Ogulata R. T., Mavruz S.; Investigation of Porosity and Air Permeability Values of Plain Knitted Fabrics.FIBRES & TEXTILES in Eastern Europe 2010, Vol. 18, No. 5 (82) pp. 71-75.

71

Investigation of Porosity and Air Permeability Values of Plain Knitted Fabrics

R. Tugrul Ogulata, Serin Mavruz

The University of Cukurova, Department of Textile Engineering,

01330 Adana, TurkeyE-mail: ogulata@cu.edu.tr

smavruz@cu.edu.tr

AbstractThe air permeability of a fabric is defined as the amount of air passed over a surface under a certain pressure difference in a unit time. This value has significance with respect to the usage area. Since knitted fabrics have a loop structure, they have more pores than woven fabrics; therefore, in general, the air permeability of knitted fabrics is higher than that of woven fabrics of the same weight. An experiment to determine the air permeability is very important as it defines the properties of keeping warm, protection against the wind, breathability etc. of knit-ted fabrics used as clothing. In this study, it has been attempted to establish a theoretical model for the porosity and predicted air permeability of plain knitted fabrics. A theoretical model was created to predict the porosity and air permeability of a knitted structure depending on the geo-metrical parameters, such as the courses per cm, wales per cm, stitch length, fabric thickness, yarn count, diameter of yarn and fiber density. For this purpose, a theoretical model of porous systems based on D’Arcy’s law was used, the validity of which was confirmed by experimental results using 100% cotton plain knitted fabrics produced from ring and compact yarns of differ-ent yarn number linear density and tightness.

Key words: knitted structure, porosity, air permeability, geometric modelling.

Designations usedA1 -cross-sectionalareaofpore,cm2At -fabricareatested,cm2c -numberofcoursespercentimeterdh -hydraulicdiameterofapore,cmdp -porediameter,cmdy -yarndiameter,cmf -frictioncoefficientm -numberofporespersquaren -coefficientindicatingtheflowregimeQ -totalflowrateoftheair,m3/sR -airpermeability,mm/sRe -Reynoldsnumberrp -poreradius,cmry -yarnradius,cmt -fabricthickness,cmUm -meanairflowvelocity,m/sw -numberofwalespercentimeterr -airdensity,kg/m3ry -yarndensity,g/cce -rateofvoidareav -kinematicviscosityoftheair,m2/sh -dynamicviscosityoftheair,Pa.sDP -pressuredrop,Pal - coefficient of laminar and turbulent

flow

n Introduction Knittingistheprocessofformingfabricbyinterlopingyarninaseriesofconnect-edloopsusingneedles.Knitfabricspro-vide outstanding comfort qualities andhave longbeenpreferred inmany typesof clothing. In addition to comfort im-partedbytheextensibleloopedstructure,knits also provide lightweight warmth,wrinkleresistance,andeaseofcare[1].

Suchknittedstructureshaveamoreopencharacter when compared to other tex-tilefabricstructures,suchaswovenandbraided[2].

Airpermeability isoftenused in evalu-ating and comparing the ‘breathability’

ofvariousfabrics(coatedanduncoated)forsuchendusesasraincoats,tentsanduniform shirtings. It helps evaluate theperformanceofparachutessails,vacuumcleaners, air bags, sail cloth and indus-trialfilterfabrics[3-6].

Airpermeabilityisdefinedasthevolumeof air in liters which is passed through100cm2 (10cm×10cm)of the fabricinoneminuteatapressuredifferenceof10mmheadofwater[7].

Due to themanner in which yarns andfabrics are constructed, a large propor-tion of the total volume occupied by afabric is usually airspace. The distribu-tionofthisairspaceinfluencesanumberof important fabric properties such aswarmthandprotectionagainstwindandraininclothing,andtheefficiencyoffil-trationinindustrialcloths.

Airpermeabilityisanimportantfactorinthecomfortofafabricasitplaysaroleintransportingmoisturevapourfromtheskin to the outside atmosphere.The as-sumption is that vapour travels mainlythroughfabricspacesbydiffusioninairfromonesideofthefabrictotheother[8].

Theporosityofaknittedstructurewillin-fluenceitsphysicalproperties,suchasthebulkdensity,moistureabsorbency,masstransfer and thermal conductivity [2].

