The contact angle of nanofluids as thermophysical property

Droplet volume and temperature affect contact angle significantly. Phase change heat transfer processes of nanofluids – suspensions containing nanometre-sized particles – can only be modelled properly by understanding these effects. The approach proposed here considers the limiting contact angle of a droplet asymptotically approaching zero-volume as a thermophysical property to characterise nanofluids positioned on a certain substrate under a certain atmosphere. Graphene oxide, alumina, and gold nanoparticles are suspended in deionised water. Within the framework of a round robin test carried out by nine independent European institutes the contact angle of these suspensions on a stainless steel solid substrate is measured with high accuracy. No dependence of nanofluids contact angle of sessile droplets on the measurement device is found. However, the measurements reveal clear differences of the contact angle of nanofluids compared to the pure base fluid. Physically founded correlations of the contact angle in dependency of droplet temperature and volume are obtained from the data. Extrapolating these functions to zero droplet volume delivers the searched limiting contact angle depending only on the temperature. It is for the first time, that this specific parameter, is understood as a characteristic material property of nanofluid droplets placed on a certain substrate under a certain atmosphere. Together with the surface tension it provides the foundation of proper modelling phase change heat transfer processes of nanofluids

"Real world" problems

We consider it important that pre-service teachers master both mathematical problem solving and the choice and analysis of problems, together with the way of posing them in the classroom, so that pupils’ thinking processes may be better stimulated. The teacher must make several decisions about the organisation of their own teaching: these relate to the choice and systematisation of ‘good’ problems, the management of pupils’ personal solutions in the sharing phases (discussion), the possible ways for making these personal solutions evolve towards expert solutions, which are the main goal. In this context, a priori analysis becomes one of the professional tools helping teachers to formulate their choices and decisions (Charnay, 2003). The “Real world” problems proposal sits within a set of activities that stimulate work with problems starting from a suitable a priori analysis, in order to identify the mathematical concepts at stake and to determine whether, how and with what aims they can be used in teaching