Stability of laminar viscoplastic flows down an inclined open channel

Linear stability of viscoplastic flows down an incline

“…Here, we summarize the theoretical formulation of the problem, details are given in [32,33,34]. Figure 1 shows the flow domain, where we denote the tilt angle as θ ∈ (0, π/2), the length of the domain as L and the upper free surface (not a priori known) as y = h(x, t) with H = max{h}.…”

“…Since there is still an open debate regarding the yield stress existence [25,26,27,28,29], viscosity regularization methods have mainly been used in order to avoid the issues due to the inherent singularity in the study of viscoplastic flows. "Regularized" constitutive equations are characterized by the introduction of a parameter, which is positive and provides the approximation level, and through which the "exact" model can be retrieved [30,34].…”

“…Our study focuses on the analysis of theoretical and numerical works regarding linear stability of viscoplastic flow down an inclined plane by using "regularized" models [32,33,34]. In particular, the theoretical study has been performed through the long-wave approximation approach in the case of Regularized Bingham and Casson-like materials [32,33].…”

“…In particular, the theoretical study has been performed through the long-wave approximation approach in the case of Regularized Bingham and Casson-like materials [32,33]. The numerical study has been performed by using the Papanastasiou model (a Bingham law regularization) through a spectral collocation method that makes use of Chebyshev polynomials [34].…”

“…The theoretical background on the mathematical formulation of the problem and the main features of a "regularized" fluid flowing down an inclined plane in Section 2 and Section 3, respectively. Then, Section 4, similarly to [32,34,36], summarizes the analysis of linear stability through both analytical and numerical approaches, i.e. the long-wave approximation and spectral collocation method, respectively.…”