Effect Of Contact Angle Research Articles

Adsorption of paraffin vapor on oxidized molybdenum substrates at nano- and micro-scales

Sputtered oxidized molybdenum surfaces were exposed at room temperature for different times to paraffin vapors obtained at 150 °C. Scanning polarization force microscopy (SPFM), optical and confocal microscopy were used to characterize the surfaces. The condensed morphologies are complex and strongly dependent upon the quantity of vapor molecules deposited on the substrate surface. A thin paraffin film is initially formed and quite uniform nano-height drops are nucleated randomly over it within 10–20 s time exposures. Their average contact angle ranged between 1°–2.5°. Further vapor deposition led to a more complex regime where nano-height drops do not show a clear interface with the film, while micro-sized drops do. The tangent approximation method adopted by Salmeron and Xu for the nano-drop regimes was extended to the micro-sized drop regime obtaining an averaged effective contact angle equal to 4°–5°. Both nano-height and micro-sized drops shape and effective contact angles have been discussed taking into account their interactions between the film and the drops.

Dynamic wetting of Boger fluids

The impact of fluid elasticity on the dynamic wetting of polymer solutions is important because many polymer solutions in technological use exhibit non-Newtonian behaviors in the high shear environment of the wedge-like flow near a moving contact line. Our former study [G.K. Seevaratnam, Y. Suo, E. Ramé, L.M. Walker, Phys. Fluids 19 (2007) Art. No. 012103] showed that shear thinning induced by a semi-flexible high molecular weight polymer reduces the viscous bending near a moving contact line as compared to a Newtonian fluid having the same zero-shear viscosity. This results in a dramatic reduction of the dependence of the effective dynamic contact angle on contact line speed. In this paper, we discuss dynamic wetting of Boger fluids which exhibit elasticity-dominated rheology with minimal shear thinning. These fluids are prepared by dissolving a dilute concentration of high molecular weight polymer in a “solvent” of the oligomer of the polymer. We demonstrate that elasticity in these fluids increases curvature near the contact line but that the enhancement arises mostly from the weakly non-Newtonian behavior already present in the oligomeric solvent. We present evidence of instabilities on the liquid/vapor interface near the moving contact line.

Dynamic wetting of shear thinning fluids

The impact of non-Newtonian behavior on dynamic wetting is critical since many fluids exhibit such behavior somewhere in the high-shear environment inherent in the wedge flow near a moving contact line. This impact will be different for two broad categories of non-Newtonian behavior, shear thinning, and elasticity. In this paper, we discuss the steady-state wetting of a fluid, aqueous solutions of xanthan gum, dominated by shear thinning but with negligible elasticity. In the shear thinning fluid, viscous bending near the contact line is greatly reduced compared to a Newtonian fluid having the same zero-shear viscosity. Concomitant with this reduction in viscous bending, the effective dynamic contact angle has a much weaker dependence on capillary number, Ca, than is observed in, or predicted for, Newtonian fluids. A simple lubrication model using a constitutive relation with power-law shear thinning at high shear rates and a Newtonian plateau at low shear rates mimics the trends seen in our data and elucidates the origins of the reduced viscous bending.

Effective creases and contact angles between membrane domains with high spontaneous curvature

We show that the short-scale elastic distortions that are excited in the vicinity of the joint between different lipidic membrane domains (at a scale of approximately 10nm) may produce a "crease" from the point of view of the standard elastic description of membranes, i.e., an effective discontinuity in the membrane slope at the level of Helfrich's theory. This "discontinuity" may be accounted for by introducing a line tension with an effective angular dependence. We show that domains bearing strong spontaneous curvatures, such as biological rafts, should exhibit creases with a finite contact angle, almost prescribed, corresponding to a steep extremum of the line energy. Finite contact angles might also occur in symmetric membranes from the recruitment of impurities at the boundary.

