Can random deposition create dense non-overlapping material feeding? The question is very fundamental for the research of particle packing, while the answer is of great importance for any industrial process that applies single object operation. To gain an insight into this issue, we studied the overlap problems of convex particles in the manner of uniformly random deposition. The overlap probability of two convex particles with arbitrary shapes and sizes is formulated, and the coverage fractions of free particles and sticking particles (particles of the bottom layer) are precisely predicted. Simulations with rectangular particles verified the theory. Surprisingly, free particles can only occupy less than 7.5% of the plane area, much smaller than what is intuitively expected. Sticking particles, however, can easily cover 19%, a factor of 2.5 times larger. The finding is of great value for applications that need to create dense non-overlapping feeding.

An innovative route for plastics recycling is proposed, based on a combination of a logarithmic sorting process and colour plus high-resolution near-infrared (NIR) sensors. Although counterintuitive, it is shown that such a technology could sort clean flakes from rigid packaging waste into a very large number of different plastic grades with modest sorter capacity, provided that the chosen sensor is able to differentiate correctly between any two grades of plastics in the waste. Tests with high-resolution NIR on single pixels of transparent flakes from different types and brands of packaging show that this is indeed the case for a selection of 20 different packaging items bought from shops. Moreover, the results seem to indicate, in line with previous research, that high-resolution NIR data can be linked to important physical plastic properties like the melt flow viscosity and tensile strength. The attraction of deep sorting of waste plastics with relatively cheap sensors and modest sorter capacity is that the present industrial practice of tuning plastic grades to specific applications could coexist with commercial high-grade recycling at high levels of circularity and low carbon footprint. Therefore, advanced recycling technology is likely to be a societal alternative to phasing out plastics for rigid applications.