10 Joseph D. Barry et al. eq. 4). This is because the first layer of bubbles always flows. The ratio of the intrinsic timescale of the VF Model to the external timescale (as imposed by the nominal shear rate ˙ ϵ = V/L ), otherwise known as the Deborah number D$_{e}$ , is given by While not shown here, similar simulation runs have been performed for a monodisperse foam ( µ$_{2}$ ( A ) = 0). The localisation length is found to be independent of λV and is determined to be l = ¯ A 1 / 2 (the same as l$_{min}$ in our polydisperse simulations). Our simulation results are broadly consistent with the findings of Katgert et al. [19, 20], where the localisa- tion length is found to decrease with increasing V , and rate independence of localisation length is found in the monodisperse case. We wish to gain an understanding of these VF sim- ulation results by attempting to capture the observed behaviour by a continuum model. Such a model must include a constitutive relation which relates the local where c$_{d}$ is the drag coefficient and b is the drag exponent (the Bretherton law gives b = 2 3 [5]). These two expres- sions can be related by a force balance, which leads to the following differential equation [14, 30] Up until now, we have discussed microscopic (bubble scale) models of 2D foam rheology. An alternative way of describing a foam is to treat it as a continuum. The generalised Continuum Model [28, 30] (for steady shear) combines the Herschel-Bulkley constitutive relation (see eq. 1) with the following expression for the variation of (wall) drag force F$_{d}$ per unit area as a function of local velocity v (wall) drag force of the VF model to an averaged drag force in the continuum description. However, this would not be enough to explain the observed simulation results, as (according to the general Continuum Model [28]) it would result in a zero localisation length in all cases. Therefore, results suggest that internal dissipation (rep- resented by the shear rate term in the HB relation; see eq. 1) should also be included, although it is not clear how this dissipation arises in the VF simulations. We will also appeal to the idea of the existence of a stress overshoot in order to explain the variation of localisation length at low λV . 5 The Continuum Model D$_{e}$ = ( λV ) ¯ A γL , (9) as defined in [21]. A small Deborah number ( D$_{e}$ ≪ 1) indicates that the foam has enough time available to re- equilibrate, even as the applied shear attempts to bring the foam out of equilibrium (and vice versa for large D$_{e}$ ). In our simulations, 0 . 001 ≤ D$_{e}$ ≤ 0 . 03. We therefore conclude that we are close to the quasi-static regime in all of the discussed simulations. F$_{d}$ = − c$_{d}$v b , (10)