Airflowthroughtextilesismainlyaffect-edbytheporecharacteristicsoffabrics.Itisquiteclearthatporedimensionanddistributionisafunctionoffabricgeom-etry. The yarn diameter, surface forma-tion techniques and thenumberof loop

countsperunitareaarethemainfactorsaffectingtheporosityoftextiles.Thepo-rosityofa fabric isconnectedwithcer-tainofitsimportantfeatures,suchasairpermeability,waterpermeability,dyeingpropertiesetc.[9,10].

Mostofthepreviousstudiesinvestigatedthe relationship between the air perme-ability and structural characteristics ofplainknittedfabrics.Forexample,Oinu-ma(1990)showedthatthestitchlength,porosity and air permeability increaseand the thermal retaining property de-creases fordry relaxedcotton1×1 ribknitted fabrics [11]. Marmarali (2003)investigated the air permeabilityof cot-ton/spandex single jersey fabricswithintheirdimensionalandphysicalpropertiesandcomparedresultswithfabricsknittedfromcottonalone.Itprovedthat theairpermeabilityof fabricscontainingspan-dex was lower [12]. Karaguzel (2004)calculated values of pore size and porevolume for plain knitted fabrics. Thoseoftheporesizeweremeasuredwithim-age analysis and fluid extrusion proce-dures.Itwasfoundthattherewasano-ticeabledifferencebetweentheestimatedandmeasuredvalues[8].Onthebasisofcomputerimageanalysis,thesurfacepo-rosityofknittedfabricswasevaluatedforplain double-layered and lining knittedfabricsbyWilbik-Halgasetal.(2006).Itwasfoundthatairpermeability,contrarytowatervapourpermeability, is a func-tionofthethicknessandsurfaceporosityof knitted fabrics [13]. Benltoufa et al.(2007) investigated methods of deter-miningjerseyporosity,whichprovedthatgeometrymodellingisthemostsuitableandeasiestmethodofdeterminingporos-

FIBRES & TEXTILES in Eastern Europe 2010, Vol. 18, No. 5 (82)72

ity[14].Thethermalpropertiesandther-malbehaviourofcellulosetextilefabrics(airpermeability,porosity)wereinvesti-gatedbyStankovicetal.(2008),inwhichtheyfoundthatairpermeabilityandheattransferthroughfabricsiscloselyrelatedtoboththecapillarystructureandsurfacecharacteristicsofyarns[15].

Dias andDelkumburewatte, (2008) cre-atedatheoreticalmodeltopredictthepo-rosityofaknittedstructure.Itwasdeter-mined that porosity depended on fabricparametersandrelaxationprogression[2].MavruzandOgulata,(2009)investigatedairpermeabilityofcottonknittedfabrics.Before manufacturing the fabrics theequationof regressionwasused to pre-dictairpermeability,dependingonsomefabricproperties[16].

Establishing a more complex theory toexpress air permeability related to allfabric parameters will have difficulties.Tosimplifythematter,certainimportantparameterssuchastheporeofthefabric

The Reynolds number is calculated asfollows:

νhm dU .

Re =

(2)

whereUm is themeanflowvelocity,dhthehydraulicdiameterofapore,andvisthekinematicviscosityoftheair[4,18].

The pressure drop of the flow througha duct over the thickness of the fabricisrelatedtothefrictionfactor f throughD’Arcy’sformulation.

2

2m

h

UdtfP r=D (3)

wheretisthethicknessofthefabric,andristheairdensity[19].

Knittedfabrichasaporousstructure.Forthisreason,theairvelocityinporesmustbetakenintoconsideration.

emU

U = (4)

whereUistheairvelocitythroughpores,andeisrateofthevoidarea(porosity)[4].

Figure 2 shows theporewithina loop.Our theoretical model was created byconsidering one repeating unit cell ofa knitted structure. By determining thecourse (c) per cm, wale (w) per cm,thickness(t),yarndiameter(dy)andlooplength(l), theporositycanbeshownasfollows[14]:

volumeTotalvolumeYarn1−=e (5)

Yarnvolume=422 ld yp =

2

2ld yp (6)

Totalvolume= twc11 =

cwt (7)

Finally,

tlcwd y

21

2pe −= (8)

Theairvelocitythroughporesofthefab-ric does not usually have a high value.Therefore, thefluidflow in thepores islaminar.According to kinetic theory, iftheReynoldsnumberisbelow2320,theflow in the tube is laminar [4, 18]. Forthisreason,themeanairvelocitythroughoneporecanbeexpressedas:

Pt

dU h

m D

=

h32

2

(9)

Theflowrateofairforafabricofporousmaterial,Q,becomes:

were taken into account in the calcula-tionofairpermeability.Threefactorsaremainlyconsideredthatarerelatedtotheporesinfabrics.1) Cross-sectionalareaofeachpore,2) Depthofeachporeorthethicknessof

thefabricand3) Thenumberofporesperunitareaor

thenumberofcoursesandwalesperunitarea.

