Using numerical simulations, we investigate the effects of Marangoni stresses induced by surfactants on the effective slip length of liquid-infused surfaces (LIS) with transverse grooves. The surfactants are assumed soluble in the external liquid shearing the surface and can adsorb onto the interfaces. Two different adsorption models are used: a classical Frumkin model and a more advanced model that better describes the decrease of surface tension for minuscule concentrations. The simulations show that LIS may face even more severe effects of surfactants than previously investigated superhydrophobic surfaces. Constructing an analytical model for the effective slip length, we can predict the critical surfactant concentration for which the slip length decreases significantly. This analytical model describes both adsorption models of LIS on a unified framework if properly adjusted. We also advance the understanding of when surfactant advection gives rise to highly skewed interfacial concentrations: the so-called partial stagnant cap regime. To a good approximation, this regime can only exist below a specific surfactant concentration given by the Marangoni number and the strength of the surfactants.

Viscoelastic flow instability, which is compelled by elastic effects rather than inertia, can be driven to a chaotic state termed elastic turbulence (ET) manifested as strong velocity fluctuations with an algebraic decay in the frequency spectrum and increased mixing. We report the first spatiotemporally complete description of ET by considering a broad volume within a novel three-dimensional ordered porous medium, reconstructing flow at a micrometre characteristic length scale ($\text {Reynolds numbers} \ll 1$) via time-resolved microtomographic particle image velocimetry. Beyond a critical Weissenberg number of 2, we observe an elastic flow instability accompanied by an enhanced pressure drop with spectral characteristics typical of ET. Polymer chains in the ET flow state are advected along increasingly curved streamlines between pores such that they accumulate strain and generate a local flow instability evaluated per an established instability criterion based on local evaluation of elastic tensile stress and streamline curvature. The onset of ET leads to increased pore-scale resistance and positive feedback on upstream streamline curvature. ET is thus characterized by a continuous evolution between states of laminar and unstable flow: pores with unstable flow flood their adjacent peers and thus encourage straightened streamlines and flow stability across the array, while positive feedback from flow resistance on streamline curvature results in the instability propagating upstream along the array. By employing a geometrically ordered medium, we permit flow state communication between pores, yielding generalized insights highlighting the significance of spatial correlation and flow history, and thus provide new avenues for explaining the mechanisms of ET.

Understanding the mechanism of thermal instability in nanofluids is of fundamental importance to explore the reasons behind the enhancement of heat transfer efficiency. Since Buongiorno (ASME J. Heat Transfer, vol. 128, 2006, pp. 240–250) proposed his theoretical model of nanofluids, most studies focusing on the thermal instability analysis exclusively considered Brownian motion and thermophoresis as the main diffusion mechanisms of nanoparticles. All the analyses concluded that a nanofluid layer is much more unstable than its pure counterpart as it is heated from below. However, a recent experimental observation on Rayleigh–Bénard convection appears to contradict the theoretical prediction, implying that some mechanisms neglected in the previous model may have a significant impact on the onset of thermal convection. In the present study, we revise the convective transport model of nanofluids proposed by Buongiorno and find that the gravitational settling of nanoparticles is a crucial factor influencing the thermal instability behaviour of nanofluids. By performing a linear stability analysis based on the novel model, the effect of gravity settling exhibits a stabilizing mechanism to resist the destabilizing effect of thermophoresis. Furthermore, the onset of instability can be delayed once the nanoparticle diameter exceeds a certain threshold, which explains the phenomenon observed in experiments. Particularly, the oscillatory mode is found to emerge and dominate the flow instability when the gravity settling effect is competitive with the effect of thermophoresis.

The local eddy diffusivity model for the turbulent scalar flux is widely used to understand and predict scalar transport in turbulence. However, local approximation in space and time is not always valid for actual turbulent flow. An exact non-local expression for the scalar flux was previously derived by the author using Green's function. Even though the profile of the non-local eddy diffusivity in a turbulent channel flow was evaluated, its model expression was only discussed phenomenologically. In this study, the non-local eddy diffusivity approach was validated with help of direct numerical simulation (DNS) data of homogeneous isotropic turbulence with an inhomogeneous mean scalar to propose a systematic model expression. Initially, it was verified that the non-local expression for the scalar flux agrees with the value directly obtained from the DNS. In addition, the non-local effect accounts for the overestimation of the scalar flux by the local model and the counter-gradient diffusion phenomenon. The temporal behaviour of the non-local eddy diffusivity was further evaluated using the DNS data. Its model expression being proportional to the two-point velocity correlation was proposed in a manner customary in the statistical theory of turbulence. The profile of the non-local eddy diffusivity obtained from the model expression agrees well with the DNS value, and the non-local model reproduced the scalar flux. These results substantiate the potential of the non-local eddy diffusivity model.