陶瓷墨水测试仪器
doi: 10.1098/rspa.2001.0954
, 2039-2051458 2002 Proc. R. Soc. Lond. A B. Y. Tay and M. J. Edirisinghe
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10.1098/rspa.2001.0954
Time-dependent geometrical changes
in a ceramic ink droplet
By B.Y.Tay a n d M.J.Edirisinghe
Department of Materials,Queen Mary,University of London,
Mile End Road,London E14NS,UK
Received17July2001;revised30July2001;accepted6December2001;
published online3July2002
Ceramic ink droplets have been deposited on two fundamentally di?erent types of substrate and the evolution of contact angle,width of the ink–substrate interface and droplet height was measured as a function of time from digital images of the droplet captured on video.On substrate type I,with a lower surface free energy than the surface tension of the ceramic ink,after reaching stability in a few seconds, the contact angle decreased and the width of the ink–substrate interface remained stationary.Subsequently,the contact angle stayed constant and thereafter reduced again,while the width of the ink–substrate interface decreased and remained constant thereafter.On substrate type II,with a higher surface free energy than the surface tension of the ceramic ink,stability was achieved instantaneously and the contact angle decreased rapidly,while the width of the ink–substrate interface increased initially but thereafter remained constant.The corresponding variation of droplet height due to spreading and evaporation,and volume shrinkage rate were also found to be much faster on the type-II substrate.
Keywords:ceramic;drying;ink;wettability;substrate;shrinkage
1.Introduction
The evaporation of a liquid droplet on a solid surface has been investigated in sev-eral instances and various models for the kinetics of drying have been proposed. Many factors a?ect the behaviour of a droplet deposited on a horizontal non-porous substrate,e.g.the wetting characteristics of the substrate(Birdi&Vu1993;Lau &Burns1973),atmospheric conditions(Erbil1999;Ray et al.1988),temperature (Chandra et al.1996),the presence of surfactant(Chandra et al.1996)and the size of dispersed particles in the droplet(Maenosono et al.1999).
Shannahan&Bourges(1994)showed that a liquid droplet placed on a smooth surface experienced three stages during evaporation.In the?rst stage,the width of the droplet at the liquid–solid interface remains constant while the contact angle and droplet height decrease.In the second stage,the width and height decrease con-comitantly while maintaining a constant contact angle.In the last stage,all three parameters decrease sporadically as the droplet volume diminishes to zero.If the droplet is a colloidal suspension,the shape changes during drying are more com-plicated due to the accumulation of particles near the solid–liquid–vapour interface
c 2002The Royal Society Proc.R.Soc.Lond.A(2002)458,2039–2051
2039
2040 B.Y.Tay and M.J.Edirisinghe
(Maenosono et al.1999;Parisse&Allain1996,1997).Such research has been lim-ited to a single suspension and substrate,with the former containing ca.25vol.%of particles(Parisse&Allain1997;Taniguchi et al.1999).
The printing of ceramic particles according to a predetermined architecture has recently involved the positioning of droplets that are produced from dilute suspen-sions or precursor liquid.These droplets can be ejected into position on a substrate via a jet printer(Tay&Edirisinghe2001)or by electrostatic atomization(Sato et al. 1999).The spreading of the droplet on the substrate,the evaporation of the liquid and the accompanying shrinkage are crucial features in determining the mesostruc-tures containing the ceramic relics.
In this paper,the shrinkage of zirconia ink droplets during drying is investigated. These inks are used for printing ceramics(Tay&Edirisinghe2001).Two substrates that are fundamentally di?erent from each other are used to deposit the ink droplets. Silicone release paper(type I)and acetate sheet(type II)have surface free energies lower and higher,respectively,compared with the surface tension of the ceramic ink. Wettability was studied by observing the variations in contact angle and the width of ink–substrate interface.The variation of droplet height was also observed.These changes were recorded continuously on video and thus we are able to calculate the volume shrinkage of the droplet.
