The Measurement of Wetting Angle by Applying an ADSA Model of Sessile Drop on Selected Textile Surfaces

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Jarosław Gocławski, *Wiesława Urbaniak-Domagała The Measurement of Wetting Angle by Applying an ADSA Model of Sessile Drop on Selected Textile Surfaces

Technical University of Łódź, Abstract Computer Engineering Department, This paper presents a method of liquid-solid contact (wetting) angle measurement for ul. Żeromskiego 116, 90-543 Łódź, Poland selected textile surfaces, assuming the angles to be less than 90°. The method uses a special e-mail: [email protected] apparatus for acquisition of sessile drop images. Specialised image processing methods involving edge filtering, image morphology and a prior knowledge of the drop boundary *Department of Fibre Physics location are used to extract droplet edges and the bottom line of a solid textile surface. Then and Textile Metrology, ADSA profile optimisation is applied to find the liquid contact angle with respect to the e-mail: [email protected] bottom line. The ADSA trajectory is fitted to the drop edge data using a trust – region, nonlinear optimisation algorithm, with a proposed definition of distance error measurement. The image processing and analysis methods mentioned above are implemented in a MATLAB 7.0 environment; the results of individual measurements are shown in MATLAB windows as well. Key words: ADSA model, sessile drop, wetting angle, contact angle, capillary constant, edge detection, dilation.

as well as during the refining of products tact point and the assignment of the drop (such as printing, gluing, making apprets profile tangent at this point. Neumann [7, in liquid phase, lamination) and also when 8] replaced the procedure of subjectively producing good mechanically resistant setting the tangent and reading the con- composite materials [3, 4]. tact angle with an ADSA numerical model (Axisymmetric Drop Shape Analysis). Among the many methods of contact an- Since then, it has been possible to carry gle measurement, the sessile drop method out angle measurement automatically [5] is noteworthy. It analyses the menis- with a small margin of error - ca. 0.1°. cus shape of a liquid drop put on the flat This margin of uncertainty is specific for surface to be examined. The use of a small smooth, planar and homogeneous sur- amount of liquid to investigate the surfaces – in such cases where the contact face, and the possibility of observing the line of the drop with respect to a bottom kinetic phenomenon of wetting in its lo- solid surface is precise and easily visible. cal zones, is an unquestionable advantage of the sessile drop method. This effect is Textile surfaces are rough to a degree; impossible to achieve using the Wilhelmy depending on the structure of the inter- method [5] or wicking method [6], where lace of yarn strands, the fibres infill and the end measurement result applies to their arrangement in the product (woven n Introduction the whole sample perimeter. The basic fabrics, knitted products and needled uncertainties of contact angle evaluation nonwoven). The application of the ADSA The behaviour of liquids in contact with in the sessile drop method are the preci- model for such surfaces requires a specif- solid surfaces can be different. Some sion of the base (bottom) line location, ic approach as far as setting the base line liquids spread over surfaces making a identification of the liquid-solid-air con- is concerned: textile surface - the liquid film, whereas others wet them to a limited extent, creating drops at a given contact angle.

That contact angle between a liquid and 5 a solid surface is a sensitive indicator of changes in the level of surface energy 8 and changes in the chemical and super- molecular structure of the surfaces to be 4 modified [1]. Knowledge of the contact angle enables estimation of the type of 1 3 6 7 interaction between surfaces and liquids 2 (dispersive and polar interactions) [2] and has a wide range of practical applications. Figure 1. A block diagram of an apparatus for measuring textile wettability. 1 - light source, It helps to predict the course of reaction 2 - diffuser, 3 - measuring table, 4 - liquid droplet, 5 - manual syringe, 6 - camera lenses, during the chemical processing of surfaces 7 - CCD camera, 8 - PC computer with an image acquisition card and image processing in a liquid environment (washing, dyeing), applications.

