"Going with the flow  Computational Rheology"


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1 LF Prifysgol Cymru Abertawe University Of Wales Swansea "Going with the flow  Computational Rheology" Inaugural Lecture of Professor Mike Webster Department of Computer Science ISBN O ll November, 2001 Taliesin Arts Theatre
2 UNIVERSITY OF WALES SWANSEA PRIFYSGOL CYMRU ABERT AWE LIBRARY I LLYFRGELL Classmark l?\'2.t 1 ' S.:C..S'?_fj a \ Location ~ I 111 First published December 2001, by University of Wales Swansea CiJpies ohtainah/e fr om: The Department of Planning and Marketing University of Wales Swansea Singleton Park Swansea SA28PP Copyright  Professor Mike Webster All rights reserved. No part of this publication may be reproduced, stored in c1 retrieval system or transmitted in any form, or by any means, electroni c, mechanical, photocopying, recording or otherwise, without the permission of thi:> copyright owner. E ISBN
3 "Going with the flow  Computational Rheology"!11a11g11ral Lecture!Darlith Agoriadol 12 Novemher 2001 Professor Mike Webster Department of Computer Science The title chosen for my lecture today, ' Going with the flow ', was coined first by the 1 Government sponsoring agency, Engineering & Physical Sciences Research Council (EPSRC). Rheology is the science offlowi11g mater ial . Con;p11tatio11al Rheology implies the S111l0' <?f Newto11ia11.f711id/low, via the use of comp11ters. The two pictures shown illu strat _e key issues that we shall addre ss: to the left, contrast of rheological properties and response of different fluids, here within splashing experiments ; to the right, comparison between simulation and experiment, as in contraction flows. We begin by setting the scene, with a sample of what you are about to see, relating to nonnewtonian fluids. Jn fact, tliis is the trailer for our Institute of non Newtonian Fluid Mechanics (INNFM) film on the subject  an educational and research tool available in video and CD format, work sponsored by EPSRC under Public Understanding and Awareness. Here, you see some clips for everyday fluids and standard experiments. The multimedia menu sections illustrate the aspects of science involved : Introduction, Viscometry, Rheometry, & nonnewtonian effects ; each indi vidually selectable. By way of introduction, the area of science we pursue leads us to compute solutions (Computer Simulation) to the flows of complex nonnewtonian materials. Domain s may be as complicated as required. By complex materials we are referring to their rheological behaviour. Under complicated domains, we mean space (3D)time, often relating to industrial setting. Hence, we are concerned with pioneering the development of numerical algorithms to solve mathematical problems  themsel ves models, devised to represent flows in reallife situations (i.e. processing). Typically, such algorithms must translate systems of mixedt ype, no_nlinear partial differential equations, into associated algebraic forms (discretisation), and perform their mechanical solution. This procedure is embodied in computer software (parallel
4 computation and visualisation), which is implemented on modern computer hardware. Here, we seek tractability for largescale problems  implying efficiency in computation and speedy turnround times. Today, results of our research shall be demonstrated through a series of wellchosen 'Case Studies'. This demands theory beyond that dealing with classical fluid dynamics and takes us from CFO to compuiational rheology. Hence, \Ve focus upon the complex material within the flow, rather than simpler fluids in complex flows (as in other areas of CFO) First, we need to provide some feel for everyday nonnewtonian fluids, and through illustration, indicate depanure from Newtonian behaviour. An overview of case studies covers both those of a general nature (left) and those of direct industrial relevance (right). Many are clearly recognisable from their title. A selective san~ple (in bold) will illustrate the many facets of our work and its relevance to modern everydaylife. The geographical co~linearity of the groups within University of Wales fnnfm is striking, involving Bangor, Aberystwyth and Swansea. This multidisciplinary Institute (colleagues present in the audience) of mathematicians, _ engineers and computer scientists, has expanded over the past ten years. It has been recoonised as a Centre of Expertise (WDA), and draws down considerable external 0 funding ( 3 million, since 1998) from EU, UK government and industry. Over