Measuring the impact of channel length on liquid flow through an ideal Plateau border and node system

The phenomenon of foam drainage is a complex multi-scale process that unites molecular level interactions with bulk foam characteristics. Foam drainage is primarily governed by the flow of liquid in the channels and junctions that form between bubbles, which are known as Plateau borders (PBs) and nodes respectively. Existing theoretical work predicts the surface rheology of the PB and node air-liquid interface to influence liquid flow rates; however, direct experimental observations of this phenomenon remain scarce. This study recognises the clear need for a reproducible, accurate and standardised approach to directly studying liquid flow at the scale of a theoretically 'ideal' PB-node architecture. Measurements of PB geometric profiles and their apparent surface shear viscosities, μs, were made for an aqueous solution of Sodium Dodecyl Sulphate (SDS) at varying PB lengths, l1, and liquid flow rates in the range 10 μl min-1 ≤ Q ≤ 200 μl min-1. Geometric profiles displayed previously unobserved transitions between PB relaxation and expansion towards the node, with expansion dominating under conditions approaching conventional foam drainage. Average values of μs in the PB relaxation regions showed virtually inviscid behaviour, with magnitudes of 10-8 g s-1 < μs < 10-4 g s-1 for l1 in the range 27.5 mm ⪆ l1 ⪆ 8.0 mm. Decreasing magnitudes of μs and degrees of shear thinning were observed with increasing l1. This was attributed to a compressibility of the interface that was limited by an SDS concentration dependence on l1. Numerical evaluation predicted the appearance of Marangoni forces that scaled strongly with liquid shear rates, and could therefore have been responsible for the apparent shear thinning behaviour.