Shear localisation with 2D Viscous Froth and its relation to the Continuum Model 11 which can be solved using the boundary conditions v (0) V and v ( L ) = 0. These are equivalent to the boundary conditions imposed in our VF simulations; see eq. 5 (al- beit that here the distance y is measured downward from the shearing boundary). Upon inspection, it is clear that that a velocity profile of the following form satisfies eq. 11, and exhibits flow localisation: an alternative definition to that of the previous section; see eq. 8. Inserting eq. 12 into eq. 15 leads to the follow- ing expression for localisation length as a function of the shearing velocity V , Its relation to the definition of localisation length l$_{int}$ (see eq. 8) is where y$_{0}$ and n may be obtained by inserting eq. 12 into eq. 11 and equating prefactors and exponents [27]. This gives as given by [27]. For a < b (as is the case for our VF simulations; see Sec. 6), localisation length therefore de- creases as the shearing velocity V is increased . The possibility of having a range of localisation lengths at low V (as in Fig. 7) can be accounted for by extending the Continuum Model to incorporate what we will refer to as a stress overshoot. This we will now proceed to do. In a recent paper [28], Weaire et al. introduced the idea of distinct yield σ$_{y}$ and limit σ$_{l}$ stresses as a possi- ble mechanism for localisation in the absence of viscous drag. An illustration of the typical stress vs strain pic- ture is shown in Fig. 8. The constitutive stress relation thus becomes Eq. 12 clearly satisfies the first boundary condition, v (0) = V of eq. 11. The second boundary condition is satisfied if we take our sample size L → ∞ [27]. This approach is valid so long as the size of the sample is much greater than the localisation length ( L ≫ l ) which may be defined as where σ$_{l}$ denotes the limit stress. When the magnitude of the stress overshoot, Δ = σ$_{y}$ − σ$_{l}$ is set to zero we recover the original Herschel-Bulkley relation (see eq. 1). σ = σ$_{l}$ + c$_{v}$ ˙ ϵ a (18) l = ∣ ∣ ∣ V dv (0) dy ∣ ∣ ∣ , (15) y$_{0}$ = 1 + a a − b $^{(}$a (1 + b ) c$_{v}$V a − b (1 + a ) c$_{d}$ ) 1 1+ a (13) n = 1 + a a − b . (14) v ( y ) = V (1 − y/y$_{0}$ ) n (12) l$_{int}$/l = (1 + a ) / (1 + 2 a − b ) , (17) l = $^{(}$a (1 + b ) c$_{v}$ (1 + a ) c$_{d}$ ) 1 1+ a V a − b 1+ a . (16) d dy ∣ ∣ dv ( y ) dy ∣ ∣ a = − c$_{d}$ c$_{v}$ v ( y ) b , (11) and