Droplet on a liquid substrate: Wetting,dewetting, dynamics,instabilities

Droplets on a liquid substrate (‘liquid lenses’) play an important role in various branches of engineering, including microfluidics, chemical engineering, environment protection, etc. In the present paper, we discuss basic phenomena characteristic for liquid lenses. We recall classical results on the shape of an equilibrium droplet and the kinds of droplet wetting. We overview briefly the main theoretical approaches used for the analysis of droplet dynamics, discuss the phenomena accompanying a droplet impact, physical effects used for droplet manipulations, and the factors that determine the interaction between droplets. We describe the main types of droplet instabilities leading to oscillations, self-propulsion, and disintegration of droplets. Some promising directions of further research are listed.     

Individual bottle brush molecules in dense 2D layers restoring high degree of extension after collapse-decollapse cycle: Directly measured scaling exponent

We prepared dense films of adsorbed brush-like macromolecules on mica substrate by transfer of compressed Langmuir monolayers from water subphase. The main macromolecular contours in the dense films were clearly resolved by SFM. The films were subjected to successive treatments by ethanol and water vapours. In accordance with previous results for isolated macromolecules, the films underwent collapse and subsequent decollapse morphological transformations in the changing vapour environment. Statistical analysis of the macromolecular dimensions in the films allowed us to measure the values of the scaling exponent determining the correlation between mean lateral and linear dimensions of the macromolecules. The analysis showed that the macromolecular conformations in the film as transferred were similar to the previously described conformations of the same macromolecules deposited directly on mica as isolated chains at much lower surface densities. The determined was close to the 0.75 value corresponding to the 2D SAW statistics. We assumed that the molecules retained the high degree of extension during the compression step due to suppressed reorganisation of the side chains. Differently from previous observations for isolated macromolecules, the restored conformations in the dense films after collapse-decollapse cycle were more extended with the of about 0.73 value. A theoretical explanation of the high degree of re-extension is proposed.     

Robot Manipulations: A Synergy of Visualization, Computation and Action for Spatial Instruction

This article considers the use of a learning environment, RoboCell, where manipulations of objects are performed by robot operations specified through the learner's application of mathematical and spatial reasoning. A curriculum is proposed relating to robot kinematics and point-to-point motion, rotation of objects, and robotic assembly of spatial puzzles. Various instructional methods are supported by the RoboCell robot system, such as interactive demonstrations, modeling, computer simulations and robot operations, providing diverse activities in spatial perception, mental rotation and visualization. Pre-course and post-course tests in two middle schools and a high school indicated significant student progress in the tasks related to the categories of spatial ability which were practiced in the course. This revised version was published online in July 2006 with corrections to the Cover Date.     

Students’ geometric thinking with cube representations: Assessment framework and empirical evidence

While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In order to assess students’ thinking about 3D shapes, we constructed an assessment framework based on existing research studies and data from G7-9 students (aged 12–15). We then applied our framework to assess students’ geometric thinking in lessons. We report two cases of qualitative findings from a classroom experiment in which Grade 7 students (aged 12–13) tackled a problem in 3D geometry that was, for them, quite challenging. We found that students who failed to answer given problems did not mentally manipulate representations effectively, while others could mentally manipulate representations and reason about them in order to reach correct solutions. We conclude with the proposition that this finding shows the framework can be used by teachers in instruction to assess their students’ 3D geometric thinking.     

Adsorption of polyampholytes on charged surfaces

We have studied the adsorption of neutral polyampholytes on model charged surfaces that have been characterized by contact angle and streaming current measurements. The loop size distributions of adsorbed polymer chains have been obtained using atomic-force microscopy (AFM) and compared to recent theoretical predictions. We find a qualitative agreement with theory; the higher the surface charge, the smaller the number of monomers in the adsorbed layer. We propose an original scenario for the adsorption of polyampholytes on surfaces covered with both neutral long-chain and charged short-chain thiols. Received 22 February 2002 and Received in final form 23 April 2002