2.Experimental details
(a)Ink
The volume fraction of zirconia powder in the ink was set at2.5vol.%(18wt%),as in our previous work(Tay&Edirisinghe2001).It was dispersed in methylated spirit using a water–methoxy polyethylene glycol dispersant.A binder(polyvinylbutyral), a plasticizer(dibutyl sebacate)and NH4NO3,which makes the ink conductable,were also added,to make the formulation that corresponds to a practical jet-printing ink containing36.7vol.%of zirconia,before addition of methylated spirit.Full details of the constituents,the composition and the preparation procedure are given in our previous work(Tay&Edirisinghe2001).
The surface tension of the ink was measured with a Wihelmy plate(Adamson& Gast1997)suspended from a torsion balance(White Electrical Instrument Co.Ltd, Worcestershire,UK).Five measurements were made and the surface tension was determined as24mN m?1.
(b)Mass loss
The mass loss of ceramic ink droplets on both substrates was measured at21?C in air under natural convection by weighing with an electronic precision balance. Unloaded substrates of the same cross-sectional area(10×10mm2)were used and their masses were?rst monitored every15s over a period of600or900s,for type-I and type-II substrates,respectively.Subsequently,an ink droplet was deposited on each substrate and the mass changes were recorded over the same period.The same procedure was repeated twice for each substrate type.The mass changes of the ink droplet on the substrate,as a percentage of the initial mass,are presented,with appropriate correction made for the mass changes of the unloaded substrate due to equipment drift.
Proc.R.Soc.Lond.A(2002)
Time-dependent geometrical changes in a ceramic ink droplet2041
H
W
substrate
θlθr
ink
droplet
Figure1.Schematic representation of a sessile ceramic ink droplet.
(a)(b)(c)
1mm
Figure2.Illustration showing drop deposition procedure used in this investigation:(a)pendent droplet,(b)detaching droplet,and(c)detached droplet.The dotted line indicates the baseline.
(c)Substrates
Two substrates were used.The?rst(type I),silicone release paper supplied by Sterling-Lohja,Glossop,UK,has a surface free energy of20mN m?1,which is lower than the surface tension of the ink.The second(type II),supplied by O?ceSmart, Twickenham,UK,was acetate sheet used for photocopying and laser printing.It has a surface free energy of42mN m?1,which is higher than the surface tension of the ink.Details of the estimation of the surface free energies of these and other substrates are found in our previous work(Tay&Edirisinghe2001).Both substrates were immersed in methylated spirit for250s,during which any thickness changes were examined every5s using an optical microscope.No signi?cant swelling was observed in these two substrates over this period and the corresponding changes in thickness measured were negligible.
(d)Contact angle and droplet dimensions
The changes in geometry during drying of a single droplet of ink on both substrates were studied at21?C in air under natural convection with a FT?A200Dynamic Contact Angle Analyser(First Ten?A ngstroms,Portsmouth,USA).The analyser is equipped with a zoom microscope.Images of the droplets during the drying pro-cess were captured and analysed by the image-analysis software associated with the instrument.A spherical?t of the deposited droplet was assumed to calculateθ,which
Proc.R.Soc.Lond.A(2002)
2042 B.Y.Tay and M.J.Edirisinghe
20
40
6080
0200400
6008001000
time (s)
r e s i d u a l m a s s (%)Figure 3.Mass changes of ceramic ink droplets placed on type-I and type-II substrates at 21?C during evaporation.Initial droplet volumes are 7and 10mm 3on type-I and type-II substrates,respectively.is the average of the left-hand (θl )and right-hand (θr )side contact angles,the width of the base of the droplet (W )and the height of the droplet (H ),as illustrated in ?gure 1.Prior to experiments,angle measurement was checked with a 90?standard and magni?cation was calibrated against an object of known dimensions.
