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Spreading Kinetics of Shear-Thinning Fluids in Wetting and Dewetting Modes Alain Carre´* and Florence Eustache Corning S.A., Fontainebleau Research Center, 7 bis Avenue de Valvins, 77210 Avon, France Received July 28, 1999. In Final Form: November 22, 1999 The spreading dynamics of non-Newtonian fluids, in wetting and dewetting modes, plays a key role in numerous applications in particular in coating, adhesive bonding, and printing. The very common case of the shear-thinning behavior has been considered in this study. The wetting dynamics has been studied by depositing sessile drops on glass slides. The dewetting kinetics has been evaluated by measuring the rate of growth of dry zones nucleated in an unstable liquid film formed on Teflon-coated glass slides. The spreading kinetics of a liquid on a rigid substrate is governed by viscous dissipation in the liquid, the capillary driving force being compensated for by the braking force resulting from viscous shearing in the liquid. In the case where the liquid is not Newtonian but shear-thinning or pseudoplastic, a deviation from the classical hydrodynamic theory (Newtonian behavior) for wetting is obviously observed, in particular a slower wetting kinetics corresponding to an apparent increase of the liquid viscosity as the spreading speed decreases. The shape, slightly nonspherical, of shear-thinning drops having a size smaller than the capillary length, is also simply interpreted, observing that the actual viscosity increases from the edge to the center of drops during wetting, near the solid surface. In the dewetting mode no drastic changes are observed when compared with the general behavior of Newtonian liquids. The rate of growth of dry zones nucleated in an unstable liquid film stays constant, as for Newtonian liquids, at least at the early stages of the growth of dry patches. The proposed adaptation of the hydrodynamic theory is supported by several experimental results concerning the kinetics of spreading in the wetting and dewetting modes. A good agreement is observed between the proposed theory and the results.
Introduction The spreading of liquids on solid surfaces is of considerable interest and importance in many fields of activity. The dynamic aspects of spreading are particularly relevant in several practical applications in industry, such as coating, adhesive bonding, printing, and composite manufacturing. When inks or paints are applied, they must wet their substrates before solidifying. Similarly, good spreading is required to ensure interfacial contact between two phases when applying a polymeric adhesive or in the manufacturing of composite materials. Capillary phenomena are also essential in tribology and in many biological systems, such as blood circulation and eye irrigation, involving the formation and persistency of the lachrymal film. The objective of this study is to predict how the liquid rheology impacts wetting and dewetting dynamics of nonNewtonian fluids on rigid substrates, the spreading of Newtonian liquids having been largely described in the literature from the hydrodynamic theory.1-5 The spreading dynamics of non-Newtonian fluids, in wetting and dewetting modes, plays a key role in numerous applications evoked above and in particular in coating, adhesive bonding and printing. Controlling the dewetting of liquids may be potentially more important for some industrial uses. The very common case of the shear-thinning behavior will be considered in this study. The wetting dynamics has been studied in depositing sessile drops on glass slides * Corresponding author. (1) Huh, C.; Scriven, L. E. J. Colloid Interface Sci. 1971, 35, 85. (2) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827. (3) Cox, R. G. J. Fluid Mech. 1986, 168, 169. (4) Brochard, F.; Redon, C.; Rondelez, F. C. R. Acad. Sci. 1988, 306, 1143. (5) Redon, C.; Brochard, F.; Rondelez, F. Phys. Rev. Lett. 1991, 66, 175.
and the dewetting kinetics in measuring the rate of growth of dry zones nucleated in an unstable liquid film formed on Teflon-coated glass slides. The spreading kinetics of a liquid on a rigid substrate is governed by viscous dissipation in the liquid, the capillary driving force being compensated for by the braking force resulting from viscous shearing in the liquid. In the case where the liquid is not Newtonian but shearthinning or pseudoplastic, a deviation from the classical hydrodynamic theory for wetting is observed. The slightly nonspherical shape of shear-thinning drops having a size smaller than the capillary length may be also simply interpreted by calculating that the actual viscosity increases from the edge to the center of drops in the wedge shape formed during wetting near the advancing liquid front. No drastic changes are observed in the dewetting mode as compared with the general behavior of Newtonian liquids. The rate of growth of dry zones nucleated in an unstable liquid film stays constant, as for Newtonian liquids, at least at the early stages of the growth of dry patches. In this paper, an adaptation of the hydrodynamic theory is developed to take into account the specific behavior of shear-thinning liquids. Theoretical 1. Wetting Dynamics of a Newtonian Liquid. The viscous dissipation in a liquid wedge has been described for Newtonian liquids by the hydrodynamic theory.1-3 Its principal results will first reviewed. During drop spreading, the driving force (“motor”), Fm, is compensated by the braking force (“brake”), Fv, controlling the kinetics of wetting. Fm results from the noncompensated surface tension forces. It is given, per unit of length of the triple (solid/liquid/vapor) line,
10.1021/la991021d CCC: $19.00 © 2000 American Chemical Society Published on Web 01/15/2000
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following the Ostwald law, where a and n are two constants. The power factor n is less than 1 (for a Newtonian liquid, n ) 1 and a is the viscosity). Therefore, the Navier-Stokes equation becomes
Figure 1. Schematic diagram of viscous flow in a Newtonian liquid wedge.