the last ;ea r or so, we have had two of om EPSRC research grant proposals, ranked first within the UK. In additio.n, we have been awarded three consecutive highlyprized " ROPA" awards, specifically targeted at the development of novel research ideas. From a personal perspective, I was attracted to Swansea in 1986 to form a new research team with Professor Peter Townsend (current Pro ViceChancellor & Registrar, Swansea). This meant a return to Wales, where I studied for a PhD in Applied Mathematics at Aberystwyth, a decade earlier, with Professor Ken Walters (FRS) and Professor Russell Davies. As one might gather from the views of Swansea and environs, this is a location of some considerable natural beauty, which is hard to beat and a place that is a pleasure to live and work in. Over the years, Swansea has had some considerable involvement within this research field, Professor Jim Oldroyd (Mathematics, UWS ) being a major figure in the 2 _Rheological community and Professor Olec Zienkiewic, (Engineering) in the Finite Element world. There is even some evidence of interaction between these two statesmen of the field. I gathered from private communication with Professor Zienkiewic2:, that Oldroyd provided the breakthrough to establishing finite element functions on triangles. This was the inathematical step required to generalise finite element topological reference  and shift consideraiion from basic brickshaped (solid) building blocks to those useful in describing deforming matter (liquids). The seminal work of Oldroyd in his Royal Society of London paper ( 1950), set the scene for constitutive models and the guiding principles for their formulation, to describe material deformation in a generalised framework. This was a contentious issue at the time and somewhat misinterpreted by American colleagues The classical work in three volumes on finite element methods, of the same name, by Zienkiewicz & Taylor, now enters its fifth edition and remains an authoritative referen ce in the field By way of a fairly rough delineation, advances in numerical methods have seen the field shift from finite difference discretisation of the 60' s, to finite elements in the 70's, launching finite volume methods 's and spectral methods in the 90's. Such methodolog y was vital to solve the complex partial differential equations ofcfd. Other aspects involved are the choice of variables (streamfunction /vo rticity/stress or velocity/pressure /stress) and the level of equations adopted (steady/unsteady and decoupled/coupled). The tools of the trade, in computing engines through this period have changed beyond recognition. from the mainframes of the 70's, to individual workstations of the mid 80's, to Supercomputers of the early 90's. Today, this has moved onto multiproce ssor servers and distributed parallel processing with cluster machine s. Computer languages have also develop~d from Algol 60 and FORTRAN of the 's, to Pascal, C and FORTRAN90, and onto High Performance Computing (HPC) of today Procedural programming has also been challenged by alternative objectoriented, logic, and f~rnctional styles. The diversity is clearly apparent. The simulation software, we have developed, embodies algorithms with finite element and/or finite volume spatial discretisation, in combination with temporal discretisation, to form a stable and accurate timestepping procedure. Parallel strategies, covering distributed and sharedmemory platforms of homogeneous and heter9geneous type, 3
5 forge parallelism over many processors. By breaking the full equation system for incompressible flow down into fractional stages, large 3D transient problems are rendered traceable. This encompasses nonnewton ian properties and nonisothermal effects. M.aterial propenies, incorporated within the modelling, include those for constant vi_scosity (Newtonian)_ fluids, shearthinning, strainhardening and softening fluids, and those that manifest memory effects (viscoelasticiry). These propenies have been illusirated earlier. In addition, fibreadditives may be accommodated. Flow geometries of all sorts may be considered, including: twodimensional (1D ) planar, axisymmetric and threedimensional (JD) forms. Also, there are those associated with moving fronts or incerfaces (such as in injection moulding), and instances where freesurfaces arise (as within extrnsion, coating, printing and mixing). Typical finite element meshes in t,;,,oand threedimensi onal settings are illustrated. For the mathematicallyminded, our modelling may