Complete Wetting of Acrylic Solid Substrate with Silicone Oil at the Center of the Substrate

Transcription

1 Complete Wetting of Acrylic Solid Substrate with Silicone Oil at the Center of the Substrate Derrick O. Njobuenwu * Department of Chemical Engineering, Loughborough University Leicestershire LE11 3TU, United Kingdom Abstract Spreading of silicone oil drop on acrylic solid substrate was investigated. The spreading was caused by both the spontaneous spreading and the constant injection of liquid through the centre of substrate, and two spreading regimes exit. At the onset of the experiment when the droplet volume was small and the radius of spreading, R(t) is less than capillary length a, [R(t) < a], the spreading was governed by capillary laws (capillary regime). As time progressed, the droplet volume increased and the silicone oil spreads out leading to a transition from a capillary regime (CR) to gravitational regime (GR) of spreading where R(t) > a. Both the spontaneous spreading and the constant source combined to give the overall power law of spreading of liquid from a constant source on a solid substrate as R(t) ω c t 0.4 and for R(t) ω g t 0.5 capillary and gravitational regime respectively. There was small deviation of the power law exponent between the experimental and the theoretical for both regimes. This little deviation is attributed to the surface roughness of the acrylic substrate. Keywords: Acrylic substrate, silicone oil, complete wetting, capillary regime, gravitational regime, spreading, power law. Introduction Many industrial and material processing operations require the spreading of a liquid on a solid substrate. Coating, adhesion, painting, welding and soldering, plant protection (Stevens 1993), gluing, oil recovery from porous rocks and lubrication (De Coninck et al. 2001) are some of the applications of the principle. Considerable progress has been made in recent years in understanding spreading of instantaneous liquid drop on solid substrate in understanding contact angle and the forces at play at the contact line, in understanding the mechanisms controlling the dynamics of wetting, and in the development of hydrodynamic models that have the possibility of describing the phenomena at the three-phase contact line (Lopez et al. 1976, Tanner 1979, de Gennes 1985, Cazabat and Cohen-Stuart 1986). An opportunity now exists to capitalize on this progress by extending it to spreading of liquid drops over solid substrates with a constant liquid source in the centre of the substrate. This realization motivated this research and it is believed that the findings would have a major impact on developing the field of interface phenomena. In this case, the spreading is caused by combinations of two processes: a spontaneous spreading and a forced flow caused by the liquid source in the centre of the substrate as * Present Address: Institute of Particle Science & Engineering, School of Process, Environmental & Materials Engineering, University of Leeds, Leeds LS2 9TJ UK. Tel.: , chedon@leeds.ac.uk, donadviser@yahoo.co.uk 163

2 illustrated in Figure 1. Two forces drive the spreading: Capillarity (small drops with negligible gravity effects) and gravity (large drops with domination gravity effects). For an instantaneous drop, the theoretical calculations for drops of completely wetting liquids on smooth, plane surfaces were carried out for both cases, namely for negligible gravity effects (small drops) by Tanner (1979) and for dominating gravity effects (large drops) by Lopez et al. (1976). Both forces decrease considerably as a drop flattens out, whereas the opposing viscous force increases. For drops of volume Q, dynamic viscosity of the liquid η, liquid density ρ, and liquid-air interfacial (surface) tension γ, the radius R of the wetted spot grows as with time, obeying the power law, R(t) = ωt n, where ω is a dimensionless parameter in the spreading regime. Many forces including the substrate surface roughness, drop lifetimes, surface and interfacial tension dynamics, surface energies solute adsorption rates at the different interfaces that join the three phase contact line (Stoebe et al. 1996) may contribute to the wetting dynamics and the transition from capillary to gravitational regime, however, only the forces at the three phase contact line are of interest here. Experimental Set-Up Materials: The solid substrate was circular sheet of acrylic solid radius 25 mm and thickness 5.0 ± 0.5 mm. An orifice of diameter of 0.4 mm was drilled in the substrate centre. This was positioned in a tripod adjustable ring. This entire system rested on an anti-vibration table to isolate the system from vibrations greater than one Hertz. Silicone oil was purchased from Brookfield. Its viscosity was measured using the rheometer AR1000 (TA Instruments) at 25 ºC. Density was measured by weight method and for measuring surface tension the Tensiometer (White, Elec. Inst., Co. Ltd.) was used. The following values were found: dynamic viscosity η = cp, density ρ = 0.96 g/cm 3, surface tension γ = 22.5 mn/m. Methods: The diagram of the experimental setup is shown on Figure 2. All experiments were carried out at temperature 25 ± 0.5 ºC. The solid substrate, 1, during usage was fixed in the ring; a syringe, 3, was positioned in the centre of the substrate and connected to the Harvard Apparatus syringe pump, 9. The flat glass substrate was placed on a horizontal support during usage. The droplets of silicone oil, 2, appeared due to the injection. The flow rates used was ml/min. θ 2 h(r, t) 1 R(t) 4 CCD CCD SYRINGE PUMP 9 Fig. 1. Schematic presentation of the spreading in the presence of the liquid source in the drop centre 1, Solid Substrate; 2, Droplet of Silicone Oil/ water; 3, Syringe; where θ is the contact angle, h(t, r) is the drop profile, and R(t) is the radius of the drop base as a function of the time, t. Fig. 2. Schematic representation of the spreading of Surfactant Solution and water on solid substrate. 1, Solid Substrate; 2, Liquid Droplet; 3, Syringe; 4, Light Source; 5, Filter with Wavelength 640nm, 6, CCD Camera; 7, Tape Recorder; 8, Personal Computer; 9, Harvard Apparatus Syringe Pump; 10, TV. 164

