Abstract
We present a modular Python library for computing many-body hydrodynamic and phoretic interactions between spherical active particles in suspension, when these are given by solutions of the Stokes and Laplace equations. Underpinning the library is a grid-free methodology that combines dimensionality reduction, spectral expansion, and Ritz-Galerkin discretization, thereby reducing the computation to the solution of a linear system. The system can be solved analytically as a series expansion or numerically at a cost quadratic in the number of particles. Suspension-scale quantities like fluid flow, entropy production, and rheological response are obtained at a small additional cost. The library is agnostic to boundary conditions and includes, amongst others, confinement by plane walls or liquid-liquid interfaces. The use of the library is demonstrated with six fully coded examples simulating active phenomena of current experimental interest.
Highlights
PyStokes is a Python library for studying phoretic and hydrodynamic interactions between spherical particles when these interactions can be described by the solutions of, respectively, the Laplace and Stokes equations
The library has been designed for studying these interactions in suspensions of active particles, which are distinguished by their ability to produce flow, and motion, in the absence of external forces or torques
Such particles are endowed with a mechanism to produce hydrodynamic flow in a thin interfacial layer, which may be due to the motion of cilia, as in microorganisms (Brennen & Winet, 1977) or osmotic flows of various kinds in response to spontaneously generated gradients of phoretic fields (Ebbens & Howse, 2010)
Summary
PyStokes is a Python library for studying phoretic and hydrodynamic interactions between spherical particles when these interactions can be described by the solutions of, respectively, the Laplace and Stokes equations. The library has been designed for studying these interactions in suspensions of active particles, which are distinguished by their ability to produce flow, and motion, in the absence of external forces or torques. Such particles are endowed with a mechanism to produce hydrodynamic flow in a thin interfacial layer, which may be due to the motion of cilia, as in microorganisms (Brennen & Winet, 1977) or osmotic flows of various kinds in response to spontaneously generated gradients of phoretic fields (Ebbens & Howse, 2010). Our software implementation uses a polyglot programming approach that combines the readability of Python with the speed of Cython and retains the advantages of a high-level, dynamically typed, interpreted language without sacrificing performance
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