CCN Activation of Pure and Coated Carbon Black Particles

The CCN (cloud condensation nucleus) activation of pure and coated carbon black particles was investigated using the University of Vienna cloud condensation nuclei counter (Giebl, H.; Berner, A.; Reischl, G.; Puxbaum, H.; Kasper-Giebl, A.; Hitzenberger, R. J. Aerosol Sci. 2002, 33, 1623-1634). The particles were produced by nebulizing an aqueous suspension of carbon black in a Collison atomizer. The activation of pure carbon black particles was found to require higher supersaturations than predicted by calculations representing the particles as insoluble, wettable spheres with mobility equivalent diameter. To test whether this effect is an artifact due to heating of the light-absorbing carbon black particles in the laser beam, experiments at different laser powers were conducted. No systematic dependence of the activation of pure carbon black particles on laser power was observed. The observations could be modeled using spherical particles and an effective contact angle of 4-6 degrees of water at their surface. The addition of a small amount of NaCl to the carbon black particles (by adding 5% by mass NaCl to the carbon black suspension) greatly enhanced their CCN efficiency. The measured CCN efficiencies were consistent with Kohler theory for particles consisting of insoluble and hygroscopic material. However, coating the carbon black particles with hexadecanol (a typical film-forming compound with one hydrophobic and one hydrophilic end) efficiently suppressed the CCN activation of the carbon black particles.

Extended wedge covariance for wetting and filling transitions

Fluid adsorption on nonplanar and heterogeneous substrates is studied using a simple interfacial model. For systems with short-ranged forces, we find that, by tuning the local strength of the substrate potential, it is possible to find the exact equilibrium interfacial profile as a functional of the wall shape psi x. The tuning of the local substrate potential takes the form of a gauge condition theta x=+/-psi x, where theta x can be interpreted as a local effective contact angle. For wedgelike geometries with asymptotic tilt angle alpha, the midpoint interfacial height and roughness satisfy the same covariance relations previously found for simple linear wedges. For troughlike geometries satisfying the gauge condition, covariance is also found for the two-point correlation function. Predictions for more microscopic Landau and Ising models are also discussed.

Effect of curvature of coating die edges on the pinning of contact line

AbstractCoating die edges are not mathematical corners, they are rounded. Contact lines do not actually pin. The effects of the radius of curvature of the downstream edge of slot dies on contact line location, effective contact angle, and low‐flow limit—air‐fingers penetrating from downstream and breaking apart the coating‐bead—are examined by solving the Navier‐Stokes system for Newtonian flow. The geometry of the die surface is represented by two straight lines and an arc of circle connecting them. The local contact angle is treated as a specified equilibrium value. The system of equations is solved by Galerkin's method and finite element basis functions. The results show how the edge rounding affects the contact line position and stability of the flow, and indicate the minimum radius of curvature necessary to apparently pin the contact line. © 2005 American Institute of Chemical Engineers AIChE J, 2006

Wetting in infiltration of alumina particle preforms with molten copper

The high-temperature wettability of alumina particulate preforms by copper is investigated by means of infiltration experiments conducted at 1473 K under low oxygen partial pressure. Wetting is quantified in terms of drainage curves, which plot the volume fraction of metal in the porous medium vs. the applied pressure. Mercury porosimetry is also used on similar preforms for comparison. The effect of volume fraction, particle geometry and capillary parameters on the drainage curve are studied and compared with the expression proposed by Brooks and Corey. The influence of the particle volume fraction and capillary parameters characterizing wetting in the two systems is discussed to derive an effective contact angle for wetting of alumina particles by molten copper.

Droplets, bubbles, and vesicles at chemically structured surfaces

Liquid droplets, gas bubbles, and membrane vesicles which are in contact with chemicallystructured substrate surfaces can undergo morphological transitions or shape transformations.The structured surfaces considered here consist of two types of surface domains,γ and δ, which attract and repel the droplets, bubbles, and vesicles, respectively. For droplets on a stripedγ domain, one has to distinguish droplets with fixed end caps from those with freely movingend caps. Both types of channels undergo morphological wetting transitions. For vesicles,one has a strong adhesion regime in which the vesicle shapes have constant mean curvatureand exhibit effective contact angles. One can then map the shape bifurcation diagram forvesicles onto the one for droplets if one includes the constraint of fixed membrane area. Wealso report preliminary experimental observations of the adhesion of vesicles to chemicallystructured surfaces.

