Shear localisation with 2D Viscous Froth and its relation to the Continuum Model 3 logical changes of the foam structure (see Fig. 1). Two neighbouring bubbles (A and B) lose a common edge which is subsequently gained by two proximate bubbles (C and D), which become neighbours. We describe the incorporation of these topological changes into the VF Model in Sec. 2. dence of shear localisation in 2D foams. In this case, however, the velocity profiles are not exponential. Such non-exponential velocity profiles, together with their ve- locity dependence can be obtained from an extension or generalisation of the original Continuum Model [28, 30]. Furthermore, these experiments show that the locali- sation length decreases as the velocity of the moving boundary increases. In this paper, we show velocity pro- files from our VF simulations which exhibit qualitatively similar behaviour. Of particular current interest in these types of exper- iments is the dependence of (local) shear stress on shear rate. This effect is captured by the Herschel-Bulkley con- stitutive relation, When flow is concentrated in one region and not in another, the flow is said to have localised. Debreg´ eas et al. [8] were the first to report definitive evidence of shear localisation in 2D aqueous foams. Their experiments ex- hibit shear localisation next to a moving boundary in a Couette geometry, with an exponential decay in the mea- sured foam velocity profiles. Similar results have been re- ported by Wang et al. [25] and Krishan and Dennin [23] for straight and circular geometries, respectively. These results have been interpreted within the framework of the Continuum Model [6, 14, 15] where shear localisation is attributed to the presence of a drag force. This notion is further supported by the work of [12] which studies the effects of drag forces at high shear rates using the VF Model. However there are also quasi-static simulations showing localisation (discussed below) in which there is no such wall drag. This suggests that there is more than one mechanism that may lead to shear localisation. We will return to this point in Sec. 5. Experimental work by Katgert et al. [19, 20] on the shearing of bidisperse foams in a Hele-Shaw cell (straight geometry, that is, simple shear) shows Herschel-Bulkley behaviour (discussed below) and supplies further evi- where σ is stress, σ$_{y}$ is the yield stress, the coefficient c$_{v}$ is the so-called consistency, ˙ ϵ is strain rate and a is the HB exponent. Katgert and co-workers report a = 0 . 36. They also note that in the monodisperse case (i.e. bubbles of equal size), the localisation length is found to be independent of shear rate. We too find this to be the case in our simulations; see Sec. 4. Shear localisation has been studied computationally using other microscopic (bubble scale) models. Quasi- static models, as explored by [2, 13, 31, 32] might shed light on behaviour at very low strain rates. Results re- ported by Kabla [16, 18] show localisation next to the boundaries in quasi-static shearing simulations ( µ$_{2}$ ( A ) ≈ σ = σ$_{y}$ + c$_{v}$ ˙ ϵ a (1)