Unsteady fluid-structure interactions in a soft-walled microchannel: A one-dimensional lubrication model for finite Reynolds number

Flow-induced periodic snap-through dynamics

“…On the other hand, for an extensible flat membrane embedded in a channel, the effects of the Reynolds number and tension applied to the membrane on the membrane deformation have been investigated (Jensen & Heil 2003; Inamdar, Wang & Christov 2020). Jensen & Heil (2003) theoretically obtained the critical condition for the onset of self-excited oscillations in terms of the Reynolds number and reported that the critical Reynolds number strongly depended on the tension on the membrane and the length of the rigid parts located at the front and back of the membrane.…”

Interfacial instability of thin films in soft microfluidic configurations actuated by electro-osmotic flow

“…In the following sections we determine the steady-state deformation d ss (x) and the corresponding eigenfunctions f with eigenvalues σ by solving numerically the steady-state boundary value problem (23) and the corresponding eigenvalue problem (24) subjected to the boundary conditions (18). Additional details of the numerical method are provided in appendix B.…”

“…Configurations involving viscous flows bounded by elastic structures are relevant to a wide spectrum of applications such as fabrication of flexible microelectro-mechanical systems [8,9], suppression of viscous fingering instabilities [10][11][12], impact mitigation [13], fabrication of microfluidic devices [14][15][16][17][18][19] and soft robotics [20][21][22][23]. In particular, Inamdar and Christov [24] studied the transient fluid−structure interaction in a two-dimensional elastic micro-channel and developed a one-dimensional lubrication model, which accounts for bending and nonlinear induced tension, as well as the inertia of solid and liquid. Meanwhile, Martínez-Calvo et al [25] extended the steady analysis of Christov et al [19] for a slender geometry to the transient case by accounting for fluid and solid inertia in the lubrication and Kirchhoff−Love equations, respectively.…”

“…Solid lines represent the asymptotic solution(27) in the case of pure hydrostatic stress, whereas dashed lines represent the numerical solution which takes into account both tension and hydrostatic terms. (b) The growth rate σ as a function of EEOF/|EEOF,CR,G|, obtained from a linear stability analysis by solving(24). Gray dots correspond to the pure gravitational contribution, whereas black dots correspond to the case when the tension contribution is included.…”

“…In the first method, which was used to study the linear stability analysis (Sec. III), we solved numerically the steady-state boundary value problem (23) and the corresponding eigenvalue problem (24) subjected to the boundary conditions (18), using MATLAB's Chebfun package. The Chebfun package uses a spectral expansion in Chebyshev polynomials and solves Appendix C: Variation of growth rate with EEOF and k Figure 11(a) presents the growth rate σ as a function of E EOF for three values of the wavenumber, k, showing that for k = 1 the growth rate monotonically increases as |E EOF | increases and approaches zero only for a negative value of E EOF with E EOF,CR = −6.51.…”