A theory of angel hair: Analytic prediction of frictional heating of particulates in pneumatic transport

Abstract

An analytic prediction of the frictional temperature rise of materials in pneumatic transfer systems is developed, with the aim of anticipating from first principles the onset of problematic formation of melt structures such as ‘angel hair’. Specifically, particulates of size d passing at velocity V through a 90° bend of radius R experience a maximum surface temperature rise ΔT = μdV2(Vρ/kcR)0.5, where μ,ρ,k,c are the particle friction coefficient, density, thermal conductivity and heat capacity respectively. Limits of applicability of this idealized (but conservative) model are discussed, and simple corrections for the mitigating effects of pipe texture and gas cooling are discussed. The expression predicts temperature increments of many tens of Kelvin for 5 mm polyethylene granules at speeds of >40 m/s, but only a few K for 1 mm organic grains at 30 m/s in a planned pneumatic sampling system for a planetary exploration mission.