The force exerted by a monolayer foam on a transverse plate

It is shown that the force exerted by a monolayer bubble cluster on a confining plate, in the absence of gravity, equals one half of the cluster surface energy per unit length along the bubbles including the surface energy of the Plateau borders (PBs). The contribution of the PBs to the force can be accounted for in terms of their (negative) line tensions which oppose but never overcome the contractile film tensions. The PB line tension τ can be related to its excess energy ɛ defined as the energy of the PB surfaces minus the energy of the film prolongations into the PB, leading to τ = ɛ/2 in fairly dry foams, as found for other triple lines studied in the literature. At constant volume of gas in the bubbles, the force decreases as the liquid fraction ϕL increases from zero, but may go through a minimum at intermediate ϕL. For a honeycomb foam this minimum occurs for ϕL ≅ 0.05. When the height, h, of the cluster is changed at constant volumes of gas and liquid, the force F decreases linearly with h−1/2. The effect of gravity on the force exerted on a transverse horizontal plate is briefly discussed.