by the expression
Fm ) γ[cos θ0 - cos θ(U)]
3ηlU θ(U)
v(z) )
(3)
where h is the height of liquid above the solid surface (Figure 1). Therefore, the wetting dynamics of a drop of a Newtonian liquid satisfies the following relationship (Fm ) Fv)
cos θ0 - cos θ(U) )
3ηlU γθ(U)
(4)
which becomes, in logarithmic form:
log[cos θ0 - cos θ(U)] ) log
( )
leads to
(∂P∂x )
(z - h)1/n
( )
U 3ηl + log γ θ(U)
(5)
∂P ∂τ(z) ) ∂x ∂z
(6)
where x is the distance from the virtual sharp edge of the drop (Figure 1). P is the pressure and τ(z) the shear stress at a height z above the solid surface. A shear-thinning liquid is characterized by a shear stress dependence on the shear rate as
( )
n
(7)
∂v(z) ∂z
1/n
)a
(9)
The second integration with the boundary condition of no slip at the solid surface, (v(z) ) 0 for z ) 0), gives the following expression for v(z):
1 ∂P 1 a1/n 1 + 1 ∂x n
( ) )
(
1/n
[(hz - 1)
h1+(1/n)
1+(1/n)
]
+ (-1)1/n
(10)
In expressing the liquid flow Q from 0 to h, which is equal to the product Uh, we obtain the speed profile in x as
1 2+ n z U -1 v(z) ) (-1)1/n 1 + 1 h n
( (
) [( )
1+(1/n)
)
]
+ (-1)1/n
(11)
(For n ) 1, corresponding to a Newtonian liquid, eq 11 reduces to eq 3.) The viscous energy dissipated per unit of length of the triple line (S/L/V) and time is obtained by integrating the product τ(z) ∂v(z)/∂(z) from 0 to h and then from xm to R (xm , R). Considering that this dissipated energy is equal to FvU, we finally obtain
Fv ) aR
2. Wetting Dynamics of a Shear-Thinning Liquid. The above theory has been extended to the case of a shearthinning liquid. The calculation of Fv for a shear-thinning behavior has been developed by starting from the NavierStokes equation. This is written as written as
∂v(z) τ(z) ) a ∂z
∂v(z) | )0 ∂z h(x) ) h
v(z) )
3U (2hz - z2) 2 2h
(8)
|
(2)
where η is the liquid viscosity and l is the logarithm of the ratio of the drop radius R, divided by a microscopic cutoff length, xm, of the order of a molecular length. Around xm, the liquid wedge is curved by long-range van der Waals forces. In this analysis, the speed gradient has a parabolic distribution. The boundary conditions are assumed to be: no slip at the solid surface and no shear at the free liquid surface. This leads to a distribution of speed, v(z), as a function of distance from the solid surface, z, given by
n
The first integration of eq 8 with the boundary condition of no shear at the free liquid surface
(1)
where γ is the liquid surface tension, θ(U) the dynamic contact angle at a spreading speed U, and θ0 the static contact angle at the solid/liquid/vapor (SLV) triple line at equilibrium (U ) 0. U ) dR/dt, where R is the drop radius at time t). For a Newtonian liquid, it has been demonstrated2 that the viscous braking force, Fv, per unit of length of the triple line, is equal to
Fv )
( )
∂P ∂ ∂v(z) )a ∂x ∂z ∂z
(2 + n1)
( )
U (1 - n) θ(U)
1-n
n
with n < 1
(12)
Therefore, the braking force, Fv, depends now of the ratio U/θ(U) to the power n (n < 1), replacing the linear dependence seen for Newtonian liquids. Considering the equality between the driving and braking forces, we obtain the following equation describing wetting kinetics
γ[cos θ0 - cos θ(U)] ) K
( ) U θ(U)
n
(13)
where K, which contains R and a and n may be considered constant in the experiments described below. Therefore, the wetting dynamics of a shear-thinning fluid satisfies
cos θ0 - cos θ(U) )
( )
K U γ θ(U)