Comparison of two dynamic contact line models for driven thin liquid films

The modeling of the motion of a contact line, the triple point at which solid, liquid and air meet, is a major outstanding problem in the fluid mechanics of thin films [2, 9]. In this paper, we compare two well-known models in the specific context of Marangoni driven films. The precursor model replaces the contact line by a sharp transition between the bulk fluid and a thin layer of fluid, effectively pre-wetting the solid; the Navier slip model replaces the usual no-slip boundary condition by a singular slip condition that is effective only very near the contact line. We restrict attention to traveling wave solutions of the thin film PDE for a film driven up an inclined planar solid surface by a thermally induced surface tension gradient. This involves analyzing third order ODE that depend on several parameters. The two models considered here have subtle differences in their description, requiring a careful treatment when comparing traveling waves and effective contact angles. Numerical results exhibit broad agreement between the two models, but the closest comparison can be done only for a rather restricted range of parameters. The driven film context gives contact angle results quite different from the case of a film moving under the action of gravity alone. The numerical technique for exploring phase portraits for the third order ODE is also used to tabulate the kinetic relation and nucleation condition, information that can be used with the underlying hyperbolic conservation law to explain the rich combination of wave structures observed in simulations of the PDE and in experiments [3, 15].

Transitions from static wetting to steady dewetting and deposition of liquid-film on partially wettable polymer surface

The transitions from static to steadily moving wetting perimeter and further to deposition of a liquid-film on partially wettable surface were studied with the same system under the same conditions. A polyethylene terephthalate (PET) tape was vertically withdrawn at constant velocity from glycerol–water mixture. Elevation L of the three-phase contact line above the liquid level was measured under static, steady, and dynamic wetting. The static receding Θ R and the apparent dynamic angles Θ app at different withdrawal velocities U were calculated from the static relationship Θ( L). It was found that the limiting static angle Θ R,min, at which the wetting perimeter starts moving, depends on withdrawal velocity. Extrapolation of the Θ R,min/ U dependence to U = 0 yields the quasi-static value of this parameter Θ R , min 0 , that coincides with the relaxation static angle Θ R,rlx achieved after meniscus motion ceases. This conclusion holds also for the wetting mode, where the limiting static advancing angle Θ A , max 0 = Θ A,rlx. Both the limiting and relaxation angles could be used for calculation of the effective Young's contact angle on non-ideal surface following Adam's suggestion [N.K. Adam, Adv. Chem. Ser. 43 (1964) 53.]. The critical velocity U cr anfd apparent dynamic angle Θ app,cr, at which transition between steady dewetting and dynamic wetting occurs, were determined. The value of Θ app,cr = 0° ± 5° agrees with our previous results [R.V. Sedev, J.G. Petrov, Colloids and Surfaces, 53 (1991) 147] implying a quasi-static shape of the moving meniscus up to U cr. At U > U cr, the speed V of the contact line relative to the solid wall is independent of withdrawal velocity and thickness of the deposited film. The present data confirm the earlier findings [J.G. Petrov, R.V. Sedev, Colloids and Surfaces, 13 (1985) 317, T.D. Blake, K.J. Ruschak, Nature, 282 (1979) 489] that at U = U cr, V reaches its maximum value V max, which is most important parameter of dewetting kinetics. Weak linear decrease of Θ app with U was found above Ca = 2.4 × 10 −5 up to the critical capillary number Ca cr = 4.1 × 10 −4. Below Ca = 10 −5 the apparent receding angle depends much stronger on withdrawal velocity. The hydrodynamic (HD), and the simple and more general versions of the molecular-kinetic (MK) and molecular-hydrodynamic (MHD) theories of the wetting dynamics were used for quantitative characterization of the system in the steady dewetting regime. The effective Young's angle was used in the MK and MHD treatment of the experimental data following our previous publication [J.G. Petrov, J. Ralston, M. Schneemilch, R. Hayes, J. Phys. Chem B, 107(7) (2003) 1637]. The HD theory only qualitatively satisfies our experimental data giving physically unreasonable value of the hydrodynamic cut-off (slip) length and too small static receding angle at U = 0. The MK theory gives acceptable values of the oscillation frequency K 0 of the molecules at the contact line. Its more general version, including the viscous dissipation in the contact line vicinity, yields higher oscillation frequency. Very large distance λ between adsorption centers on the solid substrate (about five times the diameter of a glycerol molecule) was obtained with both MK and MHD theories. The too small frequency K 0 obtained with the simple MHD theory is removed by the more general version, accounting for contact line and viscous friction in the inner and intermediate zone of the moving meniscus. All theories show discrepancies between theoretically expected and experimentally estimated values of some of the parameters of wetting dynamics.

