Evolution and breakup of viscous rotating drops

We study the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity $Omega$ or constant angular momentum L surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. The analysis is carried out by combining asymptotic analysis and full numerical simulation by means of the boundary element method. We pay special attention to the stability/instability of equilibrium shapes and the possible formation of singularities representing a change in the topology of the fluid domain. When the evolution is at constant $Omega$, depending on its value, drops can take the form of a flat film whose thickness goes to zero in finite time or an elongated filament that extends indefinitely. When evolution takes place at constant L and axial symmetry is imposed, thin films surrounded by a toroidal rim can develop, but the film thickness does not vanish in finite time. When axial symmetry is not imposed and L is sufficiently large, drops break axial symmetry and, depending on the value of L, reach an equilibrium configuration with a 2-fold symmetry or break up into several drops with a 2- or 3-fold symmetry. The mechanism of breakup is also described

Determination of the uptake and translocation of nitrogen applied at different growth stages of a melon crop (Cucumis melo L.) using 15N isotope.

In order to establish a rational nitrogen (N) fertilisation and reduce groundwater contamination, a clearer understanding of the N distribution through the growing season and its dynamics inside the plant is crucial. In two successive years, a melon crop (Cucumis melo L. cv. Sancho) was grown under field conditions to determine the uptake of N fertiliser, applied by means of fertigation at different stages of plant growth, and to follow the translocation of N in the plant using 15N-labelled N. In 2006, two experiments were carried out. In the first experiment, labelled 15N fertiliser was supplied at the female-bloom stage and in the second, at the end of fruit ripening. Labelled 15N fertiliser was made from 15NH415NO3 (10 at.% 15N) and 9.6 kg N ha−1 were applied in each experiment over 6 days (1.6 kg N ha−1 d−1). In 2007, the 15N treatment consisted of applying 20.4 kg N ha−1 as 15NH415NO3 (10 at.% 15N) in the middle of fruit growth, over 6 days (3.4 kg N ha−1 d−1). In addition, 93 and 95 kg N ha−1 were supplied daily by fertigation as ammonium nitrate in 2006 and 2007, respectively. The results obtained in 2006 suggest that the uptake of N derived from labelled fertiliser by the above-ground parts of the plants was not affected by the time of fertiliser application. At the female-flowering and fruit-ripening stages, the N content derived from 15N-labelled fertiliser was close to 0.435 g m−2 (about 45% of the N applied), while in the middle of fruit growth it was 1.45 g m−2 (71% of the N applied). The N application time affected the amount of N derived from labelled fertiliser that was translocated to the fruits. When the N was supplied later, the N translocation was lower, ranging between 54% at female flowering and 32% at the end of fruit ripening. Approximately 85% of the N translocated came from the leaf when the N was applied at female flowering or in the middle of fruit growth. This value decreased to 72% when the 15N application was at the end of fruit ripening. The ammonium nitrate became available to the plant between 2 and 2.5 weeks after its application. Although the leaf N uptake varied during the crop cycle, the N absorption rate in the whole plant was linear, suggesting that the melon crop could be fertilised with constant daily N amounts until 2–3 weeks before the last harvest.