Jsef Dembický Technical University f Liberec Studentská 2, 461 17 Liberec, Czech Republic E-mail: jsef.dembicky@tul.cz Simulatin f the Cating Prcess Abstract Cating prcesses play a significant rle in the area f tetile prductin. They are used fr technical tetiles and special prtective clthes t achieve characteristic material prperties, fr eample water-repellency, fire resistance, high temperature prtectin, etc. In these prcesses a lt f parameters influence the cating layer s prperties, which are the distance between the knife and material, the speed f the cated material ging alng the prductin line, cating paste parameters viscsity, surface tensin and density, and finally the cating material s prperties surface energy and rughness. In this paper a simulatin f the knife ver rll cating prcess is intrduced and cmpared with eperimental data taken frm the measurement f cating that was applied by a labratry cating device, Basecater COATEMA-type, wrking n the basis f knife ver rll technlgy. Key wrds: cating, tetile, fluid, cating machine, knife cating, blade cating, simulatin f cating, viscsity, surface tensin, cating thickness. Intrductin Cating technlgy is generally a very interesting area in which many prblems can be develped and slved. This paper presents a new mathematical mdel fr the determinatin f the cating layer thickness after a cating prcess based n blade cating. S far there has been n such mdel described in literature which wuld fit the real prcess. Current mdels are nt sufficient [2, 10]. The mdel in this study was checked eperimentally by use f a labratry semiindustrial device. Theretical principles f cating The frmatin f a layer n a fabric surface is typical fr cating prcesses. The cating material parameters and substrate prperties f a film are frmed n the substrate surface accrding t the settings f the cating machine. The cating film btained has gt certain characteristics. Fr characterising the prtective behaviur, the physical-mechanical prperties f the cating film are imprtant, and ne f the mst cnsiderable physicalmechanical parameters f cating is the thickness f the cating layer [3]. The analysis and mdeling f cating thickness is the main subject f this paper. Wet cating applicatin is a prcess where material in the frm f a liquid is cated by mving. The ttal macrscpic frce balance is btained by applicatin f the principles f elementary liquid vlume mvement. The frce acting n the liquid vlume is btained frm the change in the mvement speed f the surrunding liquid. Net frces F acting in an directin n the liquid element mved by the liquid speed are attained by the additin f frce F B (impact f vlume element weight) and frce F S (impact f tensin created in the directin) (equatin (1) [5]. F = F B + F S (1) F frces acting n the liquid element in the directin in N F B impact f the weight f the vlume element in N F S impact f tensin created in the directin in N Fr an element f differential mass, ρd dy dz, equatin (1) becmes ρd dy dz(du/dt) = = ρd dy dz g cs β + + ( τ / + τ y / + + τ z / )d dy dz (2) d,dy,dz apprpriate elements f distance in m ρ density f cating fluid in kg. m-3 which, n rearranging, reduces t equatin (3), ρdu /dt = g cs β + ( τ / + + τ y / + τ z / ) (3) where u velcity f the fluid element in the directin in m. s -2 ρ density f the fluid element in kg. m -3 g acceleratin due t gravity in m. s-2 β angle the fluid element makes with the ais t time in s τ, τ y, τ z cmpnents f stress acting in the directin in Pa By substituting the values f stress and rearranging the equatin, we get a Navier-Stkes equatin (4). This is an equatin fr the mtin f the elemental vlume in the directin, which is used fr analysis f the hydrdynamics f cating [10]. An equatin describing the mvement f the elementary vlume in the directin, the s-called Navier-Stckes s equatin, is used fr the hydrdynamic descriptin f catings (equatin 4). u + u y + u z + = t 1 p η = g cs β + 2 2 2 ρ u u u ρ + + 2 2 2 + (4) 1 η y u z + + + 3 ρ where u, u y, u z speeds f elements f the cating material in the, y and z directins in m. s-1 p pressure due t element mvement in the directin in Pa η cating material viscsity in Pa. s In the case f blade cating prcesses, the cating thickness is btained frm the distance between the knife and tetile material. Frm the pint f view f easy analysis, the thickness f the cating layer is given as a functin f 5 variables, which are the knife-substrate distance, substrate speed, viscsity, density and surface tensin f the cating material. If the cating material is mving in the directin, equatin (4) can be reduced t a frm crrespnding t equatin (5) [3]. p 2 η u = + g ρ 2 (5) Dembický J.; Simulatin f the Cating Prcess. FIBRES & TEXTILES in Eastern Eurpe 2010, Vl. 18, N. 1 (78) pp. 79-83. 79