The effects of thin and ultrathin liquid films on dynamic wetting

We examine the effects of thick (micron scale) fluid films and thin molecular scale (10–100 Å) films on the hydrodynamics near advancing contact lines by measuring the liquid–vapor interface shape of a meniscus and comparing the measurements to three models. Using flow visualization, we directly observe the fluid flow field near the moving contact line and give a qualitative description of the stagnation point and dividing streamline emanating from the contact line region. For thick films, when the capillary number satisfies Ca(a/d)3/2⩽O(1) (where d is the film thickness and a is the macroscopic length scale of the system), the liquid–vapor interface is bent only slightly by the viscous flow and the effective dynamic contact angle is close to zero. As Ca approaches O(1/ln(a/d)), a modulated wedge-like region appears at some distance from the film and expands both away from and toward the film as Ca increases. The dynamic contact angle approaches the classic power law behavior as this region expands. For molecularly thin films, the liquid–vapor interface shape within microns of the moving contact line is correctly described by theoretical models based purely on hydrodynamics and without disjoining pressure effects.

The possibility of different time scales in the dynamics of pore imbibition

To model the imbibition of liquids into porous solids, use is often made of the Lucas–Washburn equation, which relates the distance of penetration of a liquid at a given time to the pore radius, the viscosity and surface tension of the liquid, and the effective contact angle between the liquid and the solid. In this paper, we extend previous large-scale molecular dynamics simulations to show how this tool can be used to study the details of liquid imbibition, including the impact of the contact angle on the dynamics of penetration and the evolution of the internal flow field. In particular, we show that the asymptotic behavior of the contact angle versus time for a completely wetting liquid is given by ∼ t −1/4.

Method for inferring contact angle and for correlating static liquid hold-up in packed beds

Static liquid hold-up (SLH), which is an upper bound measure of the passive liquid volume fraction in packed beds, comes into play in several reaction–separation–transport design models and in correlations of fundamental hydrodynamic variables such as total liquid hold-up, wetting efficiency and pressure gradient. Early reported experimental SLHs in packed beds seemed to level off at a plateau of ca. 5% when capillary force dominates over gravity. Hence, most of the published correlations were constructed taking this asymptotic feature into account, despite the fact that reliable SLH values well beyond 5% were also reported particularly for Bond numbers tending towards zero. Thermodynamics and dimensional analysis of the interfacial momentum balance (Young–Laplace) equation suggests that SLH depends, besides the Bond number ( Bo) and some packing and bed characteristic lengths, on an effective contact angle at the junction where the gas–liquid interface and the packing–gas boundary meet. The contact angle, being difficult to measure, was generally disregarded in most analyses, and in practice, seldom incorporated as a computable quantity in the majority of published SLH correlations. Therefore in this work, a method was proposed for inferring theoretically the contact angle from an energy analysis of the meniscus interfaces’ area obtained from solving the 2-D Young–Laplace equation for two vertically aligned touching equivalent spheres. The approach showed that the intuited contact angles matched the measured ones, when available, with an average error of 8.6%. Following this determination, a new SLH correlation based on the contact angle ( θ c ), the Bond number ( Bo), the solid-to-void volume ratio (1− ε)/ ε, the packing sphericity ( φ), and the bed-to-packing volume ratio, BPR, was proposed and analysed in the light of most published SLH data, i.e., 239 measurements over the past five decades. The SLH correlation yielded an average error of 23%. Sensitivity analysis of its weights showed an important impact of the contact angle as an input variable. The correlation was also found to capture SLH values exceeding 5% in the limit of Bo→0.

Vesicles in haptotaxis with hydrodynamical dissipation.

We analyze the problem of vesicle migration in haptotaxis (a motion directed by an adhesion gradient), though most of the reasoning applies to chemotaxis as well as to a variety of driving forces. A brief account has been published on this topic. We present an extensive analysis of this problem and provide a basic discussion of most of the relevant processes of migration. The problem allows for an arbitrary shape evolution which is compatible with the full hydrodynamical flow in the Stokes limit. The problem is solved within the boundary integral formulation based on the Oseen tensor. For the sake of simplicity we confine ourselves to 2D flows in the numerical analysis. There are basically two regimes (i) the tense regime where the vesicle behaves as a "droplet" with an effective contact angle. In that case the migration velocity is given by the Stokes law. (ii) The flask regime where the vesicle has a significant (on the scale of the vesicle size) contact curvature. In that case we obtain a new migration law which substantially differs from the Stokes law. We develop general arguments in order to extract analytical laws of migration. These are in good agreement with the full numerical analysis. Finally we mention several important future issues and open questions.