No pre-treatment was applied to either substrate,but new,clean sheets of the materials were stored in a closed container before use.The silicone release paper was mounted on a platform using adhesive tape.The acetate sheet did not require taping.The horizontal position of the supporting platform was con?rmed with a spirit level.An ink droplet was dispensed from a plastic syringe ?tted with a disposable blunt-ended stainless steel needle of 174μm internal diameter.The syringe was secured vertically on a stage ?tted with a stepper motor to dispense the ink onto the sub-strate.Pumping was set at a slow rate of 1mm 3s ?1to form a pendant droplet at the needle tip (?gure 2a ).The platform was then raised slowly until the substrate just touched the bottom of the droplet (?gure 2b )and subsequently lowered slowly to detach the droplet from the needle.For droplets deposited on type-I substrate,data were taken 2.5s after they were detached completely from the needle.This time period was necessary to allow the droplets to stabilize.For the type-II sub-strate,data were taken after the droplets were detached completely from the needle.At the same time,the pump was reversed to prevent any dripping of the ink onto the sessile droplet.A sequence of images of the droplet drying on the substrates was captured on video over periods of 300and 200s for type-I and type-II substrates,respectively,with adequate lighting to enhance contrast at the edge of the droplet.Images were captured at 1.2s per frame and 0.5s per frame,for type-I and type-II substrates,respectively,with a period multiplier of 1.05.Only data collected after complete detachment of the droplet were analysed.Each experiment was repeated twice on each substrate.
Proc.R.Soc.Lond.A (2002)
Time-dependent geometrical changes in a ceramic ink droplet
2043
substrate
substrate
ink droplet ink droplet Figure 4.Initial observation of ink droplets after detachment on
(a )type-I and (b )type-II substrates.
3.Results and discussion
(a )Mass loss
Figure 3shows the mass lost during evaporation.Mass loss occurred at a constant rate for ca .130s,but then was faster on the type-II substrate due to more spreading of the ink,as discussed below.
(b )Initial contact
After the droplet detached from the syringe tip and came into contact with the substrate,it spread during the ?rst 2s (?gure 4).Concurrently,there were rapid reductions in θand H on the type-II substrate,but on substrate type I a slight increase in θand H was observed.
The increase in θand H on the type-I substrate was the result of vibration in the droplet when it came into contact with the substrate.A careful examination of the droplet after initial contact in ?gure 5a shows blurring of the image at the top.Thus,the droplet was still in motion when detached from the needle tip and only stabilized after ca .2.5s (?gure 5b ).In a separate experiment,where the droplet was released from a height of 30mm,as shown in ?gure 6,it deformed severely on impact with the substrate.This phenomenon was not detected for ink droplets landing on the type-II substrate.In substrate type II,with a higher surface free energy than the ink’s surface tension,there was greater wettability,i.e.lower θ.The movement of liquid due to the increased wettability helped to establish stability rapidly when the droplet was deposited.This resulted in a higher W and lower H values to begin with Proc.R.Soc.Lond.A (2002)
2044 B.Y.Tay and M.J.Edirisinghe
(a)
(b)
Figure5.Ceramic ink droplet in contact with the type-I substrate:(a)immediately after detach-ment,and(b)a stabilized drop.The arrow shows blurring at the top in(a)and the dotted line indicates the baseline.
Figure6.Severe deformation of a ceramic ink droplet released from a height
of30mm to the type-I substrate.The dotted line indicates the baseline.
Proc.R.Soc.Lond.A(2002)
Time-dependent geometrical changes in a ceramic ink droplet 2045
Table 1.Values of volume,average contact angle θ,width W and height H of stabilized ceramic
ink droplets deposited on each substrate (see also ?gure 1)
(The average values for each substrate are given in bold and in the case of width and height are taken as W 0and H 0,respectively.)
substrate
volume (mm 3)θ(deg)W (mm)H (mm)I 1.7
36 2.970.482.0
37 3.120.532.1
38 3.070.521.9±0.2
37±13.05±0.080.51±0.03II
2.5
29 3.650.463.0
31 3.790.472.3
30 3.490.452.6±0.430±13.64±0.150.46±0.01
time (s)(d e g )θFigure 7.Variation of contact angle (θ)of ceramic ink droplets deposited on both substrates.(table 1)and,indeed,a higher W/H ratio.Thus,a stable droplet with a lower centre of gravity was accommodated on substrate type II and this dampened its vibration.
