An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Film-free laser forward printing of transparent and weakly absorbing liquids

A laser-based technique for printing transparent and weakly absorbing liquids is developed. Its principle of operation relies in the tight focusing of short laser pulses inside the liquid and close to its free surface, in such a way that the laser radiation is absorbed in a tiny volume around the beam waist, with practically no absorption in any other location along the beam path. If the absorbed energy overcomes the optical breakdown threshold, a cavitation bubble is generated, and its expansion results in the propulsion of a small fraction of liquid which can be collected on a substrate, leading to the printing of a microdroplet for each laser pulse. The technique does not require the preparation of the liquid in thin film form, and its forward mode of operation imposes no restriction concerning the optical properties of the substrate. These characteristics make it well suited for printing a wide variety of materials of interest in diverse applications. We demonstrate that the film-free laser forward printing technique is capable of printing microdroplets with good resolution, reproducibility and control, and analyze the influence of the main process parameter, laser pulse energy. The mechanisms of liquid printing are also investigated: time-resolved imaging provides a clear picture of the dynamics of liquid transfer which allows understanding the main features observed in the printed droplets.