Transient peristaltic transport of grains in a liquid

Abstract

Abstract. Pumping suspensions and pastes has always been a significant technological challenge in a number of industrial applications ranging from food processing to mining. Peristaltic pumps have become popular to pump and/or dose complex fluids, due to their robustness. During the transport of suspensions with peristaltic pumps, clogging issues may arise, particularly during transient operations. That is a matter of particular concern whenever the pumping device is used intermittently to generate flow only on demand. Further understanding of the transient dynamics of such systems and of the conditions that can lead to jamming would result in more robust peristaltic pump design. To achieve these goals, an experimental setup that simplifies the statorrotor assembly of a peristaltic hose pump was used. In this setup, a roller transfers momentum to a liquid suspension, upon application of a constant load. The evolution of the velocity of the roller was recorded for different concentrations of mono-dispersed spheres of different diameters. The flow is found not to be strongly dependent on the dispersed particle volume fraction, if the size of the suspended phase is comparable with the hose diameter. Conversely, the flow is strongly slowed down when their size is small and the particle concentration is increased. These findings could help improving the design of peristaltic pumps by a more appropriate sizing, given the diameter of the hose and that of the particles to be transported.

Shape optimization of peristaltic pumps transporting rigid particles in Stokes flow

“…This mechanism is known as peristalsis. Computationally, the forward problem of simulating the particle transport for a given peristaltic wave shape has been considered in a number of works; a few recent ones that consider various physical scenarios include [24,6,1,19,23]. However, the inverse problem of finding the optimal wave shapes (e.g., that minimize the pump's power loss) received little attention, primarily owing to the computational challenges associated with its solutionevery shape iteration requires time-dependent solution of a rigid (or deformable) particle motion through constrained geometries in Stokes flow.…”

“…) ensuring that the shape perturbations (i) are periodic, (ii) prevent any deformation of the end sections Γ ± p along the axial direction, and (iii) prevent vertical rigid translations of the channel domain. The provision θ ∈ C 1,∞ 0 (Ω all ) ensures that (a) there exists η 0 > 0 such that Ω η (θ) Ω all for any η ∈ [0, η 0 ], (b) the weak formulation for the shape derivative of the forward solution (see (19)) is well defined in the standard solution spaces, and (c) traces of θ and ∇θ on ∂Ω η are well-defined. Since here shape changes are driven by Γ, the support of θ may be limited to an arbitrary neighborhood of Γ in Ω.…”

“…Adjoint problem. The shape derivative J (Γ) involves the forward solution derivatives u, f , x solving problem (19). Finding the latter therefore seems at first glance necessary for evaluating J (Γ; θ) in a given shape perturbation θ, but in fact can be avoided with the help of an adjoint problem defined at any time t by the weak formulation:…”

“…Shape derivative using adjoint solution. Now, combining the derivative problem (19) and the adjoint problem (23) with appropriate choices of test functions, we obtain an expression of J (Γ; θ) that no longer involves the derivative solution:…”

“…Proof. The test functions (v, q, g, k, ρ) are set to (û, p, f , ĥ, x) in the derivative problem (19) and to ( u, p, f , h, x) in the adjoint problem (23), and the combination (19a) + (19b) + (19c) + (19d) − (23a) + (23b) − (23c) − (23d) then evaluated (using û = ∂ f G on Γ, implied by (23b), along the way). This results in…”