Spreading of Liquid Drops over Thick Porous Layers: Complete Wetting Case

The spreading of small silicone oil drops (capillary regime of spreading) over various dry thick porous substrates (permeable in both normal and tangential directions) was experimentally investigated. The time evolution of the radii of both the drop base and the wetted region on the surface of the porous substrate was monitored. It was observed that the total duration of the spreading process can be divided into two stages: a first stage, when the drop base expands until its maximum value is reached, and a subsequent second stage, when the drop base shrinks. It was found that the dynamic contact angle remains constant during the second stage of spreading. The latter fact has nothing to do with the contact angle hysteresis, as there is no hysteresis in the system. Appropriate scales are used, with a dimensionless time, to plot the dimensionless radii of the drop base and of the wetted circle on the surface of the porous substrate, the relative dynamic contact angle, and the effective contact angle inside the porous substrate. All these experimental data fell onto universal curves when the spreading of different silicone oils is done on porous substrates of similar pore size and porosity.

Three-Phase Effective Contact Angle in a Model Pore

We consider a model pore (2D) in which a sharp interface between two fluids contact a third fluid which wets the solid boundary. If the configuration is capillary dominated, the geometry can be determined analytically in terms of the effective contact angle. This angle depends not only on the interfacial tensions, but also on the capillary pressures. However, if the height of the cusp formed by the wetting fluid is much smaller than the pore width, the effective contact angle is a simple function of the interfacial tensions. It turns out to be the same function as in the case of an undeformed wetting layer of molecular thickness. The analytical expression for the effective contact angle has been confirmed by a numerical technique, known as the lattice-Boltzmann method. This method, in turn, has been validated with Neumann's law for the three-phase contact angles.

Shapes, contact angles, and line tensions of droplets on cylinders

Using an interface displacement model we calculate the shapes of nanometer-size liquid droplets on homogeneous cylindrical surfaces. We determine effective contact angles and line tensions, the latter defined as excess free energies per unit length associated with the two contact lines at the ends of the droplet. The dependences of these quantities on the cylinder radius and on the volume of the droplets are analyzed.

Effective and microscopic contact angles in thin film dynamics

We introduce and analyse a class of quasi-self-similar solutions of the thin film equation to describe the dynamics of expanding liquid films on a solid surface. Using these solutions as intermediate asymptotics profiles, we obtain a quantitative expression for the shape of the film and a relation between the speed of the contact line and the macroscopic and microscopic contact angles.

Contact-Angle Hysteresis Caused by a Random Distribution of Weak Heterogeneities on a Solid Surface

A model according to which contact-angle hysteresis arises as the result of a random distribution of irregularities on the solid surface is investigated on the basis of probability theory. An estimate is obtained of the mathematical expectation of the number of stable equilibria when the effective angle between the liquid–gas surface and the solid surface with which the liquid is in contact deviates from the value, say θ0, which would obtain if the solid surface were uniform, i.e., free from irregularities. It is found that when the effective contact angle deviates from θ0 by less than a critical value, then the expected number of stable equilibria increases exponentially with the length of the contact line; therefore such a contact angle can occur under static conditions. But if the deviation of the contact angle from θ0 exceeds the critical value, then the expected number of stable equilibria decreases exponentially with the length of the contact line, so a stable equilibrium is not possible for a macroscopic length of the contact line. The method is applicable only if the random deviations of the spreading power (defined as the solid–gas surface tension minus the sum of the liquid–gas and liquid–solid surface tensions) from its average are sufficiently small. It is found that the critical deviation of the contact angle from θ0 is, apart from a slowly varying logarithmic factor, proportional to H2ρs, where H is a measure of the amplitude of the surface irregularities and ρs is the surface density (i.e., number per unit area) of the irregularities. This qualitative feature agrees with the results previously obtained by several other authors, and, moreover, there is a surprisingly close agreement of the proportionality factor with the results of some earlier work in which the method of statistical analysis was much less elaborate than here. The effect of the logarithmic factor is to make the critical deviation of the contact angle increase more slowly than the first power of H2ρs, and this is also in qualitative agreement with some earlier work.