Fr Newtnian liquid cating materials, the speed is btained by equatin (6), which is derived frm the integratin f equatin (5). A schematic descriptin f the cating applicatin is illustrated in Figure 1. Figure 1. Knife cating: h - knifesubstrate distance; - knife width; knife: h = 0, u = 0; substrate: y = h and u = u 0 [3]. (6) The bundary cnditins assumed are as fllws: the fluid is mtinless n the blade (knife), i.e. u = 0; the fluid velcity n the web is the same as that f the web velcity, u = u 0 at y = h. The gap between the blade and the web is h, which is small cmpared t the blade width (Figure 1). The cater is mre like a channel, and a parallel plane flw mdel is used. Fr a Newtnian fluid, by integrating equatin (5) twice and applying the abve bundary cnditins, the velcity is btained as u = u 0 y/h + 1/2η (dp/d ρg)(y 2 hy) Fr the ttal amunt f cating material, Q, ging thrugh the gap in units f length and time, equatin (7) is valid [9]. u (u 0 ) velcity in g. m -2 dp/d pressure gradient in Pa. s -1 80 (7) The cating thickness is btained frm equatin (8), created by multiplicatin f the cating amunt Q by the substrate speed u 0. (8) A pressure gradient is reached fr the surface tensin f the cating material with respect t the balance frce acting alng the meniscus at the tp f the gap, frm which we btain equatin (9). (9) where σ in N.m-1 is the surface tensin f the fluid material. Then cating thickness equatin (10) can be frmed frm a cmbinatin f equatins (8) and (9) [3, 9]. (10) W thickness f the fluid material after cating in m h gap knife/fabric in m η viscsity f the fluid in Pa. s σ surface tensin f the fluid in N. m -1 u 0 speed f the fabric ging thrugh the machine in m. s-1 ρ density f fluid material in kg. m-3 An analysis f knife cating leads t the cnclusin that the cating thickness is btained by the additin f half the knife gap, and epressing its value depends n the surface tensin f the cating material, the knife gap, cating viscsity and substrate speed. Cating simulatin The abve mentined equatin (10) gives infrmatin abut the thickness f the cating material immediately after the applicatin f wet cating. In reality, the thickness achieved after plymerisatin f the cating material during the heating peratin intrduces a mre imprtant parameter regarding film prperties. This led t the creatin f a mdel describing the situatin after plymerisatin, because by the actin f heating, the thickness and mass f the cating material changes. Due t the reasns mentined, a mdel fr cating thickness determinatin was deduced. This mdel was frmed as a result f eperiments that affrded interesting results which are very different in cmparisn t epressin (10), describing wet cating thickness. Prcessing In real industrial prcesses the setting f machine parameters determine basic cating prperties. Anther imprtant aspect is that all cating machine variables can be changed directly in-line and becme immediately perative. Therefre, in this paper tw variables were selected as leading parameters and included in the mdeling f the cating prcess: the knife-fabric gap and fabric speed. The third additinal parameter used in the mdeling, als imprtant fr btaining crrect values due t the heating f the cating material, is the slid cncentratin in the cating material. The mdelling prcess was derived frm the measurement f cating layer thickness carried ut n ne hand with different gaps between the knife and cated fabric setting and n the ther with different speeds f the material guided thrugh the cating head (placed between rller and knife). Cnsidering that equatin (10) cntains physical variables η, σ, and ρ, we will perate with a system where these parameters are cnstant and in this way resemble a real prcess. The stable cncentratin f the cating material is cnsidered cnstant fr the same reasns given abve. The aim f this study is t btain a mdel crrespnding t the facts mentined abve, with practical eamples f the industrial prcess. Eperimental Acrylicurethane cating paste was prepared as the cating fluid applied t fabric later n (see Table 1). The fabric material was cttn, a detailed descriptin f which is listed in Table 2. The applicatin f the cating material n the fabric Table 1. Descriptin f fluid material used. Material Acrylicurethane Density, kg. m -3 1124 Viscsity, Pa. s 2.47 Table 2. Descriptin f tetile material used. Tetile type Material Fabric Cttn Density, kg. m-3 1560 Surface weight, kg. m-2 25 FIBRES & TEXTILES in Eastern Eurpe 2010, Vl. 18, N. 1 (78)
