch as water (sweat is nearly a kind of water), which isparallel Column Pores Model, wicking rate is determined byubiquitous and capable of strong surface interactions.the equivalent capillary radius R and length of the capillaryWater climbs up a capillary tube because of the strongtube L. In Pellets Accumulation Model, wicking rate ishydrogen-bonding interactions between the water and thedecided by the capillary radius r and length of the fiber unitair at the surface of the tube. The energetic gain from theassemble Lo .new intermolecular interactions must be balanced againstKey words: uuter trunsport; ca pillary action; parallel coluonngravity, which attempts to pull the liquid back down. Thepores model; pellets accunulation mocdel; moisture aubsorptiomnarrower the diameter of a tube, the higher the liquid will& sueat dischurge yurmclimb; clearly, a narrow column of liquid weighs less than aCLC number: TS 151Document code: Athick one. The pressure in the capillary can be determinedArticle ID: 1672 - 5220(2008)05 - 0594 -03by Young-Laplace equation41 :P= c∞sθ(1)Introductionwhere, P is the pressure in the capillary(Pa); σ is theThe water transport property is one of the key factorssurface tension of the water(N/m); R is the equivalentby which is influencing the comfort property of garments.capillary radius of fiber(m); 0 is the contact angle at theliquid- solid air interface(").Differential capillary effect fabrics were first developed byWhen profiled fiber (i.e. the shape of the fiber crossan American scientist. Japan was also developedsection is like “+”，“Y") was used to spin moistureDifferential capillary effect fabrics were also developed inJapan, which were used to design famous sportswear, suchabsorption and sweat discharge yarn, the Parallel Columnas Adidas, Nike. The capillary action model was developedPores Model can be adopted to describe the yarn structure,as shown in Fig. 1.by Wang'" to describe the influence factors. A kind ofwater transport model for knitted fabrics was developed byMeng*2]. In the mean time, wicking rate method andchannelvertical water absorption method were optimized.All the above researchers and scientists focus on fabricParallel Columnmodels and there are still few models on yarn. In thisPores Modelpaper, two yarn models on water transport property weredeveloped to investigate influence factors on wicking rate.Fig. 1 Profiled fiber and Parallel Column Pores Model1 Parallel Column Pores Model.1 Conditions of capillary actionAssumption: the diameters of all tubes are the same;Capillary action is a physical effect caused by thethe water is a kind of ditilled water; there is no中国煤化工Received date: 2007 - 08 - 24Supported by National Nature Science Fund (No. 50643014), "Yangtze S.MHC N M H Grent Plan" lnovationTeam (No. IRT 0654) and Science Research Fund of Zhejiang Sci-Tech Universty (No. UhU1065-Y).* Correspondence should be addressed to WANG Fa- ming, E-mail; faming. wang@yahoo. comJoumal of Donghu University (Eng. Ed.) Vol.25, No. 5 (2008) 595temperature change and phase change during thIt can be seen from Eq. (8) that the wicking rate oftransportation process.the fiber assembles is decided by the length of the capillaryAccording to the YoungLaplace equation, when the extratube L and the equivalent radius of the capillary tube Rpressure on the capilary is greater than or equal to the gravity(when θ and σ are constants) .produed by the liquid in the apillary, the liquid will rise upand then capillary action happens. That is:2 Pellets Accumulation Model2ccos0rR2 -rR'h0g20.(2In Pellets Accumulation Model, it was assumned thatthe shapes of cross-section of all the fibers are circular andwhere h, height of the capillary action (m); g, thethose fibers are tightly accumulated. The description ofacceleration of gravity (m/s2);P, the liquid density (kg/model is shown in Fig. 2.m');The height of the capillary action can be deduced fromthe Eq. (2)hs 2acs0(3PgRIt can be seen from the Eq. (3) that when 0, s, and pFig. 2 Pellets Accumulation Modelare constants, h is decided oaly by the equivalent radius ofSingle fiber unit model and fiber assemble unit modelthe capillary R. Consequently, in order to find a kind ofwere developed. The two unit models are shown in Fig. 3nice water transport property material, the equivalentrespectively.radius of the fiber should be as small as possible..2 Wicking rateThe height of cailary action per minute can be usedto symbolize the wicking rate v (cm/min), and thewicking rate v is given as5]:where, t is wicking time (min) .Fig.3 Single fiber unit model and fiber assemble unit modelIt is known that water is a kind of Newtonian fluid.Therefore, according