n
(14)
which will be considered under the logarithmic form:
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log[cos θ0 - cos θ(U)] ) n log
Carre´ and Eustache
( )
()
U K + log γ θ(U)
(15)
When n ) 1 (Newtonian fluid), this last equation is similar to eq 5. 3. Dewetting Dynamics of Newtonian Liquids. Let us consider a circular puddle of liquid, L, on solid, S, in the presence of liquid vapor, V. The puddle is of radius R0 and small initial thickness, e0. We suppose that holes spontaneously nucleate in the puddle and grow with radius r(t) as time, t, passes because the equilibrium contact angle, θ0, is nonzero. The liquid is unstable as a wetting film. The equilibrium thickness of a film, ec, is given by4,5
ec ) 2k-1 sin
θ0 2
(16)
where k-1 is the Laplace or capillary length (k-1 ) (γ/ Fg)1/2, in which F is liquid density and g gravitational acceleration). When the film thickness, e0, is less than ec, then it is unstable and holes may nucleate spontaneously from thermal-induced fluctuations. We will consider the range of r(t) much smaller than R0. From simple considerations of the local force balance, when ec , e0, the total driving force for dewetting per unit length of triple line, Fm, is given by
Fm ) γ + γSL - γSV ) γ(1 - cos θ0)
(17)
(where γSV and γSL are the solid/vapor and solid/liquid interfacial tension.) At the early stage of dewetting, when r(t) , R0, a rim is formed around dry dewetting zones, and the braking force results mainly from shearing of the liquid contained in the liquid rim surrounding a dry zone (see Figure 2). The profile of the rim is not very different from the profile of a spreading drop, at least at the early stages of the dewetting process when the width of the rim stays below k-1, neglecting gravitation. In these conditions, the two edges of the rim participate in the dissipation,4,5 and the total braking force, Fv, for a Newtonian liquid satisfies
Fv ≈
(18)
γθ(U)(1 - cos θ0) 6ηl
(19)
Therefore, the dewetting speed of a Newtonian liquid appears to be constant, and since U ) dr(t)/dt, where r(t) is hole, or dry zone radius, eq 19 leads to
r(t) ≈ θ(U)
[
controlled only by surface tension forces and the dewetting speed is constant.6 4. Dewetting Dynamics of Non-Newtonian Fluids. Condition and driving force for dewetting of a nonNewtonian fluid are essentially the same as for a Newtonian liquid. However, as for the wetting kinetics, the difference is in the braking force resulting from the shearing response of the material. In this case, the same arguments developed for wetting apply for dewetting and the braking force may be written as
( )
Fv ≈ 2K
U θ(U)
n
(21)
in considering that the two edges of the rim participate in the dissipation. The dewetting kinetics of a shear-thinning fluid is then deduced
U ≈ θ(U)
[
]
γ(1 - cos θ0) 2K
1/n
(22)
which leads to a radius variation of the dry zone described by
r(t) ≈ θ(U)
[
]
γ(1 - cos θ0) 2K
1/n
t
(23)
It can be deduced that, as for Newtonian liquids, the dewetting speed of a shear-thinning fluid is constant (at least during the early stages of the dewetting process when the rim has a width, λ, stays smaller than the capillary length k-1). Experimental Section
6ηUl θ(U)
assuming that the dynamic contact angles are equal at the two edges of the rim. Equating the driving and braking forces, we obtain
U≈
Figure 2. Formation of a dry zone (patch) in an unstable liquid film on a rigid substrate.
