The squirmer is a simple yet instructive model for microswimmers, which employs an effective slip velocity on the surface of a spherical swimmer to describe its self-propulsion. We solve the hydrodynamic flow problem with the lattice Boltzmann (LB) method, which is well-suited for time-dependent problems involving complex boundary conditions. Incorporating the squirmer into LB is relatively straight-forward, but requires an unexpectedly fine grid resolution to capture the physical flow fields and behaviors accurately. We demonstrate this using four basic hydrodynamic tests: Two for the far-field flow-accuracy of the hydrodynamic moments and squirmer-squirmer interactions-and two that require the near field to be accurately resolved-a squirmer confined to a tube and one scattering off a spherical obstacle-which LB is capable of doing down to the grid resolution. We find good agreement with (numerical) results obtained using other hydrodynamic solvers in the same geometries and identify a minimum required resolution to achieve this reproduction. We discuss our algorithm in the context of other hydrodynamic solvers and present an outlook on its application to multi-squirmer problems. arXiv:1903.04799v2 [physics.flu-dyn]

Self-propelled particles have been experimentally shown to orbit spherical obstacles and move along surfaces. Here, we theoretically and numerically investigate this behavior for a hydrodynamic squirmer interacting with spherical objects and flat walls using three different methods of approximately solving the Stokes equations: The method of reflections, which is accurate in the far field; lubrication theory, which describes the close-to-contact behavior; and a lattice Boltzmann solver that accurately accounts for near-field flows. The method of reflections predicts three distinct behaviors: orbiting/sliding, scattering, and hovering, with orbiting being favored for lower curvature as in the literature. Surprisingly, it also shows backward orbiting/sliding for sufficiently strong pushers, caused by fluid recirculation in the gap between the squirmer and the obstacle leading to strong forces opposing forward motion. Lubrication theory instead suggests that only hovering is a stable point for the dynamics. We therefore employ lattice Boltzmann to resolve this discrepancy and we qualitatively reproduce the richer far-field predictions. Our results thus provide insight into a possible mechanism of mobility reversal mediated solely through hydrodynamic interactions with a surface. mers 19 . In addition, chemical patterning of the surface has been shown to significantly modify the mobility of a chemical swimmer 37-41 . These man-made swimmers can also follow strongly curved surfaces, even leading them to orbit around spherical obstacles 16,18 .The orbiting of swimmers has been studied extensively using hydrodynamic descriptions 23,42 . In the far field, the associated hydrodynamic problem is typically solved using the methodof-reflections approximation 20 and Faxén's law 43,44 . Spagnolie et al. 23 account for the leading-order hydrodynamic force-dipole moment in their analysis and find that there is a critical radius for orbiting. Only pusher swimmers -ones that have an extensile flow field -enter such a trajectory 23 ; pullers on the other hand are trapped in a 'hovering' state, wherein they point straight into the surface. However, the methods of reflections is known to break down for small swimmer-obstacle separations 22 .In the lubrication regime, which captures the behavior for vanishing gap sizes, a swimmer's ability to follow a path along a planar wall has been examined 45,46 . Specifically, Lintuvuori et al. 45 studied a squirmer, which is a simple model swimmer that accounts for finite-size contributions to the flow field. The results for a squirmer near a flat wall may be readily transferred to orbiting around objects with low curvature. Unfortunately, lubrication theory does not provide substantial insight other than for the hovering state, wherein the swimmer's direction of motion is into the obstacle and no tangential displacement occurs. J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 1-13 | 1 arXiv:1904.02630v4 [cond-mat.soft] 3 Jul 2019 2 | 1-13 J o u r n a l N a me , [ y e a r ] , [ v o l . ] , *...

The surface charge of an open water surface is crucial for solvation phenomena and interfacial processes in aqueous systems. However, the magnitude of the charge is controversial, and the physical mechanism of charging remains incompletely understood. Here we identify a previously overlooked physical mechanism determining the surface charge of water. Using accurate charge measurements of water microdrops, we demonstrate that the water surface charge originates from the electrostatic effects in the contact line vicinity of three phases, one of which is water. Our experiments, theory, and simulations provide evidence that a junction of two aqueous interfaces (e.g., liquid–solid and liquid–air) develops a pH-dependent contact potential difference Δϕ due to the longitudinal charge redistribution between two contacting interfaces. This universal static charging mechanism may have implications for the origin of electrical potentials in biological, nanofluidic, and electrochemical systems and helps to predict and control the surface charge of water in various experimental environments.