to the Hagen-Poiseuille equaton[6,Assumption: The fibers in fiber assemble unit modelthe equation defines the flow through a tube and how thisare parallel to each other and there is no yarn twist in fiberflow is affected by the atributes of the tube; the lengthassemble model. In single fiber unit model, two centers ofand radius, and the atributes of the fluid; the viscosity.cross section A and B were chosen randomly, and linearThe Hagen Poiseuille equation can be expressed as follows;distance of sides AB is L (m); the spaces among thesefibers were scemed as capillary interspacesT ; All the singleQ=kR'P(5)fibers were rigid fibers, which insures the cross sectionLsbape of all the fibers cannot be changed when the fiberwhere, Q is the flow volume (L/s); k is a constant, whichassemble was in a large stress. The pores among the fibersis related to the liquid viscosity 7; L is the length of theare the main tunnels to transport liquid water, and all thecapillary tube (m) .fibers are circular fibers and those fibers were arranged aOn the other hand, Eq. (5) can be also written asshown in Fig. 3. It was assumed that the spacing sectionsQ=8_πR'P(6)among fibers are the sume triangles. The radiuis of all the fibersis the same. It can be easily docducod that the number ofwhere, 7 is the liquid shear viscosity (Pa●s).triangles equals the number of fibers around one core fiber.Substituting Eq. (1) into Eq. (6), the flow volume QEach of the triangle area s can be defined ascan be expressed, in principle, by the equations= β32-禁r°≈0. 1629)πR'acosθQ=47(7)中国煤化工each tiangle can beAs a result, wicking rate can be given by.MYHCNMHG= dh_. eRocos0(8)R=N户≈0.057r(10)dt πr° 47L596Joumal of Donghua University (Eng. Ed.) Vol. 25. No. 5 (2008)The Pellets Accumulation Model can be seen as a kindrate were also discussed. In parallel Column Pores Model,of porous media, according to Darcy's Law*i,when the 0, P, s and g are constants, the wicking rate isdecided by the equivalent capillary radius R and length of(11)the capillary tube L. In Pellets Accumulation Model, whenwhere, q is the volume flux in the flow direction (m'/0，s，k and 7 are constants， the wicking rate isdetermined by the capillary radius r and length of the fibermin), P is the capillary pressure(Pa) and Lo is the lengthunit assemble Lo.of fiber unit assemble(m), K the proportionality constant,is the flow conductivity of the porous media with respect tothe fluid. The higher the value of K, the lower the flowAcknowledgementsresistance of the fluid, and vice versa.The authors would like to express their sincerelyK is often defined as k/ 7, where k is the permeabilityof the medium, and 7 is the fluid viscosity. Then Eq. (11)thanks to the Key Lab of Advanced Textile Materials andcan be written asManufacturing Technology， Ministry of Education,Zhejiang Sci- Tech University.q=-分L(12)The wicking rate of the Pellets Accumulation ModelReferencescan be expressed as[ 1] Wang Qi. A Sudy of Moisture Absorption and Quick Dry=号(13)Fabrics [D]. Shanghai: Master's Thesis of DonghuaUniversity, 1995: 12. (in Chinese)Then substituting Eq. (1), Eq. (9)， Eq. (10) and[2] Meng Jiaguang, Pan Jianjun. Water Transmission TheoryEq. (12) into Eq. (13), one can obtainof Kntted Fabrics and Measurement[J]. Texriles Sciencev= - 219.3k ;(14)Reserch, 2005, 16(3); 18- 21. (in Chinese)7. Lo. r3[3] Dan Berger, Madsci. Network, What is Capillary Action?It can be seen from Eq. (14) that when0, s, k and 7[OL]. (1998 - 02 - 12). http: // www. madsci. org/posts/are constants (the same fiber and liquid), the wicking ratearchives/ 1998 - 02/887637827. Ch. r. html.is determined by the length of fiber unit assemble L。and[ 4 ] Gordonm. Barrow. Physical Chemistry (Fifth Edition) [M].the capillary radius r.New York: MCGraw Hill Book Company, 1988 108.Generally speaking, the permeability k can be[5] Yu Weidong， Chu Caiyuan. Textile Physics [ M ].measured by experimental and capillary radius r can beShanghai: Donghua University Press, 2002: 270 - 272. (incalculated. Consequently, different length of fibers unitChinese)assemble can be used to predict wicking rate of yarns.[6] Victor L. Streeter, Fluid Mechanics (the 9th Edition)[M]. Beijing: Tingshua University Press, 2003; 271.3 Conclusions[7 ] Zhu Fangliang, Zhang Yan, Zhuang Yi, et al., Analysison Wicking Effect of Profiled PTT Fibers[J]. SyntheticIn the paper, two water transport mathematicalFiber Indusiry, 2006, 29(3); 7- 9. (in Chinese)models of moisture absorption and sweat discharge yarns[ 8] Pronoy K Chatterlee. Absorbency: Textile Science andhave been developed. The influence factors on wickingTechnology [M]. New York: Elsevier, 1984; 36.中国煤化工MYHCNMHG