Contact line motion and dynamic wetting of nanofluid solutions

The effect that nanoparticles play in the spreading of nanofluids dynamically wetting and dewetting solid substrates is investigated experimentally, using 'drop shape' analysis technique to analyse aluminium-ethanol contact lines advancing and receding over hydrophobic Teflon-AF coated substrates. Results obtained from the advancing/receding contact line analysis show that the nanoparticles in the vicinity of the three-phase contact line enhance the dynamic wetting behaviour of aluminium-ethanol nanofluids for concentrations up to approximately 1% concentration by weight. Two mechanisms were identified as a potential reason for the observed enhancement in spreading of nanofluids: structural disjoining pressure and friction reduction due to nanoparticle adsorption on the solid surface. The observed 'lubricating effect' that the nanoparticles seem to be inducing is similar to the 'superspreading' effect for surfactant solutions spreading on hydrophobic surfaces, up to a concentration (weight) of approximately 1%, could be a result of the predicted enhanced wetting behaviour. Indeed, Trokhymchuk et al. [Langmuir, 2001, 17, 4940] observed a solid-like ordering of nanoparticles in the vicinity of the three-phase contact line, leading to an increased pressure in the fluid 'wedge'. This increased pressure leads to a pressure gradient which causes the nanofluids to exhibit enhanced wetting characteristics. Another possible cause for the observed increase in advancing/receding contact line velocity could be deposition of nanoparticles on the solid surface in the vicinity of the three-phase contact line resulting in the nanofluid effectively advancing over aluminium rather than Teflon-AF, or the contact line 'rolling' over nanoparticles at the three-phase contact line due to sphericity of nanoparticles. For either of these to be the case, the nanoparticle effect at the three-phase contact line would have to be enhanced for the lower concentration in the same way that it would have to be for the increased pressure in the fluid 'wedge'.     

Spreading of nanofluids driven by the structural disjoining pressure gradient

This paper discusses the role of the structural disjoining pressure exerted by nanoparticles on the spreading of a liquid film containing these particles. The origin of the structural disjoining pressure in a confined geometry is due to the layering of the particles normal to the confining plane and has already been traced to the net increase in the entropy of the system in previous studies. In a recent paper, Wasan and Nikolov (Nature, 423 (2003) 156) pointed out that the structural component of the disjoining pressure is strong enough to move a liquid wedge; this casts a new light on many applications-most notably, detergency. While the concept of spreading driven by the disjoining pressure is not new, the importance of the structural disjoining pressure arises from its long-range nature (as compared to the van der Waals' force), making it an important component of the overall force balance near the contact line. In this paper, we report on a parametric study of the spreading phenomena by examining the effects of nanoparticle size, concentration and polydispersity on the displacement of an oil-aqueous interface with the aqueous bulk containing nanoparticles. The solution of the extended Laplace-Young equations for the profile of the meniscus yields the position of the nominal contact line under the action of the structural disjoining pressure. Simulations show that the displacement of the contact line is greater with a high nanoparticle volume fraction, small particles for the same volume fraction, monodispersed (in size) particles rather than polydispersed particles and when the resisting capillary pressure is small, i.e., when the interfacial tension is low and/or the radius of the dispersed phase drop/bubble is large.     

Effect of hydrophobicity on the stability of the wetting films of water formed on gold surfaces

We have developed a methodology that can be used to determine disjoining pressures (Π) in both stable and unstable wetting films from the spatial and temporal profiles of dynamic wetting films. The results show that wetting films drain initially by the capillary pressure created by the changes in curvature at the air/water interface and subsequently by the disjoining pressure created by surface forces. The drainage rate of the film formed on a gold surface with a receding contact angle (θ(r)) of 17° decreases with film thickness due to a corresponding increase in positive Π, resulting in the formation of a stable film. The wetting film formed on a hydrophobic gold with θ(r)=81° drains much faster due to the presence of negative Π in the film, resulting in film rupture. Analysis of the experimental data using the Frumkin-Derjaguin isotherm suggests that short-range hydrophobic forces are responsible for film rupture and long-range hydrophobic forces accelerate film thinning.     