]
γ(1 - cos θ0) t 6ηl
(20)
However, as mentioned above, the growth of dry zones is accompanied by a rim of excess liquid with width λ (Figure 2). As the dewetting proceeds, λ increases. For short times and λ < k-1, the growth of dry patches is
Clean microscope glass slides have been chosen as smooth, flat, and horizontal rigid substrates for wetting dynamic experiments. The slides were cleaned with ethanol under ultrasonic agitation and dried by blowing with dry nitrogen. For dewetting experiments, the glass slides were coated with a thin layer (≈0.1 µm) of Teflon AF (du Pont de Nemours) as shown in Figure 2. Silicone oil (PDMS, Rhodorsil 1000) has been chosen as a model of a Newtonian liquid. Its viscosity is 1 Pa‚s, its surface tension is 21.2 mN/m, and its molecular weight Mw is 28 000. The rheological behavior of this liquid was modified by incorporating 5 wt % of hydrophobic colloidal silica (TS 720, Cab-O-Sil), with a particle size of 15 nm. This fluid (PDMS + silica) has the same surface tension as PDMS and displays shear-thinning behavior. Another fluid having a shear-thinning behavior has been considered. This liquid has a practical interest. It is a transparent acrylic typographic ink pigmented with nanometric size dies. This fluid has a surface tension of 28 mN/m. The rheological behavior of every liquid has been characterized with a cone/plate rheometer (Carri-med) at imposed shear stress, (6) The width of the rim, λ, increases with time, t, as t1/2 until the rim becomes flat due to gravitation. At this point, there is a transition to reach a long time gravity controlled regime. The corresponding growth velocity, U, decreases with time, t, as URt-1/2, whereas λ still increases as t1/2.4
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Langmuir, Vol. 16, No. 6, 2000 2939
Figure 3. Rheological behavior of PDMS, PDMS + silica and ink (Carri-med cone/plate rheometer).
Figure 4. Wetting dynamics of Newtonian and shear-thinning fluids.
τ (τ varying from 0 to 300 Pa). The rheological properties of the above three fluids are presented in Figure 3, where the shear stress, τ, is plotted as a function of the shear rate, γ˘ . The results confirm that the PDMS displays Newtonian behavior and that the two other fluids show a shear-thinning behavior. The three fluids satisfy the following relationships:
PDMS: τ ) 1.04γ˘
(Newtonian)
PDMS + silica: τ ) 9.64γ˘ 0.79 ink: τ ) 16.80γ˘
0.62
(shear-thinning)
(shear-thinning)
Contact angle measurements for the wetting dynamic study were obtained by using a contact angle goniometer (Rame´-Hart A-100) equipped with a video camera connected to a video recorder and a printer. The contact angles, θ(U), and the drop radii, R(t), were measured as a function of time, t, after deposition. It was possible to analyze up to 24 frames/s. The volume of liquid drops was kept constant at 0.1 µL. The dewetting kinetics of liquids on Teflon-coated slides was followed using a video camera placed behind a low power microscope. The device allowed us to follow the occurrence and evolution of dewetting holes or dry patches in 0.1 mm thick liquid puddles. Liquid puddles were formed after having deposited a 50 mm diameter adhesive ring (R0) of 0.1 mm thickness on the Teflon-coated slides. This adhesive flat ring acted as spacer. A microscope slide was drawn over the liquids to obtain a liquid film of about 0.1 mm thickness. At this thickness, the liquid films were unstable being much less than the equilibrium values, ec, of 1-2 mm for the liquids considered. Nucleation of dry patches occurred spontaneously, presumably due to surface defects or thermal fluctuations. The evolution and growth of dry zones was followed by measuring their radius, r(t). In our wetting and dewetting experiments, inertial effects are negligible. The Weber number (ratio of inertia forces on surface tension) and Reynolds number (ratio of inertia forces on viscous forces) are always less than 10-3.
Results and Interpretation 1. Wetting Dynamics. The dynamic contact angles of PDMS, PDMS + silica and ink have been measured over a very large range of spreading rates comprised between 10-4 and 10-7 m/s. PDMS and PDMS + silica exhibit a near-zero contact angle at equilibrium, i.e., θ0 ) 0. The ink does not fully wet the glass, having an equilibrium contact angle θ0 ) 21.6°. Following the form of equations 5 and 15, we plot the difference cos θ0 - cos θ(U) as a function of U/θ(U), on logarithmic scales in Figure 4. For each fluid, a linear relationship between the two quantities is obtained in agreement with eqs 5 and 15. For the liquid expected to show Newtonian behavior (PDMS), the slope of the linear function is equal to 0.98. This is very close to the expected value of 1 for a Newtonian liquid. However, for the two other fluids, the gradients are significantly less than 1,
Figure 5. Image of observed aspherical profile of an ink drop. The profile is related to the shear-thinning behavior of the fluid. The apparent viscosity is lower at higher shear (from the center to the edge).