In thiswork, these parameters are con-sideredtodevelopatheoreticalmodelforporosityandairpermeability.

n Theoretical ModelAknittedfabricconsistsofoneormoreloopedyarns.Plainknittedfabric,whichis illustrated inFigure 1, is one struc-ture of knitted fabric. In this paper,weconsiderplainknitted fabricswhich arecommonly used in many apparel ap-plications.W andC representwale andcourse spacing,whereasw andc corre-spondtothenumberofwalespercmandnumber of courses per cm, respectively[17].(Walespercm:thenumberofvis-ible loops per unit length in cm meas-uredalongacourse.Coursespercm:thenumberofvisibleloopsperunitlengthincmmeasuredalongawale.Stitchlength:thelengthofyarninaknittedloop).

When considering fluid flow throughtextiles, theshapearrangementandsizedistribution of voids throughwhich thefluidflowsareofgreat importance.Thefabricthicknessanddifferentialpressurebetweenthetwosurfacesofafabricaretheotherdominantfactorsthataffectper-meability.Thepressuregradientthrougha textile is a function of the viscosity,density,rateoffluidflowandporosity,asinthecaseofflowthroughapipe[9].

The dependence of the friction coeffi-cient,f,ontheReynoldsNumber,Re,forlaminar and turbulent flow is describedbytheBlasiusequation:

f=l.Re-n (1)

where λ is the coefficient of laminar orturbulentflow,andnisacoefficientindi-catingtheflowregime.

Laminarflow: λ=64,n=1Turbulentflow: λ=0.3164,n=0.25

The type of flow depends on the Rey-nolds number. The Reynolds numberrepresentstheratiooftheinertiaforcetotheviscousforce[4].

Figure 2. Stitch diagram of a plain knitted structure.

Figure 1. Representation of a plain knitted fabric.

Re

cw

32

73FIBRES & TEXTILES in Eastern Europe 2010, Vol. 18, No. 5 (82)

Q=m.A1.U(10)

wheremisthenumberofpores,andA1isthecross-sectionalareaofthepore[4]

4

2

1pd

A p= (11)

where, dp is the pore diameter (In thisstudy,theloopsareassumedtobecom-posedofidealyarnswhicharecircularincross-sectionandhaveaconstantdiam-eterthroughouttheirlength.Yarndefor-mationatthecrossoverpointsisomitted,henceitisacceptedthatdp = dh).

Thus,equation(10)canbewrittenasfol-lows:

=Q Pt

dm p D−64

10128h

pe

(m3/s)(12)

Thevalueofairpermeability(R)iscal-culatedaccordingtothefollowingequa-tion

tAQR = (13)

whereAtisthefabricareatested[7].

dp iscalculatedfromFigure 3(yarnrep-resentation)andFigure 1.

510yy

Trpr

= (14)

Volumeofyarnin1cm2=Slpry2(15)

Volumeoffreespace(cm3)in1cm2offabric=1×1×t=t-Slpry2(16)

Areaoffreespace(cm2)in

1cm2offabric=t

rSlt y2p−

(17)

Areaofopenspacewithin

oneloop=tS

rSlt y2p− (18)

Asmentionedbeforehand,iftheareaoc-cupiedbyaporeistransformedtothatofacircle,theporeradius(rp)canbewrit-tenasequation19[8].

pr =tS

rSlt y

pp 2− (19)

As indicated by equation 19, when thestitchdensity,stitchlengthoryarndiam-eterincreases,poresizevaluesdecrease.The equations developed in this studywillbeusedtopredicttheporesizeandairpermeabilityofplainknittedfabrics.

n Materials and methodsIn order to compare the values of airpermeability from theoretical model-ling and those from experiments of airpermeability,weproduced18(eighteen)knittedsampleswithvariousknittingpa-rameters.Theyarnsweremadeofcottonfibers,andthebondingtypeofeachsam-plewasplain.Plainknittedfabricswereknitted with three different tightnesses(slack,medium and tight) on a circularknittingmachineusingringandcompactyarnsof19.72,14.79and11.83tex.