(c )Geometrical changes during drying
The volume (V )of the spherical cap of ink on the substrate is calculated by Erbil (1999)as
V =πW 32?3cos θ+cos 3θ24sin 3θ
.(3.1)After detachment from the syringe and deposition on the substrate,the volume of the stabilized ink droplet was calculated using (3.1).There was 1?variation in θProc.R.Soc.Lond.A (2002)
2046
B.Y.Tay and M.J.Edirisinghe
0.2
0.4
0.6
0.8
1.0
1.2
time (s)
W /W 0
Figure 8.Variation of normalized width (W/W 0)of ceramic ink droplets
deposited on both substrates.W 0is given in table 1.0.2
0.4
0.6
0.8
1.0
1.2
time (s)H /H 0Figure 9.Variation of normalized height (H/H 0)of ceramic ink droplets
deposited on both substrates.H 0is given in table 1.
measurements,as shown in table 1,for three droplets deposited with varying volume V 0.Theoretically,the value of θon a homogenous solid surface is independent of V (Zisman 1964)and hence in our experiment the substrate surfaces were uniform.The variation of θduring drying of the ceramic ink droplet deposited on both types of substrate is shown in ?gure 7.Variations of W and H were normalized with Proc.R.Soc.Lond.A (2002)
Time-dependent geometrical changes in a ceramic ink droplet2047
ink droplet
substrate
)
Figure10.Schematic representation of drying of a ceramic ink droplet on type-I substrate at di?erent times.The dotted and solid lines indicate the droplet contour at starting and?nishing times,respectively,of each period(a)0–10s;(b)10–75s;(c)75–120s;(d)120–160s. respect to their respective values at zero time(table1)and plotted in?gures8and9, respectively.
The droplet retained the spherical pro?le,except after120and65s for the type-I and type-II substrates,respectively.Within these periods where the spherical pro?le was maintained,θ,W and H values showed a maximum standard deviation of less than±5%,expressed as a percentage of the average value.When the spherical?t could not be used,θl,θr,W and H were measured manually and there were larger variations in the data collected with the maximum standard deviation,expressed as a percentage of the average value,amounting to±12,±5and±10%forθ,W and H,respectively.
Using variations inθ,W and H,the dynamics of shrinkage of the ceramic ink droplets on the two types of substrate are illustrated in?gures10and11and dis-cussed as follows.
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B.Y.Tay and M.J.Edirisinghe
substrate
ink droplet )
Figure 11.Schematic representation of drying of a ceramic ink droplet on type-II substrate at di?erent times.The dotted and solid lines indicate the droplet contour at starting and ?nishing times,respectively,of each period (a )0–2s;(b )2–70s;(c )70–90s.
(i)Type-I substrate
After the droplet had stabilized,it remained stationary,with W virtually con-stant (?gure 10a ).At the same time,θand H were decreasing due to evaporation.After ca .10s,the droplet started to shrink as an entity,as illustrated in ?gure 10b ,while θremained virtually constant.Concomitantly,W and H were reduced.Sub-sequently,there was a reduction in θ,with W remaining constant (parts (c )and (d )of ?gure 10).