84 FIBRES & TEXTILES in Eastern Europe April / June 2008, Vol. 16, No. 2 (67) drop, establishing the contact point of the The droplet image acquired by the cam- On the basis of the above- mentioned three-phases on the base line and differ- era in PAL standard (768×576 pixels) is assumptions and observations, an algo- entiating artefacts on the meniscus of the transmitted by means of a frame-grab- rithm for establishing a drop bottom line liquid drop. Because of this many exist- ber into a computer’s memory (8) and and for wetting (contact) angle evalua- ing commercial solutions of goniometers saved on a computer disk as a bitmap tion is proposed. [9, 10] are not applicable in this case. file. The bitmap is an image data source for the “Textile Wettability Analyser” n In this series of articles, both the nu- programme created in cooperation with Description of drop shape merical procedures, made for real cases the Department of Fibre Physics and A description of a drop shape is based of textile surfaces, and the procedures Textile Metrology with the Computer on the axisymmetric drop shape analy- which would enable the identification of Engineering Department of Technical sis model - ADSA proposed by the Neu- the base line and the automatic measure- University of Łódź. An algorithm for the mann group [7, 8]. Many variations of ment of the contact angle will be pre- analyser was created as a set of functions this model have been used (ADSA-P, sented. Light absorbing, reflecting, liquid in a MATLAB 7 environment. The task ADSA-D) for sessile and pendant drop- moistened, and non-moistened surfaces of the analyser functions is to evaluate lets to determine drop-air surface tension will be taken into account, as well as sur- the contact angle by modelling the drop and wetting angles. The droplet edge can faces with single protruding fibres, tak- shape from the image acquired. All the be described as a solution to the initial ing the role of artefacts on the meniscus measurements are carried out at a con- problem concerning the system of three of the liquid drop. stant temperature of 24 °C. ordinary differential equations of the first order versus the boundary parameter –s n The measurement apparatus n Drop model assumptions [9, 11]: The apparatus used for sessile drop imag- It is assumed that a drop of liquid is po- dx/ds = cos (f), dz/ds = sin (f), (1) ing and measurement, consisting of hard- sitioned on a horizontal textile surface df/ds = 2×b - (sin (f))/x - c×z, ware components, is shown in Figure 1. in a state of balance resulting from the A flat textile specimen is placed on a hor- interaction between the force of vertical where b = 1/R0, c = g×Dr/g izontal measuring table (3). A dose of liq- gravity and the interfacial tension force tangent to the liquid surface. In the im- uid (1 µl) is injected into a textile surface Variables x, z, φ specify the abscissa, or- age acquired the drop investigated can by a manually driven syringe (5) creating dinate and polar angle of the tangent to be seen as a dark profile with a clearly a sessile droplet (4). The droplet (4) is il- (x,z) the trajectory point, where XZ is a visible edge near apex A (Figure 2). The luminated by a source of visible light (1) right-handed coordinate system originat- contact zone of the drop on the textile through a diffuser plate (2), which is seen ing in the drop apex. Parameter b stands surface is visible as a grey strip of irregu- by a CCD camera (7) equipped with an for drop surface curvature at the apex, lar width between a bright zone of air and appropriate set of lenses (6). c –capillary constant, g –gravity acceler- the dark vertical cross-section of a textile ation, γ – the interfacial tension between specimen. liquid and air, Δρ –the difference of liq- a) It is believed that the liquid drop forms uid and air densities. The initial condi- contact angles less than 90° to a textile tions are as follows: background. x(0) = 0, z(0) = 0, f(0) = 0 (2) In the contact zone the following effects can be observed: A set of differential equations (1) can be 1) A reduction in the drop edge contrast solved based on an explicit Runge-Kutta compared with the contrast between (4.5) formula using MATLAB function “ode45”. The values of apex curvature b) liquid and air near the drop apex, 2) The change in the drop edge in its b and capillary constant c should be de- shadow edge, identified by the altera- termined before the beginning of calcu- tion of the edge direction. When the lations. The values are estimated on the contact angles are less than 90°, the basis of the features of the drop geometry edge points of left and right semi-pro- and then optimised in the process of tra- files increase their distances from the jectory, fitting to the set of boundary data drop symmetry axis as they are further points. The numerical solution found has from the drop apex. Violation of this the form of a parametric trajectory curve tendency means entering the shadow (x(sj), z(sj)), j∈[1,N], representing a drop Figure 2. a) Water droplet image on an ex- edge (in the vicinity of points P1, P2 profile boundary in the XZ coordinate amined polyester textile. b) Droplet model in Figure 2b). system. showing the possible behaviour of edges (boundaries) in the background contact 3) The presence of the remains of a dark zone. A –the drop apex, CD –the droplet horizontal contact line which disap- Image segmentation edge, zB –the bottom line, MB –the mask pears as the distance grows between for bottom line location, MD –the mask of it and the three-phases contact points and analysis algorithm boundary data, θ1, θ2 –wetting (contact) angles between textile background and liq- (P1, P2) on some of the drop images Figure 3 (see page 86) show a flow dia- uid phase acquired. gram for the method proposed.