Figure 2. Eperimental data describing the impact f the knifefabric gap n the cating weight. 4 different velcities were used within the range f t 2 m/min. was carried ut by a semi industrial machine - Basecater BC 27 Catema. Tw sets f samples were prepared fr the tests. In the first test different knifefabric gaps were used, as mentined in Table 3, at a cnstant fabric speed during the whle eperiment, whereas in the secnd test samples were prcessed at different fabric speeds and cnstant knife-fabric gap (Table 3). A special gauge made frm metal plates f different thicknesses was used fr measurement f the gap between the knife and fabric within the range f 0.01 t 2 mm. The gap was measured in the area where the fabric went in the machine, which means in the surrundings f the input rller. Figure 3. Eperimental data shwing the impact f the cating machine speed n the cating weight. 4 different gaps were used within the range f t 0.8 mm. m weight f fluid material after heat applicatin in kg s rati f dry mass in fluid paste used. After the heating prcess the rati f dry mass is clse t 1. Althugh different additives are included in the fluid material, Table 3. Machine parameters adjusted during the cating prcess; + - fabric speed cnstant, - knife-fabric gap cnstant. Prcess parameter knifefabric gap, mm fabric speed, m/min 1.5 2.0 0.8 a) b) c) d) The dependence f the weight f the cating layer n the knife-fabric gap is shwn in Figure 2. A rapid tendency f an increasing cating weight is clearly visible at a gap f abut mm. Smaller gaps cause a small cating material quantity in cmparisn with greater gaps. The fabrics speed, adjusted by the cating prcess, influences the weight f cating much less than the knife-fabric gap, f which there is a decreasing trend, which is evident frm Figure 3, describing the dependence f the machine (fabric) speed n the cating weight. Accrding t the physical mdel (see equatin (10), the cating mass befre fiing in relatin t the knife-fabric gap can be described by equatin (11). (11) FIBRES & TEXTILES in Eastern Eurpe 2010, Vl. 18, N. 1 (78) Figure 4. Cating layer with gap a) mm, b) mm, c) mm, d) 0.8 mm. 81
they shuld nt be calculated as they are nt active cmpnents. Nevertheless, this quantity is negligible and des nt need t be cnsidered. a) b) c) d) e) f) A mdel was develped f the dependence f the machine speed n the cating weight, as described by equatin (12). (12) The thicknesses f particular samples were determined and acquired using scanning electr micrscpy (SEM). These data were used fr mdeling f the cating thickness. Thickness measurements themselves were carried ut by image analysis using a LUCIA G prgram, develped by Labratry imaging. The change in cating layer thickness after the heating prcess is mre cmplicated than the weight change described abve. The eperimental data were the basis fr preparatin f the semi-empirical mdel prpsed. In Figure 4 phtgraphs f catings btained frm different gaps at a cnstant machine speed f m/min are presented. As the phtgraphs shw, an increase in thickness in dependence n the blade gap between the substrate and blade can be stated. A significant increase takes place at a gap f mm, which can be cmpared by analysing the phtgraphs. Mrever, it can als be stated that a hmgenus fluid cvering the fabric surface is als pssible, which can be clearly recgnised, mstly at larger gaps ( mm, 0.8 mm) at which the fluid cver the fabric surface s much, that it des nt cpy its shape. Faults such as surface rughness and air bubbles inside the cating layer did nt appear at all. Figure 5. Cating layers prduced by machine speed f: a), b), c), d), e) 1.5, f) 2.0 m/min; knife-fabric gap was cnstant and equal t mm. Table 4. Thickness data in µm in relatin t the gap and speed f fabric. Gap, mm at fabric speed f m/min Thickness, µm Speed, m.min-1 at gap f mm Thickness, µm Catings differing accrding t machine speed settings are illustrated in Figure 5. The knife-fabric gap was cnstant and equal t mm. 39.2 5 Eperimental values f the thickness f bth eperimental variants gap and speed changes are presented in Table 4. The general dependence f the cating thickness is described by equatin (13). 82 0.3 58.3 35.3 122.9 21.5 0.5 138.6 19.1 130.3 1.5 16.0 0.7 164.7 2.0 12.7 0.8 259.1 0.9 264.3 266.9 FIBRES & TEXTILES in Eastern Eurpe 2010, Vl. 18, N. 1 (78)