be explained succinctly as follows. The differential equation system is composed of momentum transpo11 and mass balance equations, with an energy equation if nonisothermal, and a constitutive equation for stress. The variables involved are velocity 11, pressure, JI, and stress, D. Nondimensional numbers of Reynolds and Wiessenberg number (Re and We) govern levels of ine11ia and elasticity, respectively. For the numerical analysts present, the principal fe/fv algorithmic framework is that grafted onrb a fourstaged scheme over a single timestep Ot. An iterative loop is then performed to evolve forward in time. Discretisation is implied, over triangles in 1D and tetrahedra in JD, rendering the fullydiscrete matrixvector system shown  ready for algebraic solution. For viscous incompressible flow, a TaylorGalerkin scheme (predictorcone ctor stage I a,b) is combined with a pressurecorrection scheme (stage 13, for incompressibility), that is secondorder accurate and semiimplicit in time. Stress ( 0 ) is discretised, either in finiteelement or volume form. Each approach has its individual merits. Continuous piecewisequadratic interpolation is adopted for velocity (U) and linear for pressure (P). With the Fechoice, stress interpolation follows velocity; weighting is of a streamlinetype (supg) and superconvergent recovery is applied to velocity gradients. With the fvform, stress is linearly interpolated on triangular subcells within each parent fecell. Fluctuation distribution and mediandualcell constrncts are introduced via a cellvertex approximation. Again, highorder accuracy is achieved. Returning to 'Ca se Studies', we begin in some detail with our work on mixing/separating flows, which allows us a backwards, historical glance. This problem is one that manifests both transient and viscoelastic effects. The schematic diagram i I lustrates the nature of the flow, inflow of the same fluid at two arms, topright and bottomleft, outflow at the other two locations bottomright and topleft. A gap in the flow splitter i_s apparent in the centre. We are able to reflect upon our results published in two Phil. Trans. Royal Society p_apers, 1980 and 8 1, demonstrating simulation and experimental observations for increasing flow rates and the significant differences in flow response for Newtonian liquids to some viscoelastic liquids. The gradua l appearance of vortices (flow rate increasing down the image) and reversed flow structure is apparent for Newto nian fluids, both via simulation (here) and experiments. These features are absent in the equivalent elastic situations. The simulations at that time were respectable, for Newtonian fluids at least. We view modern simulations for such a problem, via motionblur animation sequences. This is a randomised spacefilling visualisation technique, which provides a directional feel for the flowing liquids through animation. First, we look at the transient buildup of flow structure for a Newto nian fluid, commencing from a parallel, but opposing flow scenario. We ask the q11estio11, which way will the.flo w develop.? Colour is used to indicate strength of flow: redforfast, greenmedium to blueforslow. Now as time advances on the counter, we observe reversed flow developing, and the buildup of a pair of vortices stai1ing at the walls, that merge gradually to a single central_ vortex. Finally, complete flow reversal dominates. Second, for a viscoelastic shearthinning fluid, we commence from a reverse flow scenario and gradually increase the flow rate. At low flow rates, we observe the Newto nianlike response.... As flow rate increases on the indicator, we begin to see the clear preference for unidirectional viscoelastic flow emerging. At the largest flow rate, there is evidence of dieswell like phenomena, across the gap zone 4
6 departing rhe splitter. Notably, the elastic situation, elusive some twenty years earlier, is now amenable to modern science. Next, we shift attention to an industrial problem, that of wirecoating, for wires, cables and glassrovings. Here, pressure monitoring is impo11ant to avoid blowout, and viscoelastici1y affects the residual stressing imparted to the coating. Minimal residual" stressing is desirable within the c~oled working product. This work has been supported by rwo separate companies over the last ten years, signifying a qua11er of a million pounds industrial investment. Here, we seek to understand the firndamenrals of the flow process when polymer melts are extruded and drawn onto a fastmoving wire (travelling