FIBRES & TEXTILES in Eastern Europe April / June 2008, Vol. 16, No. 2 (67) 85 x0(z) = = 1/2{mean[x:(x,z)∈CD, x ≤ xA] + x

(6) + mean[x:(x,z)∈CD, x ≥ xA]} x

x0 = mean{x0,(z)} (7) z

6) Determination of the vertical coordinate zB of the horizontal contact line by separately searching the location of points with the greatest distance to the symmetry axis x0 for left and right drop semi-profiles.

zB = mean(z), (x,z)∈CB, x = max|x - x0| (8)

7) Boundary data symmetrisation versus the x0 axis. It is based on evaluating the mean distance x from the edge data points (x,z) to the symmetry axis for each image row z.

8) Matching the numerical solution of drop boundary equations (1) – ase- Figure 3. A flow diagram for the method proposed. M – dilation mask for baseline detec- B quence of trajectory points (x(s ), z(s )) tion, MD – the mask of droplet boundary points, b – the curvature in the drop apex, c – the i i capillary constant, LMS(CADSA, CD) – the least mean-square error of CD data bound- to the set of boundary data pixels ary approximation by ADSA trajectory, TR(b,c) – the trust-region optimisation loop in b, CD = {Pi(xi,zi)} read from the drop c parameter space. image. It involves minimisation of the square distance between fine boundary The algorithm proposed has the follow- algorithm. An external mask MB with data pixels and their orthogonal pro- ing steps: a greater radius is applied to help with jections on the ADSA trajectory [9]. 1) Coarse drop contour detection using bottom line detection (Figure 2.b). F(b,c) = Σ((xN(sN,b,c) - xi)2 + Canny filtering [14]. i MD = I(ELMS) ⊕ K(rD), (9) (4) 2 =σ (3) + (xN(sN,b,c) - xi) ) IC (,) x z Canny ((,),,,) I0 x z T 12 T MB = MD ⊕ K(rB)

where sN –the trajectory parameter and Detection threshold T2, continuity 4) The fine drop image boundary detec- the mean trajectory points PN(xN, zN) threshold T1 and standard deviation tion using Canny filtering. The param- with the nearest Euclidean distance to of the internal Gauss filter should be eters T1, T2, σ of the filter function (3) appropriate data points (xi, zi). Initial selected to detect the best contrasting must be set to low values. Edge data parameters for F(b, c) optimisation are: upper part of the drop profile bound- points for bottom line detection and a) Curvature b = 1/R0 = bE/a2E at the ary above the contact zone. As a result for the ADSA algorithm are selected drop apex calculated for the el- a binary image IC(x,y) is obtained con- under the MB and MD masks, respec- lipse EA(aE, bE, xE, zE), matching, taining the base drop edge C1,2(x,z) tively. Only the boundary objects with in least mean square sense, to drop (Figure 5.a). the greatest area AR for each mask boundary data near the apex. The type are taken into account. This way curvilinear parameter s should not 2) Creation of ellipse E (a ,b ,x ,z ) LMS E E E E spurious edge fragments can be elimi- be greater than 1 - 2% of an esti- with centre (x ,z ) and 2a , 2b diam- E E E E nated. mated drop diameter. eters best fitted, in least mean square C (x,z) = max (I (x,z) ∩ M ) (LMS) sense, to the C (x,z) drop B C B 1,2 AR edge data. The algorithm of ellipse (5) ∩ applied, which fitted the set of pixel CD(x,z) = max (IC(x,z) MD) AR data, was published in [13].

3) The setting of the masks for bottom 5) Evaluation of the horizontal coordi- line and drop boundary points. The nate x0 of a vertical symmetry axis for ELMS ellipse boundary is mapped into the drop boundary CD. For each row z, a binary image raster, and then two cir- including edge points on the left cular dilation masks [15, 16] are built and right sides of the apex A(xA, zA) around the pixels of this mapping. A (Figure 2.b), their means x (z) are Figure 4. A picture explaining the meth- 0 od of contact (wetting) angle evaluation. symmetric, narrow mask M is used evaluated, and then the global mean D CADSA – ADSA trajectory with points (xi zi), to limit source edge data for the ADSA versus all z values. (xi+1,zi+1), θ2 = θ –wetting angle (right).

