An atomistic model for the thermal resistance of a liquid–solid interface

The thermal resistance associated with the interface between a solid and a liquid is analysed from an atomistic point of view. Partial evaluation of the associated Green–Kubo integral elucidates the various factors governing heat transport across the interface and leads to a quantitative model for the thermal resistance in terms of atomistic-level system parameters. The model is validated using molecular dynamics simulations.

The influence of fluid–structure interaction on cloud cavitation about a rigid and a flexible hydrofoil. Part 3

Experimental studies of the influence of fluid–structure interaction on cloud cavitation about a stiff stainless steel (SS) and a flexible composite (CF) hydrofoil have been presented in Parts I (Smith et al., J. Fluid Mech., vol. 896, 2020a, p. A1) and II (Smith et al., J. Fluid Mech., vol. 897, 2020b, p. A28). This work further analyses the data and complements the measurements with reduced-order model predictions to explain the complex response. A two degrees-of-freedom steady-state model is used to explain why the tip bending and twisting deformations are much higher for the CF hydrofoil, while the hydrodynamic load coefficients are very similar. A one degree-of-freedom dynamic model, which considers the spanwise bending deflection only, is used to capture the dynamic response of both hydrofoils. Peaks in the frequency response spectrum are observed at the re-entrant jet-driven and shock-wave-driven cavity shedding frequencies, system bending frequency and heterodyne frequencies caused by the mixing of the two cavity shedding frequencies. The predictions capture the increase of the mean system bending frequency and wider bandwidth of frequency modulation with decreasing cavitation number. The results show that, in general, the amplitude of the deformation fluctuation is higher, but the amplitude of the load fluctuation is lower for the CF hydrofoil compared with the SS hydrofoil. Significant dynamic load amplification is observed at subharmonic lock-in when the shock-wave-driven cavity shedding frequency matches with the nearest subharmonic of the system bending frequency of the CF hydrofoil. Both measurements and predictions show an absence of dynamic load amplification at primary lock-in because of the low intensity of cavity load fluctuations with high cavitation number.

Ice breaking by a high-speed water jet impact

Ice breaking has become one of the main problems faced by ships and other equipment operating in an ice-covered water region. New methods are always being pursued and studied to improve ice-breaking capabilities and efficiencies. Based on the strong damage capability, a high-speed water jet impact is proposed to be used to break an ice plate in contact with water. A series of experiments of water jet impacting ice were performed in a transparent water tank, where the water jets at tens of metres per second were generated by a home-made device and circular ice plates of various thicknesses and scales were produced in a cold room. The entire evolution of the water jet and ice was recorded by two high-speed cameras from the top and front views simultaneously. The focus was the responses of the ice plate, such as crack development and breakup, under the high-speed water jet loads, which involved compressible pressure ${P_1}$ and incompressible pressure ${P_2}$ . According to the main cause and crack development sequence, it was found that the damage of the ice could be roughly divided into five patterns. On this basis, the effects of water jet strength, ice thickness, ice plate size and boundary conditions were also investigated. Experiments validated the ice-breaking capability of the high-speed water jet, which could be a new auxiliary ice-breaking method in the future.

Linear stability analysis of a time-divergent slamming flow

When a liquid slams into a solid, the intermediate gas is squeezed out at a speed that diverges when approaching the moment of impact. Although there is mounting experimental evidence that instabilities form on the liquid interface during such an event, understanding of the nature of these instabilities is limited. This study therefore addresses the stability of a liquid–gas interface with surface tension, subject to a diverging flow in the gas phase, where the liquid and the gas phase are both represented as potential fluids. We perform a Kelvin–Helmholtz-type linear modal stability analysis of the surface to obtain an amplitude equation that is subsequently analysed in detail and applied to two cases of interest for impact problems, namely, the parallel impact of a wave onto a vertical wall, and the impact of a horizontal plate onto a liquid surface. In both cases we find that long wavelengths are stabilised considerably in comparison with what may be expected based upon classical knowledge of the stability of interfaces subject to a constant gas flow. In the former case, this leads to the prediction of a marginally stable wavelength that is completely absent in the classical analysis. For the latter we find much resemblance to the classical case, with the connotation that the instability is suppressed for smaller disk sizes. The study ends with a discussion of the influence of gas viscosity and gas compressibility on the respective stability diagrams.

Centrifugal spinning of viscoelastic nanofibres

The centrifugal spinning method is a recently invented technique to extrude polymer melts/solutions into ultra-fine nanofibres. Here, we present a superior integrated string-based mathematical model, to quantify the nanofibre fabrication performance in the centrifugal spinning process. Our model enables us to analyse the critical flow parameters covering an extensive range, by incorporating the angular momentum equations, the Giesekus viscoelastic constitutive model, the air-to-fibre drag effects and the energy equation into the string model equations. Using the model, we can analyse the dynamic behaviour of polymer melt/solution jets through the dimensionless flow parameters, namely, the Rossby ( $Rb$ ), Reynolds ( $Re$ ), Weissenberg ( $Wi$ ), Weber ( $We$ ), Froude ( $Fr$ ), air Péclet ( $Pe^*$ ) and air Reynolds ( $Re^*$ ) numbers as well as the viscosity ratio ( $\delta _s$ ), corresponding to rotational, inertial, viscous, viscoelastic, surface tension, gravitational, air thermal diffusivity, aerodynamic and viscosity ratio effects. We find that the nonlinear rheology remarkably affects the fibre trajectory, radius and normal stresses. Increasing $Wi$ leads to a thicker fibre, whereas increasing $\delta _s$ shows an opposite trend. In addition, by increasing $Wi$ , the fibre curvature is enhanced, causing the fibre to spiral closer to the rotation centre.