which is in good agreement with their shear-thinning behavior. The slope, n, is equal to 0.70 and 0.74 for the PDMS + silica and ink fluids, respectively. These values are fairly close to the exponent n obtained from the rheological characterization of these two fluids (0.79 and 0.62 respectively). Although the agreement is not perfect, the results of the wetting dynamics study confirm the particular behavior of the fluids, as observed with the rheometer, and lead to similar values for the factor n. The agreement is excellent for the Newtonian liquid (n ) 1 vs 0.98). For PDMS, the constant term of eq 5 allows one to estimate the cutoff length, xm, as being on the order of 1.8 nm (the analytical form of the constant K does not allow the estimation of xm for shear-thinning fluids). 2. Drop Shape. An unusual phenomenon regarding the drop shape of the shear-thinning fluids has been observed (volume ) 0.1 µL). While the liquid drops of PDMS were perfectly spherical as expected for R < 2k-1, this was not the case for the PDMS + silica and ink fluids. For the last two liquids, the drop adopted a nonspherical form similar to the shape of a “half lemon”, as illustrated by the image of an ink drop shown in Figure 5. The liquid wedge is slightly concave. This aspherical profile may be attributed to the shear-thinning behavior of the liquid drop. The apparent viscosity appears to be lower where the shear stress is higher, namely in the wedge formed near the edge of the drop where it meets the solid surface. A simple analysis of the drop profile can be performed by considering the variation of the apparent viscosity of a shear-thinning fluid from the edge of the drop where the shear stress is maximum to the center of the drop where the shear stress is minimum. At a fixed value of x (Figure 1), we can define a average value of the fluid viscosity, η(x). This parameter may be defined as
η(x) )
∫0h(x)η(x,z) dz
1 h(x)
(24)
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Carre´ and Eustache
where η(x,z) is defined as the apparent viscosity in (x,z). This is calculated by
τ(x,z) ) aγ˘ (x,z)n
(25)
τ(x,z) ) η(x,z)‚γ˘ (x,z)
(26)
which leads to the definition of the apparent viscosity in (x,z) as
η(x,z) ) a‚γ˘ (x,z,)n-1
(27)
We will consider that the shear stress can be estimated from the flow profile of a Newtonian liquid (eq 3) and is approximately
γ˘ (x,z) )
dv(x,z) 3(h - z) ) U dz h2
(28)
Figure 6. Dewetting dynamics of fluid thin films on Tefloncoated glass slides.
U1(PDMS)
Realizing that h ≈ xθ(U), we obtain
xθ(U) - z U x2θ(U)2
γ˘ (x,z) ≈ 3
U2(PDMS + silica) (29)
Equations 24, 28, and 30 yield the average viscosity as a function of h at the abscissa point x:
η(x) ≈
( )
a 3U n h(x)
n-1
(30)
For simplicity, we will consider the case where the equilibrium contact angle is near zero. In this condition, it has been demonstrated that the dynamic contact angle of a Newtonian fluid satisfies the following equation7
θ(U)3 )
6ηlU γ
(31)
Expressing θ(x1)3 as h(x1)3/x13 and θ(x2)3 as h(x2)3/x23 and replacing η(x1) and η(x2) by their expressions as a function of h(x1) and h(x2) from eq 31, we finally obtain
h(x1) h(x2)
≈
() x1 x2
3/(n+2)
(32)
Given that h(0) ) 0, this expression may be rewritten as h(x) ≈ R(x)3/(n+2). With n ) 0.79 (PDMS + silica), the liquid profile near the drop edge follows approximately the form h(x) ) R(x)1.08. This explains the “half-lemon” shape profile seen in Figure 5. For a Newtonian liquid, n ) 1, and the liquid wedge profile satisfies the expression h(x) ) Rx. 3. Dewetting Dynamics. The rates of growth of dry zones nucleated in the three fluids (PDMS, PDMS + silica, ink) on the Teflon-coated glass slides are given in Figure 6. As predicted by the proposed theory (eqs 20 and 23), the radius of dry zones increases linearly with time after nucleation. Therefore, Newtonian and shear-thinning fluids behave similarly in the dewetting of thin films. The dewetting rate for PDMS + silica is 0.030 mm/s, as compared with 0.085 mm/s for PDMS. The equilibrium contact angle of these two fluids being identical on Tefloncoated glass, it can be deduced that the driving force Fm is the same in both cases and that the lower speed for PDMS + silica comes from a higher braking force Fv. It can be deduced that
)
θ(U1) η2* θ(U2) η1
(33)
