Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals π/2 , a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free-energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.

Dynamics of colloidal particles with capillary interactions

We investigate the dynamics of colloids at a fluid interface driven by attractive capillary interactions. At submillimeter length scales, the capillary attraction is formally analogous to two-dimensional gravity. In particular it is a nonintegrable interaction and it can be actually relevant for collective phenomena in spite of its weakness at the level of the pair potential. We introduce a mean-field model for the dynamical evolution of the particle number density at the interface. For generic values of the physical parameters the homogeneous distribution is found to be unstable against large-scale clustering driven by the capillary attraction. We also show that for the instability to be observable, the appropriate values for the relevant parameters (colloid radius, surface charge, external electric field, etc.) are experimentally well accessible. Our analysis contributes to current studies of the structure and dynamics of systems governed by long-ranged interactions and points toward their experimental realizations via colloidal suspensions.

Crossover of critical Casimir forces between different surface universality classes

In confined systems near a continuous phase transition the long-ranged fluctuations of the corresponding order parameter are subject to boundary conditions. These constraints result in so-called critical Casimir forces acting as effective forces on the confining surfaces. For systems belonging to the Ising bulk universality class corresponding to a scalar order parameter the critical Casimir force is studied for the film geometry in the crossover regime characterized by different surface fields at the two surfaces. The scaling function of the critical Casimir force is calculated within mean-field theory. Within our approach, the scaling functions of the critical Casimir force and of the order parameter profile for finite surface fields can be mapped by rescaling, except for a narrow crossover regime, onto the corresponding scaling function of the so-called normal fixed point of strong surface fields. In the crossover regime, the critical Casimir force as function of temperature exhibits more than one extremum and for certain ranges of surface field strengths it changes sign twice upon varying temperature. Monte Carlo simulation data obtained for a three-dimensional Ising film show similar trends. The sign of the critical Casimir force can be inferred from the comparison of the order parameter profiles in the film and in the semi-infinite geometry.

Wetting of surfaces covered by elastic hairs

We study the wetting properties of elastic hairy surfaces. Neither our theory nor our experiments support the suggestion by Otten and Herminghaus [Langmuir 2004, 20, 2405-2408] that the interplay between wetting, capillary interactions, and elasticity is responsible for the hydrophobic behavior of the leaves of a Lady's Mantle. Instead, the corresponding observations can be attributed to pinning of the contact line.

Phoretic motion of spheroidal particles due to self-generated solute gradients

We study theoretically the phoretic motion of a spheroidal particle, which generates solute gradients in the surrounding unbounded solvent via chemical reactions active on its surface in a cap-like region centered at one of the poles of the particle. We derive, within the constraints of the mapping to classical diffusio-phoresis, an analytical expression for the phoretic velocity of such an object. This allows us to analyze in detail the dependence of the velocity on the aspect ratio of the polar and the equatorial diameters of the particle and on the fraction of the particle surface contributing to the chemical reaction. The particular cases of a sphere and of an approximation for a needle-like particle, which are the most common shapes employed in experimental realizations of such self-propelled objects, are obtained from the general solution in the limits that the aspect ratio approaches one or becomes very large, respectively.

Wetting of nanopatterned grooved surfaces

The wetting by perfluoromethylcyclohexane of a well-defined silicon grating with a channel width of 16 nm has been studied using transmission small angle x-ray scattering. Prefilling, capillary filling, and postfilling wetting regimes have been identified. A detailed comparison of the data with theory reveals the importance of long-ranged substrate-fluid and fluid-fluid interactions for determining the wetting behavior on these length scales, especially at the onset of capillary condensation and in the prefilling regime.

Line tension and the shape of nanodroplets

Various factors are discussed which might influence the equilibrium contact angle of nanodroplets placed on a solid substrate. Special emphasis is put on the possible role of the dependence of the solid-liquid interface tension [Formula: see text] on the pressure in the liquid, which in nanodrops considerably exceeds the saturation pressure. We show that certain published data regarding that dependence are meaningless because these have been deduced based on an inconsistent data analysis.

