Capillarity Effects on Viscous Gravity Spreadings of Wetting Liquids

Spreading of aqueous surfactant solutions on oil substrates: Superspreaders vs non-superspreaders

HYPOTHESIS

The question of why aqueous solutions of some surfactants demonstrate a rapid spreading (superspreading) over hydrophobic solid substrates, while solutions of other similar surfactants do not, has no definitive explanation despite numerous previous studies. The suggested hypothesis for this study assumes that once the spreading coefficient of surfactant is positive, there is a concentration range for solutions of any surfactant which demonstrates rapid spreading. As it is impossible to calculate spreading coefficients for solid substrates, we compare the spreading performance of known superspreaders and non-superspreaders on liquid (oil) substrate.

EXPERIMENTS

The kinetics of spreading of aqueous solutions of a series of branched ionic surfactants and non-ionic trisiloxane surfactants on two liquid substrates was studied and compared with the spreading of a surfactant-free liquid, silicone oil. Both dynamic and equilibrium spreading coefficients were calculated using measured surface and interfacial tensions.

FINDINGS

There is no difference in spreading rate on liquid substrate between solutions of surfactants proven as superspreaders (while spreading on solid substrate) or non-superspreaders. A rapid spreading (superspreading) with the characteristic rate of spreading O(102-103) mm2/s occurs if the dynamic spreading coefficients exceeds the positive threshold value. If the dynamic spreading coefficient is negative or slightly positive, complete wetting still occurs, but the spreading is slow with the spreading rate is O(1) mm2/s. Spreading exponents for surfactant solutions in the rapid spreading regime are considerably larger than for the surfactant-free liquid. A number of spreading and dewetting patterns were observed depending on the surfactant type, its concentration and substrate.

Paper-Based Flow Sensor for the Detection of Hyaluronidase via an Enzyme Hydrolysis-Induced Viscosity Change in a Polymer Solution

Hyaluronidase (HAase) is implicated in inflammation, cancer development, and allergic reaction. The detection of HAase is significantly important in clinical diagnosis and medical treatment. Herein, we propose a new principle for the development of equipment-free and label-free paper-based flow sensors based on the enzymatic hydrolysis-induced viscosity change in a stimuli-responsive polymer solution, which increases the water flow distance on the pH indicator paper. The detection of HAase is demonstrated as an example. This facile and versatile method can overcome the potential drawbacks of traditional hydrogel-based sensors, including complex preparation steps, slow response time, or low sensitivity. Moreover, it can also avoid the use of specialized instruments, labeled molecules, or functionalized nanoparticles in the sensors developed using the polymer solutions. Using this strategy, the detection of HAase is achieved with a limit of detection as low as 0.2 U/mL. Also, it works well in human urine. Additionally, the detection of tannic acid, which is an inhibitor of HAase, is also fulfilled. Overall, a simple, efficient, high-throughput, and low-cost detection method is developed for the rapid and quantitative detection of HAase and its inhibitor without the use of labeled molecules, synthetic particles, and specialized instruments. As only minimal reagents of HAase, HA, and paper are used, it is very promising in the development of commercial kits for point-of-care testing.

Obtaining self-similar scalings in focusing flows

The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al. [Q. Appl. Math. 210, 155 (1990)]. Extracting the related similarity scaling exponents from either numerical or experimental data is nontrivial. Here we provide two such methods. We apply them to experimental and numerical data on converging fluid films driven by both surface tension and gravitational forcing. In the limit of pure gravitational driving, we recover Diez' semianalytic result, but our methods also allow us to explore the entire regime of mixed capillary and gravitational driving, up to entirely surface-tension-driven flows. We find scaling forms of smoothly varying exponents up to surprisingly small Bond numbers. Our experimental results are in reasonable agreement with our numerical simulations, which confirm theoretically obtained relations between the scaling exponents.

