Neil Balmforth

Professor

Relevant Degree Programs

 

Postdoctoral Fellows

  • Tom Eaves (Fluid Mechanics, Continuum Mechanics, Turbulence, Multiphase Systems, Pulp and Paper, Plasticity and Creep, Global and Non-Linear Analysis)

Graduate Student Supervision

Doctoral Student Supervision (Jan 2008 - May 2019)
Mitigating impacts of temperature-oxygen squeeze in a mesotrophic-eutrophic lake: Wood Lake, BC, Canada (2017)

No abstract available.

Continuum limits of granular systems (2014)

Despite a century of study, the macroscopic behaviour of quasistatic granular materials remains poorly understood. In particular, we lack a fundamental system of continuum equations, comparable to the Navier-Stokes equations for a Newtonian fluid. In this thesis, we derive continuum models for two-dimensional granular materials directly from the grain scale, using tools of discrete calculus, which we develop.To make this objective precise, we pose the canonical isostatic problem: a marginally stable granular material in the plane has 4 components of the stress tensor σ, but only 3 continuum equations in Newton’s laws ∇ ‧σ = 0 and σ = σT. At isostaticity, there is a missing stress-geometry equation, arising from Newton’s laws at the grain scale, which is not present in their conventional continuum form.We first show that a discrete potential ψ can be defined such that the stress tensor is written as σ = ∇ × ∇ × ψ, where the derivatives are given an exact meaning at the grain scale, and converge to their continuum counterpart in an appropriate limit. The introduction of ψ allows us to understand how force and torque balance couple neighbouring grains, and thus to understand where the stress-geometry equation is hidden.Using this formulation, we derive the missing stress-geometry equation ∆(F^ : ∇∇ψ) = 0, introducing a fabric tensor F^ which characterizes the geometry. We show that the equation imposes granularity in a literal sense, and that on a homo- geneous fabric, the equation reduces to a particular form of anisotropic elasticity.We then discuss the deformation of rigid granular materials, and derive the mean-field phase diagram for quasistatic flow. We find that isostatic states are fluid states, existing between solid and gaseous phases. The appearance of iso- staticity is linked to the saturation of steric exclusion and Coulomb inequalities.Finally, we present a model for the fluctuations of contact forces using tools of statistical mechanics. We find that force chains, the filamentary networks of con- tact forces ubiquitously observed in experiments, arise from an entropic instability which favours localization of contact forces.

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Master's Student Supervision (2010 - 2018)
Locomotion over a Washboard (2015)

No abstract available.

The propagation of the gravity current of Bingham fluid : a numerical investigation (2015)

We have studied the propagation of 2D unit block of viscoplastic fluid of Bingham type over a horizontal plane, underneath another Newtonian fluid. We numerically simulate the dynamics of a two-layer fluid in a rectangle domain, using the volume-of-fluid method to deal with the evolution of the interface, and regularization scheme of the constitutive law, which replaces unyielded plugs with very viscous flow. We explore the final shape of the flow for varying yield stress, comparing the numerical results with the predictions of the asymptotic theory, a plasticity model based on slipline theory, and other past results.Numerical difficulties with the moving contact lines are encountered during the numerical simulation. A slip boundary condition is used to address this issue, the validity of which should be further investigated.

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Parametric subharmonic instability and the beta-effect (2010)

No abstract available.

 

Membership Status

Member of G+PS
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Program Affiliations

 

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