where η2* is the apparent viscosity of PDMS + silica. Since the equilibrium contact angles, θ0, are the same for both liquids on Teflon-coated glass, we can estimate the apparent viscosity of PDMS + silica, η2*, as about η1(U1/U2) ) 2.8 Pa‚s. Therefore, filing PDMS with 5 wt % of hydrophobic colloidal silica particles is equivalent to multiplying the viscosity of PDMS by a factor of 2.8 when thin films of these fluids dewet on Teflon-coated glass. Comparing the dewetting dynamics of PDMS, PDMS + silica and ink is not as simple. Ink dewets quicker than PDMS and PDMS + silica. This result may be understood realizing that the driving force, Fm, is larger (21.2 mN/m for ink vs 7.4 mN/m for PDMS). In addition, the dynamic receding contact angles are probably very different, given that the equilibrium contact angles, θ0, are very different (θ0 ) 49.5° for PDMS and 76° for ink). As a second explanation for a higher dewetting speed for ink when compared to PDMS and PDMS + silica, it can be assumed that the braking force is much smaller for the ink, probably due to the higher receding dynamic contact angle resulting in a lower shear in the liquid wedge. Taking U1 and U2 as the dewetting speeds of ink (index 1) and PDMS + silica (index 2) respectively, an estimation of the dewetting dynamic contact angles θ1(U1) and θ2(U2) may be obtained by considering that
[
]
[
]
U1 ) θ1(U1)
γ1(1 - cos θ01) 2K1
1/n1
and
U2 ) θ2(U2)
γ2(1 - cos θ02) 2K2
1/n2
and admitting that n1 ≈ n2 ) 0.7, and K1 ≈ K2. This leads to θ1(U1)/θ2(U2) ≈ 2.3. Unfortunately our experimental device is not able to give us a measurement of the dynamic receding contact angles θ1(U1) and θ2(U2). However, for θ1(U1) to be < 76° (θ01) we can deduce that θ2(U2) should be lower than 34°. Discussion and Conclusion The hydrodynamic theory of liquid spreading developed for a Newtonian liquid1-3 has been generalized to shear-
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As a further consequence of the shear-thinning behavior of a fluid, a simplified theoretical analysis has been proposed to explain the observed aspherical drop shape for a spreading drop. Hence, we show that the kinetics of wetting and the shape of drops give direct information on the rheological behavior of fluids. In conclusion, the adaptation of the hydrodynamic theory to the case of non-Newtonian fluids has allowed us to interpret the dynamics of wetting and dewetting of shear-thinning liquids and to explain the peculiar drop shapes observed for these liquids. The results of the overall study are of particular importance for industrial applications and natural systems where complex fluids are often used.
thinning non-Newtonian fluids. This new theory has been validated in wetting and dewetting modes. The wetting kinetics has been studied by following the spreading of small drops on a glass substrate. The dewetting dynamics refers to the rate of growth of dry zones nucleated in an unstable liquid film spread on Teflon-coated glass. The main result for a shear-thinning material is that for liquid spreading the braking force due to liquid shearing in a liquid wedge is no longer proportional to the spreading speed. The braking force is a function of the spreading rate to the power n, which is the power factor found in law of Ostwald. The proposed theory is more general than the classic one. It includes the case of Newtonian liquid, for which the power factor is unity. It is interesting to observe that the spreading of non-Newtonian fluids on rigid substrates is not the only case where a linear dependence of the braking force with spreading speed is no longer satisfied (gradient of eq 5 lower than 1). This phenomenon is also seen when Newtonian liquids spread on soft viscoelastic materials, forming a wetting ridge in wetting and dewetting modes.8-10 A reasonable agreement is obtained between the independent rheological characterization of fluids and their wetting and dewetting behavior.
LA991021D
(7) Hoffman, R. J. Colloid Interface Sci. 1975, 35, 85. (8) Carre´, A.; Gastel, J. C.; Shanahan, M. E. R. Nature 1996, 379, 432.
(9) Carre´ A.; Shanahan M. E. R. Langmuir 1995, 11, 3572. (10) Carre´, A.; Shanahan, M. E. R. J. Colloid Interface Sci. 1997, 191, 141.
Acknowledgment. Authors thank Professor M. Fermigier (ESPCI, Ecole de Chimie et Physique Industrielles de la Ville de Paris) for having suggested the calculation of viscous dissipation from the Navier-Stokes equation, and Professor M. E. R. Shanahan (ENSMP, Ecole des Mines de Paris, Centre des Mate´riaux) for helpful discussions. Contribution of Dr. William Birch is also acknowledged for his constructive comments.