Stability study of a constant-volume thin film flow

We study the stability of a constant volume of fluid spreading down an incline. In contrast to the commonly considered flow characterized by constant fluid flux, in the present problem the base flow is time dependent. We present a method to carry out consistently linear stability analysis, based on simultaneously solving the time evolution of the base flow and of the perturbations. The analysis is performed numerically by using a finite-difference method supplemented with an integral method developed here. The computations show that, after a short transient stage, imposed perturbations travel with the same velocity as the leading contact line. The spectral analysis of the modes evolution shows that their growth rates are, in general, time dependent. The wavelength of maximum amplitude, lambda_{max} , decreases with time until it reaches an asymptotic value which is in good agreement with experimental results. We also explore the dependence of lambda_{max} on the cross sectional fluid area A , and on the inclination angle alpha of the substrate. For considered small A 's, corresponding to small Bond numbers, we find that the dependence of lambda_{max} on A is in good agreement with experimental data. This dependence differs significantly from the one observed for the films characterized by much larger A 's and Bond numbers. We also predict the dependence of lambda_{max} on the inclination angle alpha .

Spreading of a micrometric fluid strip down a plane under controlled initial conditions

We experimentally study the spreading of a small volume of silicon oil down a vertical plane with small Bond number. The initial condition is characterized by a horizontal long fluid strip with cross sectional area A and width w(0). We find that the experiments are characterized by a unique nondimensional parameter, R proportional w4(0)/(a2A), where a is the capillary length. An empirical criterium to estimate the onset of the contact line instability is established. The later rivulet formation at the contact line leads to a pattern which is characterized by a dominant wavelength. We find that this wavelength is approximately proportional to R(-1/4).

Spreading of a thin two-dimensional strip of fluid on a vertical plane: experiments and modeling

We study the thin-film flow of a constant volume of silicon oil (polydymethilsiloxane) spreading down a vertical glass plate. The initial condition is generated from a horizontal fluid filament of typical diameter 0.4 mm. Two optical diagnostic methods are used: One based on an anamorphic system, and the other on the Schlieren method. The first one allows for a detailed characterization of the early stable stage of the spreading which is used to estimate the thickness of the precursor film needed to model the flow. The second one captures the bidimensional pattern of the transversal film instability. We use these techniques to determine the film thickness profiles, and the evolution of the moving contact line, including its shape and Fourier spectra. The numerical simulations of the stable stage of spreading are in good quantitative agreement with the experimental results. We develop a model based on linear stability theory that predicts the evolution of the modes present in the linear stage of the instability.

Global models for moving contact lines

We consider thin film flows driven by surface tension and gravity. Within the framework of the lubrication approximation, we study the contact line motion using global models where either precursor film or slip are allowed. We show that completely wetting films can be simulated under both conditions without requiring direct tracking of the contact line interface. We perform a comparative study of standard and positivity preserving numerical methods for these problems in one space dimension, with the ultimate goal of choosing the best method applicable to two-dimensional problems. We find a considerable computational advantage of the precursor film model over the slipping models.

Modeling the Evolution and Rupture of Pendular Liquid Bridges in the Presence of Large Wetting Hysteresis

A model has been developed to predict the shape evolution, rupture distance and postrupture liquid distribution of a pendular liquid bridge between two unequally sized spherical particles in the presence of wetting hysteresis. Two different simplifications of the bridge geometry were considered: a toroidal and a parabolic approximation. The liquid bridge was assumed to rupture through its thinnest neck leaving liquid distributed on each sphere. Experimental measurements showed that the rupture distance was well predicted by both profile approximations by assuming that rupture occurred when the liquid-vapor interfacial area of the bridge and the postrupture droplets was equal. Both bridge profile approximations only correctly predicted the evolution of the apparent contact angle and the extent of postrupture liquid distribution when the solid-liquid interfacial area measured throughout the separation was included in the calculations. This is because during the pendular liquid bridge elongation, the three-phase contact line usually begins to slip on at least one of the spheres. The parabolic profile approximation was slightly more accurate than the toroidal one. The toroidal approximation is more difficult to use because one of the parameters passes through infinity as the bridge changes from convex to concave in shape. In some cases the toroidal approximation was also unable to generate a solution. Copyright 2000 Academic Press.

Profilometry of a liquid-free surface with large slope variations

We describe and test a refractive method for determining the height profile of an unsteady liquid-free surface, which is adequate for regions where the slope of the surface changes strongly, as for example the head of a spreading current. The method is developed for situations in which the height depends on a single Cartesian coordinate (plane flows); however, the underlying idea could be applied to more general cases. As a test, we obtained the profiles of a transparent solid object (a cylindrical lens) and of an actual liquid flow. These profiles are determined with high accuracy even if the direction of the normal to the free surface changes approximately 150 degrees within the probed region.