The knitted samples were conditionedfor 48 hours in atmospheric conditionsof 20±2 °C temperature and65±2%relative humidity before the tests wereperformed. The air permeability of thesamples inmm/swasmeasuredaccord-ing to the method specified by Stand-ard TS 391 EN ISO 9237 [8], using aTextestFX3300airpermeability tester.Themeasurementswereperformedat aconstantpressuredropof100Pa(20cm2testarea).Foreachoneof the18fabric

types,werepeatedthismeasurementforten (10) samples, thusobtainingabodyof (18×10=)180measurements.Fur-thermore,thelooplength,walespercm,coursespercm,thicknessandweightofthe fabricsweremeasured according totherelevantstandards[20-23].

t - Slpry2

Table 1. Fabric properties and experimental air permeability values.

Sample number

Yarn typeR: Ring

C: Compact

Yarn number,

tex

Loop length,

cm

Course count

per cm

Wale count

per cm

Thick-ness, cm

Weight, g/m2

Experimental air permeabil-

ity, mm/s1 R 19.72 0.255 23.0 12.3 0.0069 161.38 11932 R 19.72 0.285 18.0 12.3 0.0057 136.78 15623 R 19.72 0.320 16.0 12.1 0.0068 136.90 15624 C 19.72 0.260 24.0 13.0 0.0060 159.48 15325 C 19.72 0.286 19.0 13.0 0.0058 143.72 16476 C 19.72 0.330 15.0 13.0 0.0062 134.22 19487 R 14.79 0.256 24.0 12.2 0.0063 120.88 20208 R 14.79 0.284 19.0 12.0 0.0059 105.72 20779 R 14.79 0.320 15.0 12.0 0.0052 87.22 3059

10 C 14.79 0.261 24.0 13.0 0.0059 126.10 245911 C 14.79 0.280 18.0 13.0 0.0060 118.24 296612 C 14.79 0.250 15.0 13.0 0.0065 107.16 370813 R 11.83 0.250 23.0 13.0 0.0053 86.98 293814 R 11.83 0.280 18.0 14.0 0.0053 75.86 350215 R 11.83 0.320 16.0 12.0 0.0061 76.62 368016 C 11.83 0.251 24.0 13.0 0.0052 98.30 312817 C 11.83 0.290 18.0 13.0 0.0056 89.58 330618 C 11.83 0.330 15.0 12.0 0.0060 76.82 4616

Figure 3. Representation of yarn in 1 cm2 of fabric; ry - yarn radius, rp - pore radius, ry - yarn density (Pierce used a value of 0.909 g/cc for cotton yarn), T - yarn linear density in tex.

19.72 tex 14.79 tex 11.83 tex

Rin

gC

ompa

ct

Figure 4. Microscopic views of the yarns.

l × S

ptS

t - Slpry2

tS

t - Slpry2

ppy105

10

FIBRES & TEXTILES in Eastern Europe 2010, Vol. 18, No. 5 (82)74

andyarndiameter.Asisknown,yarnsinthestructureofthefabricdonothaveasmoothsurfacenorasolidconstruction.There is also a lot of emptiness in theyarns. Consequently, in order to obtaincloser results, the value of the pore di-ameterofknittedfabricsproducedfrom14.79and11.83texyarnswasincreasedby15%,andthesenewvalueswereusedforcalculations.

Comparingthetheoreticalmodelmethod(Equation 13) and that using experi-mental air permeability values, we ob-tainedtheresultshowninFigure 6(seepage109).

Thematch is close, which is also indi-cated by the high values of correlationcoefficient,R2,obtainedfromthestatisti-calanalysis.Figure 7showscorrelationplots between the predicted and meas-ured values (x axis-measured values, yaxis-predictedvalues).

ThevaluesinFigure 7indicatethatthecorrelation for fabrics produced from19.72texyarnissuperiortothatforfab-

n Results and discussion Fabric properties (yarn number, looplength,coursecountpercm,walecountper cm, thickness,weight) and the (ex-perimental) air permeability valuesmeasuredarepresentedinTable 1.

Itcanbeseenthatthefabricsdifferedinterms of the yarn linear densities, yarntype, courses per cm and loop length.The thicknessof thefabricsvariedwiththe loop lengthandcoursecount.Sincethewale count per cm usually dependsonthemachinesettings,aconstantrangefrom12-13shouldbemaintained.

According to Table 1, the fabric withthelowestcoursecountpercmandyarnnumberintexhasthehighestairperme-abilityvalues.Therefore,therisinglooplengthresultedinaloosersurfaceonthefabric,therebyincreasingtheairperme-ability.