Chemical production on a deforming substrate

The interplay between chemical reaction and substrate deformation is discussed by adapting Ranz's formulation for scalar mixing to the case of a reactive mixture between segregated reactants, initially separated by an interface whose thickness may not be vanishingly small. Experiments in a simple shear flow demonstrate the existence of three regimes depending on the Damköhler number $Da=t_s/t_c$ where $t_s$ is the mixing time of the interface width and $t_c$ is the chemical time. Instead of treating explicitly the chemical cross-term, we rationalize these different regimes by globalizing it as a production term involving a flux which depends on the rate at which the reaction zone is fed by the reactants, a formulation valid for $Da>1$ . For $Da<1$ , the reactants interpenetrate before they react, giving rise to a ‘diffusio-chemical’ regime where chemical production occurs within a substrate whose width is controlled by molecular diffusion.

Experimental validation of inviscid linear stability theory applied to an axisymmetric jet

We study the development of perturbations in a submerged air jet with a round cross-section and a long laminar region (five jet diameters) at a Reynolds number of 5400 by both inviscid linear stability theory and experiments. The theoretical analysis shows that there are two modes of growing axisymmetric perturbations, which are generated by three generalized inflection points of the jet's velocity profile. To validate the results of linear stability theory, we conduct experiments with controlled axisymmetric perturbations to the jet. The characteristics of growing waves are obtained by visualization, thermoanemometer measurements and correlation analysis. Experimentally measured wavelengths, growth rates and spatial distributions of velocity fluctuations for both growing modes are in good agreement with theoretical calculations. Therefore, it is demonstrated that small perturbations to the laminar jet closely follow the predictions of inviscid linear stability theory.

The effect of inertia and vertical confinement on the flow past a circular cylinder in a Hele-Shaw configuration

The Poiseuille flow (centreline velocity $U_c$ ) of a fluid (kinematic viscosity $\nu$ ) past a circular cylinder (radius $R$ ) in a Hele-Shaw cell (height $2h$ ) is traditionally characterised by a Stokes flow ( $\varLambda =(U_cR/\nu )(h/R)^2 \ll 1$ ) through a thin gap ( $\epsilon =h/R \ll 1$ ). In this work we use asymptotic methods and direct numerical simulations to explore the parameter space $\varLambda$ – $\epsilon$ when these conditions are not met. Starting with the Navier–Stokes equations and increasing $\varLambda$ (which corresponds to increasing inertial effects), four successive regimes are identified, namely the linear regime, nonlinear regimes I and II in the boundary layer (the ‘ inner’ region) and a nonlinear regime III in both the inner and outer region. Flow phenomena are studied with extensive comparisons made between reduced calculations, direct numerical simulations and previous analytical work. For $\epsilon =0.01$ , the limiting condition for a steady flow as $\varLambda$ is increased is the instability of the Poiseuille flow. However, for larger $\epsilon$ , this limit is at a much higher $\varLambda$ , resulting in a laminar separation bubble, of size ${O}(h)$ , forming for a certain range of $\epsilon$ at the back of the cylinder, where the azimuthal location was dependent on $\epsilon$ . As $\epsilon$ is increased to approximately 0.5, the secondary flow becomes increasingly confined adjacent to the sidewalls. The results of the analysis and numerical simulations are summarised in a plot of the parameter space $\varLambda$ – $\epsilon$ .

Capillary instability of a two-layer annular film: an airway closure model

Capillary instability of a two-layer liquid film lining a rigid tube is studied computationally as a model for liquid plug formation and closure of human airways. The two-layer liquid consists of a serous layer, also called the periciliary liquid layer, at the inner side and a mucus layer at the outer side. Together, they form the airway surface liquid lining the airway wall and surrounding an air core. Liquid plug formation occurs due to Plateau–Rayleigh instability when the liquid film thickness exceeds a critical value. Numerical simulations are performed for the entire closure process, including the pre- and post-coalescence phases. The mechanical stresses and their gradients on the airway wall are investigated for physiologically relevant ranges of the mucus-to-serous thickness ratio, the viscosity ratio, and the air–mucus and serous–mucus surface tensions encompassing healthy and pathological conditions of a typical adult human lung. The growth rate of the two-layer model is found to be higher in comparison with a one-layer equivalent configuration. This leads to a much sooner closure in the two-layer model than that in the corresponding one-layer model. Moreover, it is found that the serous layer generally provides an effective protection to the pulmonary epithelium against high shear stress excursions and their gradients. A linear stability analysis is also performed, and the results are found to be in good qualitative agreement with the simulations. Finally, a secondary coalescence that may occur during the post-closure phase is investigated.