Confined self-propulsion of an isotropic active colloid

To spontaneously break their intrinsic symmetry and self-propel at the micron scale, isotropic active colloidal particles and droplets exploit the nonlinear convective transport of chemical solutes emitted/consumed at their surface by the surface-driven fluid flows generated by these solutes. Significant progress was recently made to understand the onset of self-propulsion and nonlinear dynamics. Yet, most models ignore a fundamental experimental feature, namely the spatial confinement of the colloid, and its effect on propulsion. In this work the self-propulsion of an isotropic colloid inside a capillary tube is investigated numerically. A flexible computational framework is proposed based on a finite-volume approach on adaptative octree grids and embedded boundary methods. This method is able to account for complex geometric confinement, the nonlinear coupling of chemical transport and flow fields, and the precise resolution of the surface boundary conditions, that drive the system's dynamics. Somewhat counterintuitively, spatial confinement promotes the colloid's spontaneous motion by reducing the minimum advection-to-diffusion ratio or Péclet number, ${Pe}$ , required to self-propel; furthermore, self-propulsion velocities are significantly modified as the colloid-to-capillary size ratio $\kappa$ is increased, reaching a maximum at fixed ${Pe}$ for an optimal confinement $0<\kappa <1$ . These properties stem from a fundamental change in the dominant chemical transport mechanism with respect to the unbounded problem: with diffusion now restricted in most directions by the confining walls, the excess solute is predominantly convected away downstream from the colloid, enhancing front-back concentration contrasts. These results are confirmed quantitatively using conservation arguments and lubrication analysis of the tightly confined limit, $\kappa \rightarrow 1$ .

A comparative study on the stress image and adaptive parameter-modified methods for implementing free surface boundary conditions in elastic wave numerical modeling

The stress image method is a simple and effective approach for implementing the free surface boundary conditions in elastic wave numerical modeling. This method assumes that the normal and shear stresses perpendicular to the free surface are antisymmetric with respect to the free surface. In this way, the values of the normal and shear stresses above the free surface can be updated. However, the stress image method is based on an intuitive viewpoint and lacks a physical foundation. The adaptive parameter-modified method is a recently proposed approach for implementing the free surface boundary conditions. Through adaptive modifications of the density and elastic parameters at the free surface, the implementation of the free surface boundary conditions is achieved. Based on the adaptive parameter-modified method, a new interpretation of the stress image method is used. We determine that the stress image method is equivalent to the adaptive parameter-modified method in terms of the staggered-grid finite-difference scheme for the elastic wave equation in displacement form. This result provides a physical foundation and explanation of the stress image method. Therefore, we can further develop the stress image method from a physical viewpoint. Numerical examples are also developed to perform the theoretical analysis.

The Peregrine Breather on the Zero-Background Limit as the Two-Soliton Degenerate Solution: An Experimental Study

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

Numerical Analysis of Hydrodynamic Loads on Passing and Moored Ships in Shallow Water

In this study, hydrodynamic interactions between passing and moored ships were studied by applying a time-domain numerical simulation method. The boundary value problem for a fluid domain was formulated based on a potential flow theory. A numerical method was developed based on a finite element method with an efficient re-mesh algorithm. Regarding the free-surface boundary conditions, both double-body and free-surface models were considered for examining the free-surface effect on the hydrodynamic forces due to the passing ship. First, numerical results were validated by comparison with the model test results of Kriebel et al. (2005), where generic Series 60 hulls were considered as the target model for the passing and moored ships. In addition, hydrodynamic pressure fields and force time-series were investigated to understand the passing ship problem. Second, a series of numerical simulations were performed to study the effects of the passing ship speed, separation distance, water depth, and relative vessel size, which were used to compare the peak values of hydrodynamic forces. The applicability and limitations of the double-body and free-surface models are discussed for predicting passing ship loads.