Spreading of a suspension drop on a horizontal surface

Experimental studies were performed on the contact line motion of a suspension of PS particles on a glass surface. The base liquids were silicone oil and glycerin. The particle size was in the range of 1-6 μm and the particle loading was 0.5-5 vol %. The drop shape was determined by using a drop image and its reflection and the drop outline was traced to the subpixel level. The Tanner-Voinov-Hoffman relation was valid for suspensions as well as for pure liquids. Silicone oil suspensions showed almost no noticeable change compared with the pure fluid. Glycerin suspensions showed an increase in contact line speed at low particle loading. The difference was due to the microstructure change at the contact line region, and the microstructure change was originated from the wetting characteristics of particles. Particle alignment occurred during the spreading stage for partially wetting particles. The contact line showed a stop-and-go fashioned motion due to surface irregularities. This result can be used as the boundary condition at the contact line in the numerical simulation of suspension spreading.     

Spreading of a fluid phase on a spherical surface

The adsorption between a liquid drop and a micro-particle in an air or an air bubble and a micro-particle in water is dominated by liquid-solid or air-solid interfacial tension and wetting area of the liquid or air on the particle surface. The wetting area is determined by the spreading of the liquid drop or the bubble on the micro-particle. To explore this spreading, a wetting model of a fluid phase on a spherical particle was built. According to the theoretical results, the contact angle is constant when a fluid phase spreads on a spherical solid surface; the micro-particle can not submerge under a fluid when only interfacial tensions are involved and the wetting is not a complete wetting. The corresponding experiments were performed to confirm the theoretical results.     

A model of nanofluids effective thermal conductivity based on dimensionless groups

Thermal conductivity is an important parameter in the field of nanofluid heat transfer. This article presents a novel model for the prediction of the effective thermal conductivity of nanofluids based on dimensionless groups. The model expresses the thermal conductivity of a nanofluid as a function of the thermal conductivity of the solid and liquid, their volume fractions, particle size and interfacial shell properties. According to this model, thermal conductivity changes nonlinearly with nanoparticle loading. The results are in good agreement with the experimental data of alumina-water and alumina-ethylene glycol based nanofluids.     

Spreading of liquid drops over dry surfaces

Spreading of thin, axisymmetric, non-volatile, Newtonian liquid drops over a dry, smooth, flat solid surface is considered both theoretically and experimentally in the case of complete wetting. The drop profile is solved analytically by matching the “outer” solution for large film thicknesses, where only the capillary effects are important, with the “inner” solution for small film thicknesses, where the viscous and disjoining pressure effects are comparable to capillary effects. It is shown that the apparent radius of the wetted spot, the apex height of the drop, and the apparent advancing dynamic contact angle follow different power laws in time and the advancing dynamic contact angle follows a power law in capillary number. Both the prefactor and the exponent of each power law are derived theoretically. Good agreement between the theory predictions and experimental measurements is shown for both the prefactor and exponent of each power law. It is necessary to emphasize that the theory suggested does not include any fitting parameters.     

Stability of triglyceride liquid films on hydrophilic and hydrophobic glasses

Wetting and dewetting of solid surfaces by oily fluids were investigated in terms of the stability of the liquid film formed between an air bubble and the solid surface. With the objective of understanding how molecules with low polarity but relatively complex molecular structure behave at the solid/liquid interface, three liquid triglycerides with different chain length and saturation were chosen, namely, tributyrin, tricaprylin, and triolein. Tributyrin and tricaprylin exist in milkfat while triolein is present in vegetable oils. The stability of the liquid films may be inferred from the shape of the disjoining pressure isotherms, which represent the dependence of the disjoining pressure on the film thickness. Disjoining pressure isotherms for films of the three triglycerides on hydrophilic and hydrophobic glasses were obtained using a recently developed apparatus, based on the interferometric technique. The experimental curves are compared with the theoretical predictions of London-Hamaker. The deviations between theory and experiment are interpreted in terms of a structural component of the disjoining pressure. All triglycerides form metastable films on both hydrophilic and hydrophobic glasses which means that for disjoining pressures higher than a critical value, pi(c), a wetting transition occurs and the film ruptures. The mechanisms for film rupture are discussed and a correlation between film stability and the apolar (Lifshitz-van der Waals) and the polar components of the spreading coefficient is proposed.     