(ii)Type-II substrate
The shrinkage of the ceramic ink droplet during drying on the type-II substrate was markedly di?erent.The high surface free energy of this substrate induced an immediate and rapid spreading of suspension soon after deposition.Thus,a rapid decrease in θand an increase in W were observed initially (?gure 11a ).This caused di?culty in printing of arrays of droplets close to one another in ink-jet printing because there is a tendency for the neighbouring droplets to coalesce.This resulted in a greater area for evaporation and H decreased at rate R 1,as shown in ?gure 9.After the initial wetting and spreading of the suspension in the ?rst 2s,W remained Proc.R.Soc.Lond.A (2002)
Time-dependent geometrical changes in a ceramic ink droplet2049
(a)
(b)
Figure12.Ceramic relics on(a)type-I substrate after295s and(b)type-II substrate after202s.The length of the bar on the top left-hand side is0.5mm.
constant throughout the rest of the experiment(?gure11b)because of pinning at the contact line of the droplet and accumulation of zirconia at the droplet’s periphery. Pinning and powder migration have also been observed during ink-jet printing,where the droplets were released with an initial velocity of22.3m s?1(Tay&Edirisinghe 2001).These restricted evaporation and drying took place only in the H direction, as evidenced by its decrease(?gure11)and the reduction inθ(?gure7).
Instead of one continuous line with very small variations in slope,as in the type-I substrate,H reduces at three di?erent linear rates R1,R2and R3for droplets deposited on type-II substrate during the period of study,with R1>R2>R3. From70to90s,H decreases at rate R3,which is the slowest,and at this stage the droplet has departed from its spherical?t apart from a central region.
(d)Shrinkage during drying
Continuation of drying of the ceramic ink droplets on both substrates(greater than 160s for type I and greater than90s for type II)resulted in signi?cant deviation from the spherical-cap shape(?gure12).The a?xation of a‘foot’around the edge of the droplet described by Parisse&Allain(1997)was also observed on both substrates. Parisse&Allain(1997)also detected an advance of particles into the middle of the Proc.R.Soc.Lond.A(2002)
2050 B.Y.Tay and M.J.Edirisinghe
Figure13.Volumetric shrinkage of ceramic ink droplets on both substrates.
V0and V represent the initial and instantaneous volumes,respectively.
droplet and this resulted in an‘outgrowth’.In this work,no‘outgrowth’was observed in the middle of the dried droplet deposited on both substrates.
The volumetric shrinkage of the ink droplets over160and90s for type-I and type-II substrates,respectively,was calculated using(3.1)and is plotted in?gure13.In the case of the type-I substrate,only data collected after the droplet has stabilized (after2.5s)are considered.
The ink droplets experienced two distinctively di?erent shrinkage rates on both substrates with SR1>SR2,as shown in?gure13.In the case of the type-II sub-strate,SR1presided over a much shorter duration compared with that of the type-I substrate.Approximately the same average volumetric shrinkage of70%was experi-enced on both substrates at the end of160s for type I and90s for type II.The ink droplets deposited on the type-II substrate thus shrank about twice as fast compared with those on the type-I substrate.
4.Conclusions
The dynamics of shrinkage of an ink containing2.5vol.%of zirconia particles was found to be di?erent on substrates of widely di?erent surface free energies compared to the surface tension of the suspension.After reaching stability,droplets deposited on a substrate with lower surface free energy than the surface tension of the ink Proc.R.Soc.Lond.A(2002)
Time-dependent geometrical changes in a ceramic ink droplet2051 (type I)shrank,with the ink–substrate interface width remaining constant while the contact angle and droplet height decreased.This was followed by a second stage of shrinkage,where the contact angle remained constant while the contact interface width and droplet height reduced.The droplet then continued to shrink further,but with a stationary contact interface width and a reducing contact angle and droplet height.When deposited on a substrate with higher surface free energy than the sur-face tension of the ink(type II),the droplet shrank rapidly with an increasing contact interface width and a decreasing contact angle and droplet height.In the second stage of shrinkage,the contact angle and droplet height decreased while maintaining a con-stant contact interface width.The overall shrinkage rate of the ceramic ink deposited on the type-II substrate was almost twice as fast.
The authors thank the Gintic Institute of Manufacturing Technology,Singapore,for supporting the PhD research programme of B.Y.T.Mrs Susan Williams and her company,Linx Printing Technologies Plc,Cambridgeshire,UK,are thanked for permitting the use of the FT?A200 system.
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