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In this work, we numerically study the impact of a water droplet onto a deep oil pool. Two fluids are immiscible and the viscosity of the pool liquid is changed systematically. We focus on the cavity dynamics during the impact and especially the effects of the pool liquid viscosity and the impacting velocity. For the parameter range explored, we identify the regime where splashing occurs with corolla breaking into droplets, and the regime where no splashing is observed. Similarity is found for the time evolution of cavity depth for fixed impact velocity and different viscosity, if the cavity depth and time are nondimensionalized by the maximal depth and the time when the maximal depth is reached. Effective power-law scalings are also proposed to describe the dependence of the maximal cavity depth and the corresponding time on the impact velocity and pool liquid viscosity, in the term of Froude and Reynolds numbers.

In this study the effects of the actuation waveforms on the droplet generation in a drop-on-demand inkjet printing are studied systematically by numerical simulations. Two different types of waveforms, namely the unipolar and bipolar actuations, are investigated for three fluids with different physical properties. We focus on two key parameters, which are the dwell time and the velocity amplitude. For the unipolar driving, the ejection velocity and the ejected liquid volume are both increased as the velocity amplitude becomes larger. The dwell time only has minor effects on both the ejection velocity and the ejected liquid volume. The ejection velocity decreases significantly for large liquid viscosity, while the influences of viscosity on the ejected liquid volume are much weaker. Four different droplet morphologies and the corresponding parameter ranges are identified. The droplet radius can be successfully reduced to about 40% of the nozzle exit radius. For the bipolar waveforms, same droplet morphologies are observed but with shifted boundaries in the phase space. The minimal radius of stable droplet produced by the bipolar waveforms is even smaller compared to the unipolar ones.

In this work fingering double diffusive convection, i.e. the buoyancy-driven flow with fluid density being affected by two different scalar components, is investigated numerically with special efforts on the influences of the physical properties of two scalar components. We show that different scalar properties can affect the global transport behaviors. The concentration flux exhibits different exponents in their power-law scalings for different combinations of scalar components. The scaling exponents of heat flux, however, depend mainly on the ratio of the diffusivities of two scalars. If one uses the local parameters of the finger layer in the bulk, the behaviors are very similar to those found in the fully periodic simulations. The horizontal width of the fingers is consistent with the wavelength of the fast growing mode. For one case we observe evidences of the thermohaline staircase, namely, the typical width of the flow structures changes significantly in different layers within the flow domain.

In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro–nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom (SDOF) along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro–nano scales is set up.

The concept vortex force in aerodynamics is systematically examined based on a new steady vortex-force theory (Wu et al., Vorticity and vortex dynamics, Springer, 2006) which expresses the aerodynamic force (and moment) by the volume and boundary integrals of the Lamb vector. In this paper, the underlying physics of this theory is explored, including the general role of the Lamb vector in nonlinear aerodynamics, its initial formation, and its relevance to the total-pressure non-uniformity. As a typical example, the theory is applied to the flow over a slender delta wing at a large angle of attack. The highly localized flow structures with high Lamb-vector peaks are identified in terms of their net contribution to various constituents of the total aerodynamic force. This vortex-force diagnosis sheds new light on the flow control and configuration optimization.