Review of non-reactive and reactive wetting of liquids on surfaces

Wettability is a tendency for a liquid to spread on a solid substrate and is generally measured in terms of the angle (contact angle) between the tangent drawn at the triple point between the three phases (solid, liquid and vapour) and the substrate surface. A liquid spreading on a substrate with no reaction/absorption of the liquid by substrate material is known as non-reactive or inert wetting whereas the wetting process influenced by reaction between the spreading liquid and substrate material is known as reactive wetting. Young's equation gives the equilibrium contact angle in terms of interfacial tensions existing at the three-phase interface. The derivation of Young's equation is made under the assumptions of spreading of non-reactive liquid on an ideal (physically and chemically inert, smooth, homogeneous and rigid) solid, a condition that is rarely met in practical situations. Nevertheless Young's equation is the most fundamental starting point for understanding of the complex field of wetting. Reliable and reproducible measurements of contact angle from the experiments are important in order to analyze the wetting behaviour. Various methods have been developed over the years to evaluate wettability of a solid by a liquid. Among these, sessile drop and wetting balance techniques are versatile, popular and provide reliable data. Wetting is affected by large number of factors including liquid properties, substrate properties and system conditions. The effect of these factors on wettability is discussed. Thermodynamic treatment of wetting in inert systems is simple and based on free energy minimization where as that in reactive systems is quite complex. Surface energetics has to be considered while determining the driving force for spreading. Similar is the case of spreading kinetics. Inert systems follow definite flow pattern and in most cases a single function is sufficient to describe the whole kinetics. Theoretical models successfully describe the spreading in inert systems. However, it is difficult to determine the exact mechanism that controls the kinetics since reactive wetting is affected by a number of factors like interfacial reactions, diffusion of constituents, dissolution of the substrate, etc. The quantification of the effect of these interrelated factors on wettability would be useful to build a predictive model of wetting kinetics for reactive systems.     

Simultaneous spreading and evaporation: Recent developments

The recent progress in theoretical and experimental studies of simultaneous spreading and evaporation of liquid droplets on solid substrates is discussed for pure liquids including nanodroplets, nanosuspensions of inorganic particles (nanofluids) and surfactant solutions. Evaporation of both complete wetting and partial wetting liquids into a nonsaturated vapour atmosphere are considered. However, the main attention is paid to the case of partial wetting when the hysteresis of static contact angle takes place. In the case of complete wetting the spreading/evaporation process proceeds in two stages. A theory was suggested for this case and a good agreement with available experimental data was achieved. In the case of partial wetting the spreading/evaporation of a sessile droplet of pure liquid goes through four subsequent stages: (i) the initial stage, spreading, is relatively short (1–2 min) and therefore evaporation can be neglected during this stage; during the initial stage the contact angle reaches the value of advancing contact angle and the radius of the droplet base reaches its maximum value, (ii) the first stage of evaporation is characterised by the constant value of the radius of the droplet base; the value of the contact angle during the first stage decreases from static advancing to static receding contact angle; (iii) during the second stage of evaporation the contact angle remains constant and equal to its receding value, while the radius of the droplet base decreases; and (iv) at the third stage of evaporation both the contact angle and the radius of the droplet base decrease until the drop completely disappears. It has been shown theoretically and confirmed experimentally that during the first and second stages of evaporation the volume of droplet to power 2/3 decreases linearly with time. The universal dependence of the contact angle during the first stage and of the radius of the droplet base during the second stage on the reduced time has been derived theoretically and confirmed experimentally. The theory developed for pure liquids is applicable also to nanofluids, where a good agreement with the available experimental data has been found. However, in the case of evaporation of surfactant solutions the process deviates from the theoretical predictions for pure liquids at concentration below critical wetting concentration and is in agreement with the theoretical predictions at concentrations above it.     

Spreading Dynamics of Polydimethylsiloxane Drops: Crossover from Laplace to Van der Waals Spreading

The spreading dynamics of small polydimethylsiloxane (PDMS) drops was studied on substrates with varying surface energies. For experimental parameters near the wetting transition, we observed small PDMS drops of different drop volumes as a function of time using interference video microscopy. While for large drops the contact angle θ decreases with the well-established power-law relation θ approximately t(-0.3) (Tanner's law), the effect of dispersive van der Waals (VW) interactions must be taken into account when interpreting the evolution of small drops. Two signatures of the VW forces are observed. For a positive Hamaker constant, the disjoining pressure acts as an additional driving force, leading to an acceleration of droplet spreading as soon as the drop height becomes comparable to the range of the VW interactions. In addition, a precursor film forms ahead of the contact line, leading to an apparent volume loss, particularly noticeable for very small drops. Contact line pinning may be a problem and we describe its effect on our experimental results. We present a theory that discusses the interplay of surface tension and VW forces in the case of a spreading drop. This model predicts a new spreading regime for very thin drops, in agreement with our experimental results. Copyright 2001 Academic Press.     

