A general contact stiffness model is proposed in this paper to study the contacts between rough surfaces of machined plane joints. The proposed model uses fractal geometry for surface topography description, elastic-plastic deformation of contacting asperities, and size-dependent contact stiffness of microcontacts, where the contact stiffness is derived from Hertz contact theory. Three cast iron specimens are produced from different machining methods (milling, grinding, and scraping), and their rough surface profiles are extracted. The structure function method was used to calculate each profile’s fractal dimension and scale coefficient. Both theoretical analysis and experimental results of contact stiffness are obtained for these specimens under different contact loads. The comparison between the theoretical contact stiffness and the experimental results at the interface indicates that the present fractal model for the contact stiffness is appropriate and the theoretical contact stiffness is consistent with the experimental data.

Whether droplet jumping velocity is enhanced or weakened depends on the impact position of liquid bridge.

The mechanism of coalescence-induced droplet jumping on superhydrophobic surfaces has been relatively well-established over the years. Most of the related studies are only considering the coalescence process of equal-sized water droplets. However, the coalescence of droplets with different sizes is actually more frequently encountered and the effect of the size ratio on droplet jumping is very crucial to the hydrodynamics of this process. In this work, the effect of the initial droplet size ratio on coalescence-induced jumping of two water droplets is investigated experimentally and numerically. For the previously reported jumping droplet sizes (∼1–100 μm), it is found that the critical droplet size ratio below which the jumping does not occur is about 0.56. The results agree well with the experimental data as the size ratios of observed jumping events collapse into the predicted jumping regime. These findings will gain insights into droplet jumping which has great potential in a number of industrial processes.

The coalescence-induced droplet jumping on superhydrophobic surfaces (SHSs) has attracted considerable attention over the past several years. Most of the studies on droplet jumping mainly focus on two-droplet coalescence events whereas the coalescence of three or more droplets is actually more frequent and still remains poorly understood. In this work, a 3D lattice Boltzmann simulation is carried out to investigate the effect of initial droplet arrangements on the coalescence-induced jumping of three equally sized droplets. Depending on the initial position of droplets on the surface, the droplet coalescence behaviors can be generally classified into two types: one is that all droplets coalesce together instantaneously (concentrated configuration), and the other is that the initial coalesced droplet sweeps up the third droplet in its moving path (spaced configuration). The critical Ohnesorge number, Oh, for the transition of inertial-capillary-dominated coalescence to inertially limited-viscous coalescence is found to be 0.10 for droplet coalescence on SHSs with a contact angle of 160°. The jumping droplet velocity for concentrated multidroplet coalescence at Oh ⩽ 0.10 still follows the inertial-capillary scaling with an increased prefactor, which indicates a viable jumping droplet velocity enhancement scheme. However, the droplet jumping velocity is drastically reduced for the spaced configuration compared to that for the aforementioned concentrated configuration. Because Oh exceeds 0.10, the effects of initial droplet arrangements on multidroplet jumping become weaker as viscosity plays a key role in the merging process. This work will provide effective guidelines for the design of functional SHSs with enhanced droplet jumping for a wide range of industrial applications.

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A fractal model for analysing the thermal contact resistance (TCR) of rough surfaces is presented; it is based on the classical heat conduction theory and fractal geometry for the surface topography description, elastic-plastic deformation of contacting asperities, and size-dependent constriction resistance. Relations for the TCR in terms of contact load are obtained for heat conductive surfaces with known material properties and surface topography.With the real contact area being approximately 1 per cent of the apparent contact area or less, the microcontact area distribution has a dominant influence on the TCR. Useful design guidelines for heat contacts are extracted from the numerical results. The analytical results agree well with previous experiments.

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