around I rn/s), to form a coated product for everyday use  i.e. electrical cables. The industrialist would seek to optimise process settings to maintain product quality, maximise output and minimise product wastage. The schema illustrates the polymer coating material, the die geometry and the cable. Three animation sequences are provided. The first sequence, gives an overview of the industrial extrusion, wirecoating line. The manufacturing line itself may be 200m 300m long. The various components are builtup incrementally, using colour, shadinglighting and movement of parts. The screw extruder, that delivers the molten polymer, is exposed via 3D solidmodelling and sophisticated visualisation techniques. Graphical manipulation allows one to inspect inside the extruder. The second sequence, takes up the next phase and focuses on the wirecoating. We illustrates the wire, the individual distributor and die sections,..., and the flow of polymer through rhe geometry onto the cable. Rotation of the viewing angle provides an appreciation of the flow. _ Finally, we zoom into the region identified for simulation. In the third sequence, our numerical predictions are presented for this problem. We begin with the effect of die geometry adjustment. Optimal die positioning avoids unwanted recirculation and pressure blowout within the die. Note, the rise in pressure, on the scale, as the distributortip gets foo close to the diehousing. Retraction, too far, reintroduces backtlow. At a fixed die posi lio11, a switch of rheology in the flowing material, from Newto nian to shearthinning, has the effect of sweeping away the reverse flow (dead zones," where material would degrade). Most severity in the flow occurs at the end of the die, just before the polymer is extruded onto the cable. Stressing in rhe coating may be picked out, per design, and minimised. A clearer understanding of these effects has lead to recommendations re optimality of_process design for various polymer melt blends. This has lead to improved production and considerable savings through reduction in product wastage. Some static i111ages on field data for pressure, shearrate and extensionrate. illustrate the distribution of these quantities throughout the flow. Levels of shearing and extension are quadrupled for pressure above tubetooling designs. A second industrial exa111ple is that of reverse rollercoating, an investigation into surface instabilities and operating coaditions. This work has been sponsored by a local industrial co111pany, Alcoa. Here, the underside of aluminium alloy sheets is coated with a protective layer of solventbased lacquer (zooined view). Typically, the coated foil would be used to punch out tinlids. Processing instabilities (chatter and starvation) generate unevenness in surface finish that is aesthetically unacceptable to the consumermarket. The consequent economic loss due to wastage is considerable. Hence the motivation for the present study: to predict how, when and why such effects arise and to suggest a possible remedy. Printing processes throw up si111ilar scenarios, where product quality and increased throughput are the desired goal. At this point, we enter a multimedia view of the problem, available over the www. This exposes the high aspectratios involved and interrelates the data gathered in a meaningful manner. The alloy foil travels over a ta111bouroll, and then a series of rollers, that deliver and apply the lacquer to the foilunderside. Foil speed is around 200m/111in and the applicator rollspeed is 90% of this. The lacquer coating, without polymer additives, is characterised as a Newto nian fluid. Encapsulating the principal features, a narrow section of the process is analysed: lying from the applicatorroll takeup flow, to the flow between roller and foil, to the surfacecoating on the foil. The nipgap (between roller and foil) and the freesurface meniscus are particularly important. A parameter sensitivity analysis covers the operating window of applied conditions. We first concentrate on steady flow, with no leakage at the nip. We consider variation in foilspeed at fixed rollerspeed. We then invert this test, varying rollerspeed at fixed foilspeed. In this fashion, we are able to relate flow and deformation fields to quantities of interest, such as forces upon the foil (Ii~) and roller (drag). At standard 6 7