Figure 6. Cmparisn f eperimental data f the thickness btained and. results frm the physical mdel accrding t equatin (10) and empirical mdel accrding t equatin (14). Figure 7. Cmparisn f eperimental data f thickness btained with different machine speed values using a semi-empirical mdel accrding t equatin (15) and physical mdel accrding t equatin (10). (13) W The term describes the change in t T thickness f the wet cating befre heating, which is dependent n time and temperature. This change depends mstly n the cating material cmpsitin and its prperties. During the heating peratin, the vlume f the cating material decreases even if all the slvent is taken away. This vlume decrease is accmpanied by a thickness change. Accrding t the eperimental values btained, an empirical apprach was derived and is presented in equatin (14). (14) W M is a mdel value f the thickness established after the heating prcess; s is the percentage f the dry mass f the cating material, and term e -h is an epnencial functin f the knife-fabric gap. In Figure 6 eperimental data are cmpared with the mdel functin frm equatin (14) and the mdel frm equatin (10). A cnstant speed f m/min was applied during gap measurement. In the case f the dependence f the cating thickness n the machine speed, a mdel was develped and is presented as equatin (15). Cmparisns f the eperimental data with mdels (15) and (10) are illustrated in Figure 7. FIBRES & TEXTILES in Eastern Eurpe 2010, Vl. 18, N. 1 (78) Cnclusin (15) The aim f this paper was t develp semi-empirical mdels fr predictin f thickness and mass cating. Bth mdels result frm a physical mdel fr cating thickness determinatin that is nly valid after cating applicatin befre heating. The new mdels submitted slve the prblem after heat prcessing. The first mdel characterises the dependence f the cating thickness n the knife-fabric distance (gap), which is described by equatin (14). A cmparisn f this mdel with eperimental data btained crrespnds very well, as can be seen in Figure 6. The secnd mdel which characterises the dependence f the cating weight n the machine speed is described by equatin (15). A cmparisn f eperimental data btained with the mdel curve is presented in Figure 7. Bth mdels are suitable fr use in knife cating prcesses and can help btain necessary changes in cating thickness r weight during applicatin. Althugh eperimental checking was carried ut with the use f semiindustrial equipment, Basecater COATEMA, we can assume that the mdels will be valid fr ther machines based n the same technlgy. Hwever, it shuld be taken int accunt that the mdels develped are valid nly fr the bundary cnditins accepted. Acknwledgment This wrk was dne n behalf f the prject Výzkumné centrum Tetil II. References 1. Fung W.; Cated and laminated tetiles, Wdhead Publishing Ltd, Cambridge, 2002. 2. Tractn A. A.; Catings Technlgy Handbk, CRC Press, Taylr & Francis Grup, 2006, Bca Ratn, ISBN 1-57444- 649-5. 3. Sen A. K., Tech M.; Cated Tetiles, Technmic Publishing Cmpany, 2001, Pennsylvania, ISBN 1-58716-023-4. 4. Dembický J.; Hydrphbe und wärmewiderstandsfähige Beschichtungen, Tetilveredlung 5/6, 43.Jahrgang, pp. 18-21, 2008, Einsiedeln CH, ISSN 0040-5310. 5. Flw Prperties f Plymer Melts, J. A. Brydsn, Gerge Gdwin, Ltd. 1981. 6. The Technlgy f Plasticizers, J. Kern Sears and J. R. Derby, Wiley Interscience, New Yrk, 1982. 7. Eichert U.; Jurnal f Cated Fabrics, vl. 23, April, 1994, pp. 311 327. 8. Eichert U.; Jurnal f Cated Fabrics, vl. 24, July, 1994, pp. 20 39. 9. Wilkinsn C. L.; Jurnal f Cated Fabrics, vl. 26, July, 1996, pp. 45 63. 10. Harrera A. P., Metcalfe R. A., Patrick S. G.; Jurnal f Cated Fabrics, vl. 23, April, 1994, pp. 260 273. 11. Mewes H.; Jurnal f Cated Fabrics, vl. 19, Oct., 1989, pp. 112 128. 12. Dartman T., Shish R.; Jurnal f Cated Fabrics, vl. 22, April, 1993, pp. 317 325. 13. Cated fabric, B. Dutta, in Rubber Prducts Manufacturing Technlgy, A. K. Bhwmik, M. M. Hall and H. A. Benarey, Eds., Marcel Dekker, New Yrk, 1994. Received 18.08.2008 Reviewed 09.11.2009 83