Inordertopredictairpermeabilityvaluesfortheknittedfabrics,thefollowingwereused:valuesoftheporosity,theradiusofporesandyarns,andtheflowratecalcu-lated using the newly developed equa-tionsexpressedinthetheoreticalmodel.

Moreover, we observed microscopicviewsoftheyarnsandporesintheknit-tedfabricsfrompictures takenusinganimageanalysisdevice(Figure 4 and 5).Samplenumbersweremarkedonthepic-turesinFigure 5.

InFigure 4itcanbeseenthatastheyarncount decreased, yarn hairiness valuesfellingeneral.Furthermore,microscopicviewsrevealedthatthesurfaceofknittedsamplesproducedfromthinyarns(both

ring and compact yarns) is highly non-uniform with deformations (especiallyin loose fabrics) because of the biggerporedimensions(Figure 5).Asiswidelyknown, the compact spinning methodformsadifferentyarnstructure.Themostevidentpropertiesoftheseyarnsaretheirhigh breaking strength, high elongationandlowhairiness.Moreover,otheryarnpropertiessuchasyarnunevenness,thin/thickplacesetc.arecomparabletothoseofconventionalringyarn.Asthesurfaceof compact yarns is smoother and lesshairy, fabricsproduced fromsuchyarnscannotblockair,thusindicatinghighairpermeability. However, the differencebetweencompact andconventional ringyarnsisnottoogreat.

In order to simplify the theoretical cal-culations,loopsareassumedtobecom-posedofidealyarnsbutwithgreatvaria-bilityinporesizedistribution.Thussam-plesproducedwith14.79and11.83 texyarns have pore dimensions which arehighly variable across the fabric. It isdifficult to estimate theporosityof fab-rics by calculating the pore dimensions

Figure 5. Microscopic views of the knitted structure.

1 2 3

7 8

13 14

9

15

4 5

10

16

11

17

6

12

18

Figure 6. Air permeability values according to the experimental and theoretical models.

75FIBRES & TEXTILES in Eastern Europe 2010, Vol. 18, No. 5 (82)

ricsproduced from14.83and11.92 texyarns.Airpermeabilityinknittedfabricsisrelatedtoporesize.Asdiscussedear-lier, variability in pore size affects per-meabilityvalues.

Moreover,asdemonstratedinFigure 8,there is a near positive linear relation-shipbetweenporesizeandpredictedairpermeabilityvalues.Thus,thehighertheporesizes,thehighertheairpermeability.

n Conclusion Anexperimentalstudywascarriedouttodevelopatheoreticalmodeltopredictairpermeability values for knitted fabrics.Thetheoreticalmodelpredictsthevalueoftheairpermeabilityusingtheporesizeandsomefabricpropertiesbeforemanu-facturing.

D’Arcy’s formulation was used to es-tablish an equation expressing the rela-tionshipbetweentheairpermeabilityofknitted fabrics and fabric structure pa-rameters.

According to the experimental results,the fabricwith the lowest course countper cm and yarn number in tex has thehighest air permeability values.Moreo-ver,increasingthelooplengthproducedaloosersurfaceinthefabricandincreasedairpermeability.Astheyarngetsthinnerand the pores between loops get larger,theairpermeabilitywillincreaseaccord-ingly.According to some formulations,when the stitch density, stitch length oryarndiameter increase,poresizevaluesdecreases.

Duetothedifferencesbetweenidealandreal geometry and the randomvariationofthefabricstructure,therearenoexactdependences between experimental airpermeabilityandpredictedairpermeabil-

ityvalues.However,theclosenessoftheresultsofpredictionsbasedoncalculatedvalues from the theoretical model andexperimentalvaluesshowthatourmodelcanbesuccessfullyused for thepredic-tion of the air permeability of knittedfabrics(R2=0.87).Thismodelissimpleandefficient.

Permeability and porosity are stronglyrelatedtoeachother.Ifafabrichasveryhighporosity,itcanbeassumedthatitispermeable. Itwas also found that thereisanearpositive linear relationshipbe-tween pore size and air permeabilityvalues(R2=0.81),hencettcouldbeas-sumedthatthemodeldevelopedisappli-cable forpredicting theairpermeabilityof plain knitted fabrics produced withdifferentfibertypes.

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Figure 7. Correlation plots for predicted and measured values. Figure 8. Relationship between predicted air permeability values and pore size.

Received 29.12.2008 Reviewed 17.09.2009