86 FIBRES & TEXTILES in Eastern Europe April / June 2008, Vol. 16, No. 2 (67) Figure 5. Selected stages of image processing and analysis for a sessile water droplet on a polyester textile surface: a) detection of the coarse drop edge C1,2 using Canny filtering, b) detection of the fine drop edgeD C for the ADSA algorithm, c) the result of ADSA optimisation –CADSA trajectory and the contact angles θ1 = θ2 = θ measured at the intersection of CADSA with the bottom line zB.

b) Capillary constant c evaluated from Contact (wetting) angles θ1 = θ2 = θ at In the case of the data in Table 1: equations (1) with the assumption the intersection points of CADSA with the 2.44 that x(z) is a function describing bottom line zB are visible as well. = − ≈ ∈ = −∞ − ∪ ∞ st 10 1 3.05 RR0.05, 0.05 ( , 2.26) (2.26, ) each half of the ellipse EA: 2.40 A series of contact angle measurements 22 2.44 zbxaxa=11 − − / ,||<< has been/were carriedst out= for water10 − drop 1 ≈ 3.05- ∈ RR =( −∞ , − 2.26) ∪ (2.26, ∞ ) E( E) E (10) 0.05, 0.05 2.40 lets on a polyester textile background Functional (9) minimisation has been/ applying both computer and manual with R0.05 –a double sided critical region is performed with the MATLAB func- methods (Table 1). In the manual image of significance level equal to 0.05. tion “lsqnonlin” using the large scale method both the bottom line and elliptic trust-region algorithm [17, 23] and er- shape are manually fitted to the drop pro- The above student’s t-test gives the re- ror tolerance value “TolX = 1e-6”. The file [24]. Wetting angles are measured be- sult of 3.05 > 2,26 –critical region limit path of trajectory points (x(s), z(s)) is tween the bottom line and the automati- at a significance level of 0.05. For the defined as a polyline. In the case of cally calculated ellipse tangents. two measurement methods shown in F(b, c) calculations are much faster Table 1, the hypothesis of equal aver- when compared with the cubic spline Measurement results for the two methods age results at a significance level of 0.05 interpolation of a trajectory curve. Ad- are compared in Table 1, based on the must be rejected. This result can be eas- justing the “MaxStep” option enables same set of images. Normal distributions ily explained. In the manual method the us to get a table of trajectory points are assumed, and X, Y measurement re- ellipse is fitted to the pixels of a drop dense enough to be linearly inter- sults for the same drop objects correlated. edge intersection with a bottom line. In polated for data-trajectory distance The average value of the difference ran- this case the height of the ellipse segment measurements. dom variable Z = X-Y has student’s dis- is slightly lower than the drop apex, as tribution [18]: well as the angles of the ellipse tangents. 9) Evaluation of the liquid-textile contact The standard deviations calculated for angle θ as a polar angle of the line join- average( Z ) st =n −1 (11) both methods are greater than shown in ing two neighbouring trajectory points S Z literature examples [8] for smooth back- (x(si), z(si)) and (x(si+1), z(si+1)). The distance between these points must be where Z – a random variable of the grounds, because the surfaces of textiles intersected by the horizontal contact measurement differences, SZ – standard are usually non-uniform. For them only line zB (Figure 4). deviation of Z, n – the number of meas- average values of contact angles for a se- urements. ries of measurements make sense.

Examples and experimental Table 1. Contact angles evaluated by computer and manual methods for water drops on results polyester textile surfaces. Figure 5 presents the main algorithm steps for a sessile water drop on a horizontal Contact angles evaluted, ° No. Difference, ° polyester textile surface. The canny fil- Computer version (X) Manual version (Y) (Z = X - Y) ter parameters for coarse edge detection 1 71.70 73.06 -1.36 C1,2 (Figure 5.a) are T2 = 0.9, T1 = 0.7, 2 73.64 70.63 3.01 σ = 3 and for fine edge detection T1 = 0.1, 3 71.74 68.27 3.47 4 74.36 66.47 7.89 T2 = 0.2, σ = 1 (Figure 5.b). The algo- 5 74.34 70.81 3.53 rithm has relatively low sensitivity to T1, 6 77.07 75.14 1.93 T2, σ Canny filter parameters, so they do not need to be changed in the whole se- 7 76.65 73.39 3.26 ries of drop images acquired 8 73.74 71.65 2.09 9 68.63 69.84 -0.21 In Figure 5.c the final ADSA curve 10 68.71 67.91 0.80 average 73.15 70.71 2.44 (CADSA) is visible after optimisation in parameter space TR(b, c) (Figure 3). S.D. 2.73 2.70 2.40

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