7 settings, colour density stream fi.inction plots indicate the long thin nature of the now,.., that travels from roller, to nip and back to the foilcoating. Pressures and shearrates are high at the nip. Lift and pressure, localised to the nip (on the right of the graphs), turn out to be important factors in the process. Upon increasing foilspeed, we observe in motionblur representation (for the meniscus zone), that this draws the f1ow recirculation closer to the foil and twists the f1ow lines towards the meniscus. /11terauive i111e1pretatio11 (through graphs) of corresponding lift and drag, demonstrate the linear i11crease in fiirce.1 with increasing foilspeed. This is also true of the maxima in shearrate and pressure at the nip. In contrast, increasing the relative speed of the roller 10 the foil has the reverse effect. Now, the f1ow is drawn closer to the roller as its speed increases, and the forces rejlect a linear decrease. Here, nip shearrate maxima switch from foil to roller, as rollspeed dominates. Switching to a temporal analysis, we activate leakage at the nip to act as a flow relief mechanism. The gap at the nip may be widened, by shifting the foil vertically, instigated in a periodic manner. Two aspects have been addressed: the extent of the nipwidth widening and the frequency of periodic adjustment (high or low). The extent of the gapwidth is found to be a crucial factor in the process. By shifting the whole foil (global) vertically, from I% to 2% width of coatingflow,. nippressures fluctuate in time (graphs, p v time) and temporal swface imtabililies are detected (sho_wn at the top of the screenshot, against the timebar) These effects correspond simultaneously with changes in lift. By focusing on lift, per unit length of foil, one observes that maximum lift remains localised to the nipregion, during leakage/noleakage states. The same is true, but is even more exaggerated, if only a local ponion of the foillength is shifted. The more local the shift, the more the lift is amplified; shown at 30%, J 0% and 4% of foillength shift Notice the rise in lift to the right of the graphs approaching the nip. This is, in fact,'what one might expect in practice. The hean of the problem lies here. We speculate that control of the extent of foilmovement, through appropriate synchronisation mechanisms, will effectively control the surface instabilities. To add some variety we now swi_tch attention to a rich and varied foods study: that of dough kneading, with applications to bread and biscuit making. The MMS trailer quickly scans what was involved. Five companies (RHNI, UB, Pillsbury, Mono 8 Equipment and SASIB Bakeries) provided industrial trial data and the interdisciplinary research crossreferenced Institute experiments at Aberystwyth with modelling/visualisation at Swansea  a flagship project for the Institute (value 0.75 million, our first BBSRC grant). We were required lo: analyse the stirring of dough; gather information on mixer design choice; relate this against dough rheology; predict how to maximise stretching work input to the dough and enhance the buildup of material strncture (i.e. kneading). A grandchallenge indeed I This is a key aspect to the overall manufacturing procedure. The work involved : follyfilled and partfilled mixing; steady and unsteady situations; two and threedimensional analyses; freesurface movement of the dough; different materials, mixers and configurations.. Jn the fimr images, we illustrate an empty mixer, two different states of kneading. ' ( mixerlid removed), and a typical final baked product._ Commonly, bread mixers are n.111 vertically, biscuitmixers horizontally. The associated complex freesurface movement involves wetting and peeling on vessel and stirrers  this has demanded new. modelling algorithms. Perspective static views of flow patterns are illustrated for a filled onestirrer mixer with anticlockwise vessel rotation, shown halfway up the mixer at 50 rpm (a standard speed and model inelastic fluid) Asymmetrical structure is apparent with an offcentre vortex: pressure, shearrate and rateofwork extrema are localised to the stirrer. Each menu icon is, in fact, a programmed network (a graph) of the presentation (covering variation in speed, height, material and 1 otationtype). We contrast this case against the twostirrer instance : some symmetry is observed about the stirrers and a central figureofeight vortex emerges. In three dimensions, we are. able to appreciate the depthwisedistribution in rates of shear, extension and work against stirrers and lid. Animated views, passing through increased speeds, allows the direct crossreference of simulated data, in pressure, extensionrate and motionblur fields, against experimental f1ow visualisation (bottomleft, stirrers indicated). The correspondence in vortex structure is striking. Motionblur clips at four set speeds of vessel rotation, identify the twisting of the vortex structure with increased speed (in the direction of rotation). This is corroborated in highspeed camera, laserscatter stills of I% cmc fluid At 50 rpm, the motionblur flow patterns between one and twostirr er mixer s may be contrasted (on the left), whilst also taking the industrialist 's view with stirrers rotali11g (on the 9