Investigation of the isotherms of the disjoining pressure of wetting films of binary nonionic solutions by the ellipsometric method

The paper deals with an experimental investigation into the influence of the second component on the thicknesses of the wetting films of a nonionic solvent. A technique has been developed for the production of pure, smooth, thin glass substrates for wetting liquid films.

The use of these glass substrates enabled us to exclude the influence on the experimental results of such noncontrollable factors as roughness and pollution of the substrate surface. The isotherms of the disjoining pressure of wetting films of a number of two-component mixtures of nonionic liquids on glass substrates were experimentally determined. The film thicknesses were measured by an ellipsometric method; the disjoining pressure for the film was preset by adjusting the pressure of solvent vapours. The results obtained demonstrate a qualitative agreement with the theory of the adsorption component of disjoining pressure developed by Derjaguin and Churaev.

It is also shown that even very small additions of a polar substance to a nonpolar solvent may cause a marked change in the thickness of films. In addition to adopting the theory of the adsorption component of disjoining pressure, certain assumptions are made about the formation of the structural component resulting from the addition of a polar component to quantitatively describe the results obtained. The contribution of the adsorption and structural components of disjoining pressure to the stability of films of solution is estimated.     

Wetting of TiC by Al-Cu alloys and interfacial characterization

The wetting behavior and the interfacial reactions that occurred between molten Al-Cu alloys (1, 4, 8, 20, 33, and 100 wt% Cu) and solid TiC substrates were studied by the sessile drop technique in the temperature range of 800-1130 degrees C. The effect of wetting behavior on the interfacial reaction layer was studied. All the Al-Cu alloys react with TiC at the interface forming an extensive reaction layer. The interface thickness varied with the samples, and depends on the temperature, chemical composition of the alloy and the time of the test. Wetting increases with increasing concentration of copper in the Al-Cu alloy at 800 and 900 degrees C. In contrast, at higher temperature such as 1000 degrees C wetting decreases with increasing copper content. The spreading kinetics and the work of adhesion were evaluated. The high values of activation energies indicated that spreading is not a simple viscosity controlled phenomenon but is a chemical reaction process. The spreading of the aluminum drop is observed to occur according to the formation of Al4C3, CuAl2O4, CuAl2, TiCux mainly, leading to a decreases in the contact angle. As the contact angle decreases the work of adhesion increases with increasing temperature. Al-Cu/TiC assemblies showed cohesive fracture corresponding to a strong interface. However, using pure Cu the adhesion work is poor, and the percentage of cohesion work is also too low (27-34%).     

Truncated versus extended microfilms at a vapor-liquid contact line on a heated substrate

The microstructure of a contact line formed by a liquid and its pure vapor on a perfectly wetted superheated smooth substrate, with the disjoining pressure most often in the form of a positive inverse cubic law (nonpolar case), is routinely considered to end up in a microfilm extended over adjacent "dry" parts of the solid surface. Invoking the spreading coefficient as an additional independent parameter within this framework, we argue however that a regime with a truncated microfilm is chosen instead if the spreading coefficient is decreased below a positive (still perfect wetting) critical value dependent upon the superheat, in which case the extended-microfilm thickness is surpassed by that of the "pancake" introduced by de Gennes and co-workers. Conversely, for a given positive spreading coefficient, there is a critical superheat above which the microfilm gets truncated, whereas for a negative one (partial wetting) the truncated regime should be preferred at any superheat. A parametric study of the apparent contact angle (a nonlinear eigenvalue of the steady microstructure problem) versus the spreading coefficient is carried out. When the latter is negative, Young's law is asymptotically recovered. Microfilm fronts on a bare surface are shown to be advancing or receding in accordance with the selected regime. A slightly more general class of disjoining pressures is also touched upon. The analysis is based in part upon thermodynamic considerations and in part upon a standard one-sided model of an evaporating liquid layer in the lubrication approximation.     

Pseudopartial wetting and precursor film growth in immiscible metal systems

We explore the equilibrium wetting behavior and precursor film growth in pure and alloy metallic systems. The systems exhibit equilibrium "pseudopartial" wetting, that is, a thin film in equilibrium with a nonzero contact angle in both liquid and solid states. The film spreading kinetics clearly indicates a diffusive transport mechanism. The alloying has only a small impact on the equilibrium wetting properties but strongly affects the transport during the growth of the precursor film.     

