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Fish may take advantage of environmental vortices to save the cost of locomotion. The complex hydrodynamics shed from multiple physical objects may significantly affect fish refuging (holding stationary). Taking a model of a self-propelled flapping plate, we numerically studied the locomotion of the plate in wakes of two tandem cylinders. In most simulations, the plate heaves at its initial position ${G}_{0}$ before the flow comes (releasing Style I). In the typical wake patterns, the plate may hold stationary, drift upstream, or drift downstream. The phase diagrams of these modes in the ${G}_{0}\ensuremath{-}A$ plane for the vortex shedding patterns were obtained, where $A$ is the flapping amplitude. It is observed that the plate is able to hold stationary at multiple equilibrium locations after it is released. Meanwhile, the minimum amplitude and the input power required for the plate seem inversely proportional to the shedding vortex strength. The effect of releasing style was also investigated. If the plate keeps stationary and does not flap until the vortex shedding is fully developed (releasing Style II), then the plate is able to hold stationary at some equilibrium locations but the flapping plate has a very minor effect on the shedding vortices. However, in Style I, the released plate is able to achieve more equilibrium locations through adjusting the phase of vortex shedding. The effort of the preflapping in Style I is not in vain, because although it consumes more energy, it becomes easier to hold stationary later. The relevant mechanism is explored.

The self-propulsion of a three-dimensional flapping flexible plate near the ground is studied using an immersed boundary-lattice Boltzmann method for fluid flow and a finite-element method for plate motion. When the leading edge of the flexible plate is forced into a vertical oscillation near the ground, the entire plate moves freely due to the fluid-structure interaction. The mechanisms underlying the dynamics of the plate near the ground are elucidated. Based on the propulsive behaviors of the flapping plate, three distinct regimes due to the ground effect can be qualitatively identified. These regimes can be described briefly as the expensive, benefited, and uninfluenced propulsion regimes. The analysis of unsteady dynamics and plate deformation indicates that the ground effect becomes weaker for a more flexible plate. We have found that a suitable degree of flexibility can improve propulsion near the ground. The vortical structure around the plate and the pressure distribution on the plate are analyzed to understand propulsive behaviors. The results obtained in this study can provide some physical insights into the propulsive mechanisms of a flapping flexible plate near the ground.

Sedimentation behaviors of an oblate ellipsoidal particle inside narrow [R/a∈(1.2,2.0)] infinitely long circular tubes are studied by the lattice Boltzmann method, where R and a are the radius of the tube and the length of the semimajor axis of the ellipsoid, respectively. The Archimedes numbers (Ar) up to 70 are considered. Four periodic and two steady sedimentation modes are identified. It is the first time that the anomalous mode has been found in a circular tube for an ellipsoidal particle. The phase diagram of the modes as a function of Ar and R/a is obtained. The anomalous mode is observed in the larger R/a and lower-Ar regime. Through comparisons between the anomalous and oscillatory modes, it is found that R/a plays a critical role for the anomalous mode. Some constrained cases with two steady modes are simulated. It is found that the particle settles faster in the unconstrained modes than in the corresponding constrained modes. This might inspire further study on why the particle adopts a specific mode under a certain circumstance.

In this paper, a scheme for specifying contact angle and its hysteresis is incorporated into a multiphase lattice Boltzmann method. The scheme is validated through investigations of the dynamic behaviors of a droplet sliding along two kinds of walls: a smooth (ideal) wall and a rough or chemically inhomogeneous (nonideal) wall. For an ideal wall, the wettability of solid substrates is able to be prescribed. For a nonideal wall, arbitrary contact angle hysteresis can be obtained through adjusting advancing and receding angles. Significantly different phenomena can be recovered for the two kinds of walls. For instance, a droplet on an inclined ideal wall under gravity is impossible to stay stationary. However, the droplet on a nonideal wall may be pinned due to contact angle hysteresis. The steady interface shapes of the droplet on an inclined nonideal wall under gravity or in a shear flow quantitatively agree well with the previous numerical studies. Besides, the complex motion of a droplet creeping like an inchworm could be simulated. The scheme is found suitable for the study of contact line problems with and without contact angle hysteresis.

Zhang and Chen proposed a lattice Boltzmann method for simulations of liquid-vapor thermal flows [Zhang and Chen, Phys. Rev. E 67, 066711 (2003)]. In their numerical test, the authors show simulation results with a temperature ratio of approximately 1.2 for a thermal two-phase flow with $Tl0.8{T}_{c}$. However, we believe this to be erroneous and demonstrate the error to originate from a wrong choice of a parameter of critical importance in the Carnahan-Starling equation of state used in their work. Our numerical tests show that using the correct parameter choice, the scheme is only valid and robust to simulate temperature ratios below 1.10 and the lowest temperature in the flow field should be $0.85{T}_{c}$.

A parallel implementation of the three-dimensional Shan-and-Chen multicomponent, multiphase lattice Boltzmann method (LBM) was used to simulate the equilibrium distributions of two immiscible fluids in porous media. The simulations were successfully validated against cone-beam x-ray microtomographic data on the distribution of oil (decane), water, and air phases in a 5-mm cube of porous medium composed of packed quartz sand grains. The results confirm that LBM models allow for the straightforward incorporation of complex pore space geometry determined from x-ray microtomography measurements and that simulated wetting and nonwetting phase distributions are consistent with x-ray observations on both macroscopic and microscopic scales.

We propose a method for approximating the adhesion parameters in the Shan and Chen multicomponent, multiphase lattice Boltzmann model that leads to the desired fluid-solid contact angle. The method is a straightforward application of Young's equation with substitution of the Shan and Chen cohesion parameter and a density factor for the fluid-fluid interfacial tension, and the adhesion parameters for the corresponding fluid-solid interfacial tensions.