8 right). Next, we turn to the vertical panfilled instance (for breadmaking), with a centralstirrer, vessel rotating and wmpare the final rise surface position graphically against experiment. Agreement is encouraging. Similarly, we may combine cases with three set speeds, 25, 50 and 100 rpm, to demonstrate variation of fluid heightrise at the outer vessel. Such results are obtained by modelling the peelingoff and wettingonto the surfaces, via the adjustment of surfacefluid line segments, according to their stretch and angk from the solid boundary. Relief of limiting stretch, also relieves critical boundary stress levels. A more complicated vertical scenario is that with a single eccentric stirrer (vesselrotating). A surface triangulation (heavy on graphics) illustrates the complex shapes encountered. Different viewing angles, with lighting and shading, indicate the surface rise ahead of and dip behind the stirrer. Experimental camerastills ~t four diff~rent speeds, validate our predictions. There is increased contonion of the surface as speed gathers. The experimental buildup of surface sm1cture is animated from a rest state at 250 rpm vesselspeed. ln contrast, horizontal mixing (used for biscuitmaking), may be viewed from one end at four different times. Here, we detect wetting/peeling at the outer vessel and peeling from the stirrer as time progresses. First, we view the simulation through an animation clip. The welting/peeling at the outer vessel is a dominant feature. This may be contrasted against the corresponding experiment for a syrup at 50 rprn. The surface attachment structure around the inner section of the stirrer and the central flat. surface shape are finer detail to c~pture. Even these particular details may be predicted, by carefi.d localised adjustment of control parameters for the inner and outer stirrer sections (left image, constant factor; right image, dynamic setting). Lastly, we move to viscoelastic materials, doughlike and filled scenarios. We may observe the stretching and shear stresses across the mixer for a singlestirrer design, or one with a doublestirrer. Ma~ima in stress are localised about the stirrer, in the narrowgap between stirrer and vessel; the hoop stress dominates. Tabulations of localised workinput for the doublestirrer case, reveal that elastic work (stretching, shown in red) is dominated by viscous work (shown in blue). Here, shear influences pievail in the totalled workinput In contrast, the asymmetric singlestirrer design provides tentimes the elastic to viscous work : this is amplified for fluids with some strainhardening (as occurs with dough). So we arrive atthe punchline : optimal 10 kneading for dough is achieved with more asymmetrical mixer designs  one stirrer better than two (shades of Orwell). More complex stirrer shapes are usual ln this respect, we observe for realistic dough that flatbottomed, halfstirrer shapes, produce the best results. Note, the Multimedia presentation style of the fi.iture, with personalised, cruise controlnavigation, the green panicbutton I. We finish. with a look lo the fi.1ture, and where we are intending to take this technology. A principal plank is our pursuit of quantitative agreement between the modelling and actual fluid flows (experiments). In this respect, we look to such flows as in the contraction, seeking multimode and variety of model fits under realistic flow conditions. Here, new challenges are posed to the comparative visualisations sought. Industrial flows abound. Analysis of processing takes us into foodsrelated studies, for example tilanient stretching, as arises in deposition of food products (such as yoghwi). Printing and coating of inks is another domain where rheological input is required with the current interest in polymer additives. This brings us naturally to the link between micro and nanoscale studies, looking at stretching of liquid bridges between surfaces within the realm