Critical Casimir effect in classical binary liquid mixtures

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy with femtonewton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.

Dynamics of nanodroplets on topographically structured substrates

Mesoscopic hydrodynamic equations are solved to investigate the dynamics of nanodroplets positioned near a topographic step of the supporting substrate. Our results show that the dynamics depends on the characteristic length scales of the system given by the height of the step and the size of the nanodroplets as well as on the constituting substances of both the nanodroplets and the substrate. The lateral motion of nanodroplets far from the step can be described well in terms of a power law of the distance from the step. In general the direction of motion depends on the details of the effective laterally varying intermolecular forces. But for nanodroplets positioned far from the step it is solely given by the sign of the Hamaker constant of the system. Moreover, our study reveals that the steps always act as a barrier for transporting liquid droplets from one side of the step to the other.

Physical fitness levels among European adolescents: the HELENA study

OBJECTIVE

To report sex- and age-specific physical fitness levels in European adolescents.

METHODS

A sample of 3428 adolescents (1845 girls) aged 12.5-17.49 years from 10 European cities in Austria, Belgium, France, Germany, Greece (an inland city and an island city), Hungary, Italy, Spain and Sweden was assessed in the Healthy Lifestyle in Europe by Nutrition in Adolescence study between 2006 and 2008. The authors assessed muscular fitness, speed/agility, flexibility and cardiorespiratory fitness using nine different fitness tests: handgrip, bent arm hang, standing long jump, Bosco jumps (squat jump, counter movement jump and Abalakov jump), 4×10-m shuttle run, back-saver sit and reach and 20-m shuttle run tests.

RESULTS

The authors derived sex- and age-specific normative values for physical fitness in the European adolescents using the LMS statistical method and expressed as tabulated percentiles from 10 to 100 and as smoothed centile curves (P₅, P₂₅, P₅₀, P₇₅ and P₉₅). The figures showed greater physical fitness in the boys, except for the flexibility test, and a trend towards increased physical fitness in the boys as their age increased, whereas the fitness levels in the girls were more stable across ages.

CONCLUSIONS

The normative values hereby provided will enable evaluation and correct interpretation of European adolescents' fitness status.

Reliability of health-related physical fitness tests in European adolescents. The HELENA Study

OBJECTIVE

To examine the reliability of a set of health-related physical fitness tests used in the European Union-funded Healthy Lifestyle in Europe by Nutrition in Adolescence (HELENA) Study on lifestyle and nutrition among adolescents.

DESIGN

A set of physical fitness tests was performed twice in a study sample, 2 weeks apart, by the same researchers.

PARTICIPANTS

A total of 123 adolescents (69 males and 54 females, aged 13.6+/-0.8 years) from 10 European cities participated in the study.

MEASUREMENTS

Flexibility, muscular fitness, speed/agility and aerobic capacity were tested using the back-saver sit and reach, handgrip, standing broad jump, Bosco jumps (squat jump, counter movement jump and Abalakov jump), bent arm hang, 4 x 10 m shuttle run, and 20-m shuttle run tests.

RESULTS

The ANOVA analysis showed that neither systematic bias nor sex differences were found for any of the studied tests, except for the back-saver sit and reach test, in which a borderline significant sex difference was observed (P=0.044). The Bland-Altman plots graphically showed the reliability patterns, in terms of systematic errors (bias) and random error (95% limits of agreement), of the physical fitness tests studied. The observed systematic error for all the fitness assessment tests was nearly 0.

CONCLUSIONS

Neither a learning nor a fatigue effect was found for any of the physical fitness tests when repeated. The results also suggest that reliability did not differ between male and female adolescents. Collectively, it can be stated that the reliability of the set of physical fitness tests examined in this study is acceptable. The data provided contribute to a better understanding of physical fitness assessment in young people.