3 The spreading process was recorded using a Charge-Coupled Device (CCD) camera, 6, at 25 frames/sec and a Video Home System (VHS) recorder, 7. The camera was equipped with filters, with a wavelength of 640 nm. Such an arrangement suppresses illumination of the CCD camera by the scattered light from the substrate and, hence, results in a higher precision of the measurements. The source of light used during experiments was from Oriel Lighting system, 4. The CCD camera and the VHS recorder were connected to a personal computer, 8. The VHS images were converted to Audio Video Interleave (AVI) film format using Pinnacle Studio 7 software. The AVI files were converted to frames using irfan View software. The radius of the drop with respect to time was measured using the image analysis software, Scion Image. The substrate surface was measured using the Atomic Force Microscopy (AFM). Results and Discussion The average roughness of the acrylic substrate, R a, varied from 433 nm to 467 nm. Roughness was measured using Atomic Force Microscopy and the Microscopy microphotographs showed in Figure 3. The kinetics of spreading of silicone oil (complete wetting) on acrylic substrates was investigated. Fig. 3. Atomic Force Microscopy, AFM Surface Roughness and Image Statistics of Acrylic substrate. 165

4 Typical image frames acquired by the image analysis system described in the experimental procedure are displayed in Figure 4. The infuse rate of 0.02 ml/min was used and the frames and time of spreading are as indicated in the images shown in Figure 4. The silicone oil tested exhibited two stages of complete wetting: namely capillary spreading which starts at the commencement of the spreading process and then passed through a transition zone to gravitational stage of spreading. At the onset of the experiment when the droplet volume was small and the radius of spreading, R(t) is less than capillary length a, [R(t) < a] where a = (2γ / ρg) 1/2 = 0.21, where g is the gravity acceleration, for silicone oil the spreading was governed by capillary laws (capillary regime). As time progressed, the droplet volume increased and the silicone oil spreads out leading to a transition stage that is, transition from a capillary regime (CR) to gravitational regime (GR) of spreading where R(t) > a. In both cases the exponent is the sum of two terms: the first term corresponds to the spontaneous spreading from an instantaneous drop which obeys Tanner s law of capillary spreading regime, R(t) ω c t 1/10, where ω c is a dimensionless parameter in the capillary spreading regime (Tanner 1979, de Gennes 1985, Cazabat and Cohe-Stuart 1986) and Lopez s law of gravitational spreading regime, R(t) ω g t 1/8, where ω g is a dimensionless parameter in the gravitational spreading regime (Lopez et al. 1976, Cazabat and Cohen-Stuart 1986). The second term determined by the intensity of the liquid source gave an additional exponent term of 3/10 and 3/8 for capillary and gravitational regime respectively. Both the spontaneous spreading and the constant source combined to give the overall power law of spreading of liquid from a constant source on a solid substrate as R(t) ω c t 0.4 in the case of the capillary spreading and R(t) ω g t 0.5 in the case of gravitational spreading. Both the capillary and gravitational regimes are expressed as a function of the infuse rate (the intensity of the liquid source), I, raised to a certain exponent. (a) 0 sec, frame 100. (b) 40 sec, frame 1,000. (c) 80 sec, frame 2,000. (d) 160 sec, frame 4,000. Fig. 4. Typical Frames showing the spreading of Silicone Oil on Acrylic substrate. Infuse Rate = ml/min. 166