ofbiomechanics. A further area of multidisciplinary interest lies in consideration of compressibility for viscoelastic flows, of relevance within injection moulding. Here, Swansea has a wealth of background knowledge. ll is implied that suitable algorithms will be developed to meet the challenges posed by and the individual character of each problem in hand. I close with thanks. Note, the advanced warning of a second INNFM film (interactive /CD version  top right) on the 'History of Rheology'  the life and limes of our field. This was constructed with the help of two Olchfa students, Gareth Hunt and David Webster. It shall appear shortly. I am indebted to my research colleagues.and students within the team at Swansea and the Institute at large, for their invaluable suppmi and contributions to this body of work. We finish by playing out on a trailer for our new film. your attention. M.ike Webster 12 November 200 I 11 I thank you once again for
9 Appendix of slideimages attached. Appendix I. General slides Appendix [I : ReverseRoller Coating Multimedia Appendix Ill DoughMixing Multimedia Appendix I: General Slides 12
10 Appendix I: General slides ;ln~ ~f  f.. : ~1 PTof: Mike W b t r Computer Soh:nc, UWS.. Goinc with tb 06W" Compotatlonal Rheolo17 Introduct1o n What we do Science Application Case Studle.s l l Simulation Soltwetc Finite Element/Volume method Time Intecr Uon &. parallelbatioo Viscous hu:ompressiblc Oow Non Newtonian Noa.Isothe.mal \ a.r!..w:!!1 j''..,... "~ itt fd:i Newtoala" ildat a rlal f;, :,.~.f " Locatioo Flow Geometries Governlnl Eq11.atloo.a 2D planar I Conservation al Mass 'v 11 '"" 0 Swan e mmctric AJClay  Movln1 fronts I Free lliurfaces Interfaces, ,... 1.lflfl!J MomentumTransporl I' Rc~=Kc: u V t9 (21;dt f) j Stress Cansliluli ve Law ar µ IVe"a;" = \Veu Vr fr +2~d + We(L r + r i7 ) Re: plll We=~,ta ' L...,... Of.J,Q. o...,..... tic History Sw1uu,ea Hlstory ln the Hel4 h O.C. %lcnlll lc r...~.. 1"",,(.)\ I I Nuau:riclll AJ1orithm Taylor Gali;,,ikin/ p c achcm Staijc la l¼m+ts. j(u 00 ~  u,.., 11s. u + RcN(U)UI+ 1.Tr1 C llaheedy Studiea vieca l e etlc Rhoolop ,_ 1...;,;..:,"; ~  "F=... ~~~~!lt..n m.,lcal Me:bod, ',. S1:1~c: l r~ : ~ Page <#> Page<#>
11 I Mixing/Separating Flow I C u: Studies Doue;b Ml.xlnc wottla1 Iii. p lloc be  fully RIied a. parc lulad tnnaleat 'ld&jd. coaccatrlc & a cc ntrlc.cln"n 11lffer 1:1t 1natt1rlala a. 1co,actrlea.ppt 1lldes C se Studies CJosinc Remarks Futu,a Wlre Coating r Q.. aalltallve co,.. p111lao11 Shoulall.,11., Jrp rl111 10ta Co., cuua Oo oiuiltl,. 4 Ouida, pu,.. u,e calet1latlon Important a l a tlclty Important 111 th d l n!.rr.t.:;t ~~ , '.\t!..!.!.!.1l F ~.~ rvlaw _.. "'"'"'... odala,tn...,,a.. too la1h1atrlal Row f' Uama t o:blil IL>adel  N...,.... lc.ro o:!wce  Pria... c..,.u... lacaal'... o:,.. r.,ulbl Flllr OptkCahr, A.dvaoc.s alcorlthm ta ~It Se,il:!11d1>ttl1ol"1t11091,. tlrl11,~6dt.9ve,vlu, S,oql: N...,tonltn dl v111&/m...,oftlmlol nelull l"/uif1 NoftNIWIG!' l n /lwds!l!i. Ca e Studies Rever e, Rollerco tln1 fr urracelnat l,llltl1n..,,umal open.tins eondltlon _...,. + Reverse Roller Conling Multimedia Section r  1, I Thank you you,.~::atloa 1 Aoknowl m n<,, CFDt.. m INNFM ~ Page <#> Page<#>
12 Appendix II: ReverseRoller Coating Multimedia
13 Appendix II: ReverseRoller Coating Multimedia 404.IE...1) l'f~uf (...:;, ' (~!\~~ II.,,..:,, 1..,,.,; 2'% ~:\)}.~..:V:.!, '!t~;i/j;/(.,,,~...,
14 Appendix III: ~1 :;~::"~ jl ;_~_. ::7 ,.. t.. " ' i :. ~,...,_,.... jr...,, Doughmixing Multimedia 2
15 Appendix Ill: DoughMixing Multimedia 11\fO.Jt I~,t,e"" ' ~.. ~lll!!j=""".....,...~ 11o ,.., ~.. :.., ' l"'10 10<WIW>ll:n.; ~... 1:1<1u:11u.t,,il., MB P 1.,. t1..,/ ' _;... A2 Re  _ Peetlng criteria onaet. & adjustment._.:r:. :.', ,. <.,, ,{' :.. l;"" ::S u)u l,'.. 1.s a,t ~ j.., inl.:l c~ h.:l<i" " ici lc, ct Ml! ~lll!!j=.""'1 iffl PJ,ticlUlllU \ v ll \/41,o,,1>o1.uu,...:» 2
16 n..,,n11 {I 1::,,... r, :~ rr..,. 011\1t:;J1 l:'h,)1":f.i : k' tt'ltl :,g..ca toictn,... ti.1aew H,.. w...c ErIT(O 15i \ii;.:;,;;: lrl IPI 19 \ lltj\'"ji Mt.:tlN1; le ~ c~ "1111J1~1:t '1 i fjtli11 r;_j.. j....'''.. ~h,:arrnr~ u.:i t,io:nl mle,l:'\1",1:i,;,r.u:i,na: 1 ).,11,1.:1 : P.cl'.:,E 0.1'.:5,E2:i' mm,.,, _ a. :; ~ tl,lf ',f1. 1;,f1N4l ; t2rr111 mm _,, t~i n 1.r.u : r1 :]~i "'.:..:,.:~,....'.?~ :~ W"tmff :~, m111 11s11;,r. ~ ":~ / :1mra l't1tt1,~.,.,,r.,., ;r, ;]WI. mrr~ 1111 ffl Jffiff i:t., 11 Sl1t;1r " ;11e;in:llr.:.1lr.1tt.nl wr,rl;111n:im1, i\i: ll, ~O.l:'.!.'i, l?1.'i f 11fCI'. 3 4
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