Diffusion Effects in the Wetting of a Contaminated Surface

Industrial wetting situations often involve the presence of a third component near an interface, potentially modifying the local effective capillary balance. We here consider a simplified situation in which a drop is placed on a substrate supporting a thin layer of "contamination." As spreading of the drop to equilibrium occurs, the contaminant diffuses into the drop, modifying the effective substrate/drop interfacial free energy (increasing it, it is assumed). Thus the kinetics of spreading are altered. The essential effect when the final equilibrium contact angle is zero is that of accelerating the process. However, when the final value of contact angle is finite, "overshoot" may occur. The drop spreads beyond its equilibrium state and then retracts to attain its equilibrium state asymptotically at long times. Copyright 2000 Academic Press.     

Can contact-angle measurements determine the disjoining pressure in liquid nanofilms on rigid substrates?

The disjoining pressure of lubricant nanofilms used in the magnetic recording industry controls the equilibrium wetting, the dynamics of film restoration, and the evaporation kinetics of the film. It has been claimed that by measuring the contact angle of nonpolar and polar liquids on lubricant films, the disjoining pressure can be extracted using the method of Girafalco and Good, and such analyses have appeared in the literature. The approximations underlying the method have been discussed before in the literature. In view of the importance of measuring disjoining pressure in nanofilms of lubricants, it is timely to revisit these assumptions to understand the validity of the contact-angle method presently in use. We re-derive the relevant equations using a thermodynamic-interaction-energy approach which is free of the problems inherent in the original derivation and make explicit the assumptions which must be made in the derivation. General interaction energy arguments are then invoked to demonstrate that it does not appear possible to obtain the disjoining pressure in the film from contact-angle measurements in an unambiguous manner.     

Effect of nanoparticle sizes and number densities on the evaporation and dryout characteristics for strongly pinned nanofluid droplets

A microfabricated linear heater array operating in a constant voltage mode has been used to study the effect of nanoparticle size on the evaporation and dryout characteristics of strongly pinned nanofluid droplets. Four different nanofluids have been tested, containing 2-nm Au, 30-nm CuO, 11-nm Al2O3, and 47-nm Al2O3 nanoparticles, each of 5-muL droplets with 0.5 vol % in water. Nanofluid droplets show strong pinning along the droplet perimeter and, upon evaporation, leave a ring-shaped nanoparticle stain. Particle size is seen to have a clear and strong effect on the dryout stain pattern, while heater temperature seems to have little effect. With the assumption of axi-symmetry, tomographic deconvolution of measured data from the linear heater array allows for examination of the spatially and temporally resolved temperature and heat flux characteristics of the evaporating nanofluid droplets.     

Electrowetting of aligned carbon nanotube films

Electrowetting is one approach to reducing the interfacial tension between a solid and a liquid. In this method, an electrical potential is applied across the solid/liquid interface which modifies the wetting properties of the liquid on the solid without changing the composition of the solid and liquid phases. Electrowetting of aligned carbon nanotube (CNT) films is investigated by the sessile drop method by dispensing deionized (DI) water or 0.03 M NaCl droplets (contacted by Au wire) onto aligned CNT films assembled on a copper substrate. The results demonstrate that electrowetting can greatly reduce the hydrophobicity of the aligned CNTs; the contact angle saturation for DI water and 0.03 M NaCl droplets occurs at 98 and 50 degrees , respectively. The combined effects of the geometrical roughness and the electrical potential on the contact angle are briefly discussed and modeled. Such a strategy may be invoked to controllably reduce the interfacial tension between carbon nanotubes (CNTs) and polymer precursors when infiltrating the monomers into the prealigned nanotube films.     

Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films

A liquid film of thickness h<100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure Pi. Since Pi dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives Pi=Pi(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h-->0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of Pi that depends on the slope h(x) as well as the height h of the film. When this theory is implemented for Lennard-Jones liquid films, the new Pi=Pi(h,h(x)) is bounded near a contact line as h-->0. Thus, the singularity in Pi(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new Pi can capture all three regimes of drop behavior (complete wetting, partial wetting, and pseudo-partial wetting) without altering the signs of the long and short-range interactions. We find that a drop with a precursor film is linearly stable.