Soft streaming – flow rectification via elastic boundaries

Abstract

Viscous streaming is an efficient mechanism to exploit inertia at the microscale for flow control. While streaming from rigid features has been thoroughly investigated, when body compliance is involved, as in biological settings, little is known. Here, we investigate body elasticity effects on streaming in the minimal case of an immersed soft cylinder. Our study reveals an additional streaming process, available even in Stokes flows. Paving the way for advanced forms of flow manipulation, we illustrate how gained insights may translate to complex geometries beyond circular cylinders.

Multicurvature viscous streaming: Flow topology and particle manipulation

“…Viscous streaming refers to the steady, rectified flows that emerge when a fluid oscillates around a localized microfeature, typically a solid body or a bubble ( 15 – 17 ). Such microfeatures have the ability to concentrate stresses ( 18 , 19 ), and thus distort and remodel the surrounding flow and its topology ( 20 – 23 ). The result is a remarkably consistent, controllable, and convenient machinery to shape both flow and particle paths.…”

Three-dimensional soft streaming

“…The fluid oscillates with velocity V(t) = aω cos ωt, where , ω and t represent the non-dimensional amplitude, angular frequency and time. Following our previous set-up for a soft two-dimensional cylinder (Bhosale et al 2022a), we kinematically enforce zero strain and velocity near the sphere's centre by 'pinning' the sphere with a rigid inclusion Γ of radius b < a, the boundary of which is denoted by ∂Γ . We choose to 'pin' the sphere to suppress its rigid-body motion and simplify mathematical treatment.…”

“…In viscous streaming applications, typically we have small non-dimensional oscillation amplitudes 1 (Wang 1965;Bertelsen, Svardal & Tjøtta 1973;Lutz et al 2005), density ratio α and viscosity ratio β of O (1), and Womersley number M ∼ O (1) (Marmottant & Hilgenfeldt 2004;Lutz et al 2006). For the Cauchy number Cau, we apply the same treatment as in Bhosale et al (2022a), where we use Cau = 0 for a rigid body and Cau = κ with κ = O (1) for elastic bodies. The latter assumption implies that Cau 1, which physically means that the body is weakly elastic.…”

“…First, we choose Cau to be small to simplify the treatment of hyperelastic materials, whose nonlinearities become mathematically challenging for Cau ≥ O (1). Second, matching Cau with simplifies the asymptotic expansion, while preserving the practical generality of the results (for details, see supplementary material § 2 of Bhosale et al (2022a)).…”

“…Recently, the use of multi-curvature streaming bodies has expanded the ability to manipulate flows, leading to compact, robust and tunable devices for filtering and separating both synthetic and biological particles (Parthasarathy, Chan & Gazzola 2019;Bhosale, Parthasarathy & Gazzola 2020;Chan et al 2022;Bhosale et al 2022b). More recently yet, motivated by medical and biological applications and building upon past theoretical studies (Wang 1965;Riley 1966Riley , 1998Riley , 2001Rednikov et al 2006;Rednikov & Sadhal 2011;Sadhal 2012;Sadhal, Laurell & Lenshof 2014), the effect of body compliance has been considered (Anand & Christov 2020), with one of the studies yielding a first two-dimensional streaming theory for soft cylinders (Bhosale, Parthasarathy & Gazzola 2022a). Its major outcome is encapsulated in the relation…”