5 However, there is one interesting point for the two regimes in the spreading processes. If the liquid source is blocked the drop will spread according to the power law R(t) t 1/10 for capillary regime. This is in agreement with Tanner s law of capillary spreading for an instantaneous drop (Tanner 1979, de Gennes 1985, Cazabat and Cohen-Stuart 1986). Similarly, for gravitational regime, the spreading law will obey the power law for the spreading of instantaneous drop R(t) t 1/8 which agrees with previous works (Lopez et al. 1976, Cazabat and Cohen-Stuart 1986). This goes to confirm that the spread is caused by two processes: instantaneous spreading and spreading due to the continuous injection of the silicone oil. Complete Wetting Capillary Regime The experimental data are plotted and shown in Figure 5. The lines of best fit were also determined with corresponding exponent n = 0.30 and pre-exponential constant C c = mm/sec 0.4. The deviation from the theoretical value of n (n = 0.40) may be attributed to the surface roughness of acrylic substrate and other forces at the contact line. The data obtained correspond to the capillary stage of spreading, and were plotted in terms of the spreading law proposed by Holdich et al. (2005) as R(t) = ω c (γi 3 /η) 0.1 t 0.4 to examine the theoretically (R(t) C c t n ) suggested n = 4 and the capillary constant C c. The average value of n, capillary constant C c and correlation coefficients (R 2 ) calculated from experimental data of silicone oil spreading on acrylic substrate using power regression analysis and assuming that the kinetics of spreading are described by R(t) = C c t n, ml/min infuse rate are n = 0.30, preexponential constant C c = mm/sec 0.4 and respectively. The deviation from the theoretical value of n (n = 0.40) may be attributed to the surface roughness of acrylic substrate and other forces at the contact line. Complete Wetting Gravitational Regime Similarly, the spreading equation for gravitational regime is R(t) = ω g (ρgi 3 /η) 1/8 t 0.5. The experimental data were plotted following the power law R(t) C g t n as shown in Figure 5. The data were fitted using power law and the line of best fitted were draw to yield the value of exponent and pre-exponential constants for the various infuse rate used. The exponent for spreading of silicone oil on acrylic substrate was approximately 0.44 while the preexponential constant C g and correlation coefficients (R 2 ) were mm/sec 0.5 and respectively. There is a deviation from the theoretical predicted value n = Ln R(t) -1.5 Capillary Length, a Exp., CR Exp., GR Exp., TR Theory CR, n=0.4 Theory GR, n= Ln t Fig. 5. Complete spreading for 100 cp Silicone Oil on Acrylic Substrate. CR = capillary regime, GR = gravitational regime. 167

6 Conclusion The spreading of liquids over solid substrate caused by liquid injection through an orifice is investigated from both theoretical and experimental points of view. Two regimes of spreading for complete wetting of acrylic substrate with a diameter of the orifice 0.4 mm by silicone oil droplets were observed: capillary regime and gravitational regime with a transition regime in between them. The transition stage is at the capillary length, a, for the silicone oil used a = Acknowledgements The author acknowledges the fruitful discussion with Professor Victor M. Starov of Loughborough University, United Kingdom and Professor Ramon Rubio of Universidad Complutense, Madrid, Spain. References De Coninck, J.; de Ruijter, M. and Voue, M Dynamics of Wetting. Current Opinion in Colloid and Interface Science 6: Holdich, R.; Starov, V. M.; Prokopovich, P., Njobuenwu, D. O.; Rubio, R.; Zhdanov, S. and Velarde, M. G Spreading of Liquid Drops from a Liquid Source. Colloids and Surfaces A: Physicochemical Engineering Aspects 282-3: Lopez, J.; Miller, C. A. and Ruckenstein, E Spreading Kinetics of Liquid Drops on Solids. J. Colloid Interface Sci. 53: Starov, V. M.; Kalinin, V. V. and Chen, J. D Spreading of Liquid Drops over Dry Surfaces. Adv. Colloid Interface Sci. 50: Stevens, P.J.G Organosilicone Surfactants as Adjuvants for Agrochemicals. Pesticide Sci. 38: Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D. and Davis, H. T Surfactant-Enhanced Spreading. Langmuir 12: Tanner, L. H The Spreading of Silicone Oil on Horizontal Surfaces. J. Phys. D 12: