We consider flow in a finite-length channel, one wall of which contains a membrane under longitudinal tension. The upstream flux and downstream pressure are prescribed and an external linear pressure distribution is applied to the membrane such that the system admits uniform Poiseuille flow as a steady solution. The system is described using a one-dimensional model that accounts for viscous and inertial effects. A linear stability analysis reveals that the uniform state is unstable to static (or divergent) and oscillatory instabilities. Asymptotic analysis in the neighbourhood of a Takens–Bogdanov bifurcation point shows how, when the downstream rigid section of the channel is not substantially longer than the membrane, an oscillatory mode arises through an interaction between two static eigenmodes. Perturbations to the uniform state exhibit the dynamics of a weakly dissipative Hamiltonian system for which low-frequency self-excited oscillations are forced by the divergent instability of two nearby steady solutions, before ultimately growing to large amplitudes. Simulations show that the subsequent dynamics can involve slamming motion in which the membrane briefly comes into near-contact with the opposite rigid wall over short length scales.

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Flow driven through a planar channel having a finite-length membrane inserted in one wall can be unstable to self-excited oscillations. In a recent study (Xu, Billingham & Jensen J. Fluid Mech., vol. 723, 2013, pp. 706–733), we identified a mechanism of instability arising when the inlet flux and outlet pressure are held constant, and the rigid segment of the channel downstream of the membrane is sufficiently short to have negligible influence on the resulting oscillations. Here we identify an independent mechanism of instability that is intrinsically coupled to flow in the downstream rigid segment, which becomes prominent when the downstream segment is much longer than the membrane. Using a spatially one-dimensional model of the system, we perform a three-parameter unfolding of a degenerate bifurcation point having four zero eigenvalues. Our analysis reveals how instability is promoted by a 1:1 resonant interaction between two modes, with the resulting oscillations described by a fourth-order amplitude equation. This predicts the existence of saturated sawtooth oscillations, which we reproduce in full Navier–Stokes simulations of the same system.

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Microfibril cellulose (MFC), which is detrimental to soil cultivation and environmental protection, is derived from waste pineapple leaves. Hexagonal boron nitride (h-BN) was modified with polydopamine (PDA)—PDA@h-BN named pBN, and then combined with MFC to prepare a novel hybrid powder. The effect of PDA on h-BN and the binding effect between pBN and MFC were characterized by X-ray photoelectron spectroscopy (XPS), Thermogravimetric (TG), scanning electron microscopy (SEM), and Fourier Transform-Infrared (FT-IR). Poly (vinyl alcohol) (PVA) was used as an eco-friendly polymeric matrix to prepare a pBN-MFC-PVA composite film. The mechanical strength, hydrophobicity, and thermal conductivity of the film were studied and the results confirmed that h-BN was chemically modified with PDA and was uniformly distributed along the MFC. The thermal conductivity of the pBN-MFC-PVA composite film increased with the addition of a pBN-MFC novel powder. MFC acted as “guides” to mitigate the h-BN agglomerate. In addition to the possible usage in the pBN-MFC-PVA composite film itself, the pBN-MFC hybrid powder may be a potential filler candidate for manufacturing thermal interface materials and wearable devices or protective materials.

An inclusion of particles in a Newtonian liquid can fundamentally change the interfacial dynamics and even cause interfacial instabilities. For instance, viscous fingering can arise even in the absence of the destabilizing viscosity ratio between invading and defending phases, when particles are added to the viscous invading fluid inside a Hele-Shaw cell. In the same flow configuration, the formation and breakup of a dense particle band are observed on the interface, only when the particle diameter d becomes comparable to the channel gap thickness h. We experimentally characterize the evolution of the fluid-fluid interface in this new physical regime and propose a simple model for the particle band that successfully captures the fingering onset as a function of the particle concentration and h/d.

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