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The ecological interaction between bacteria and sinking particles, such as bacterial degradation of marine snow particles, is regulated by their encounters. Current encounter models focus on the diffusive regime, valid for particles larger than the bacterial run length, yet the majority of marine snow particles are small, and the encounter process is then ballistic. Here, we analytically and numerically quantify the encounter rate between sinking particles and non-motile or motile micro-organisms in the ballistic regime, explicitly accounting for the hydrodynamic shear created by the particle and its coupling with micro-organism shape. We complement results with selected experiments on non-motile diatoms. The shape-shear coupling has a considerable effect on the encounter rate and encounter location through the mechanisms of hydrodynamic focusing and screening, whereby elongated micro-organisms preferentially orient normally to the particle surface downstream of the particle (focusing) and tangentially to the surface upstream of the particle (screening). Non-motile elongated micro-organisms are screened from sinking particles because shear aligns them tangentially to the particle surface, which reduces the encounter rate by a factor proportional to the square of the micro-organism aspect ratio. For motile elongated micro-organisms, hydrodynamic focusing increases the encounter rate when particle sinking speed is similar to micro-organism swimming speed, whereas for very quickly sinking particles hydrodynamic screening can reduce the encounter rate below that of non-motile micro-organisms. For natural ocean conditions, we connect the ballistic and diffusive limits and compute the encounter rate as a function of shape, motility and particle characteristics. Our results indicate that shear should be taken into account to predict the interactions between bacteria and sinking particles responsible for the large carbon flux in the ocean's biological pump.

This paper presents a bottom-up approach to derivation of orientation tensor closures for fiber suspension flow models. To begin with, we consider polynomial approximations based on the two-dimensional (2D) versions of the linear, quadratic, natural, and orthotropic smooth closures for reconstruction of the fourth-order orientation tensor. A numerical study is performed for simple flows. The investigation of planar closures provides new insights and boundary conditions for the design of orthotropic closures in three dimensions. The proposed extensions use finite element shape functions to interpolate the data at principal orientation states and additional points. The results for 3D simple flows indicate that natural closures based on (extended) quadratic and piecewise-linear interpolation provide a far better description of the 3D orientation dynamics than any other orthotropic closure considered in this study.

Most theoretical fibre suspension models currently used for predicting the flow-induced evolution of microstructure in the processing of reinforced thermoplastics are based on the Jeffery model of dilute suspensions in a Newtonian suspending fluid or phenomenological adaptations of it that account for fibre-fibre interactions. An important assumption of all these models is the Newtonian character of the fluid in which the fibres are suspended. In industrial practice, the considered fluids are in general molten thermoplastics that exhibit a viscoelastic behaviour. Even though few counterparts of the Jeffery theory exist for second-order fluids, they have been rarely considered and, to our knowledge, never taken into account at the macroscopic scale. In this paper, we address the modelling of short fibre suspensions in second-order fluids throughout the different description scales, from microscopic to macroscopic. We propose a simplified modelling framework that allows one to extend to viscoelastic suspending fluids the standard Folgar and Tucker model widely used in industrial simulation software.

We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek–Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological description of hydrodynamic interactions between agents at high density. Stokes equations describe a low Reynolds number fluid. These two dynamics are coupled by the interaction between the agents and the fluid. The fluid contributes to rotating the particles through Jeffery’s equation. Particle self-propulsion induces a force dipole on the fluid. After coarse-graining we obtain a coupled Self-Organised Hydrodynamics–Stokes system. We perform a linear stability analysis for this system which shows that both pullers and pushers have unstable modes. We conclude by providing extensions of the Vicsek–Stokes model including short-distance repulsion, finite particle inertia and finite Reynolds number fluid regime.

When addressing the flow of concentrated suspensions composed of rods, dense clusters are observed. Thus, the adequate modelling and simulation of such a flow requires addressing the kinematics of these dense clusters and their impact on the flow in which they are immersed. In a former work, we addressed a first modelling framework of these clusters, assumed so dense that they were considered rigid and their kinematics (flow-induced rotation) were totally defined by a symmetric tensor \\[{\\mathbf {c}}\\] with unit trace representing the cluster conformation. Then, the rigid nature of the clusters was relaxed, assuming them deformable, and a model giving the evolution of both the cluster shape and its microstructural orientation descriptor (the so-called shape and orientation tensors) was proposed. This paper compares the predictions coming from those models with finer-scale discrete simulations inspired from molecular dynamics modelling.

In this paper, an Integrated Radial Basis Function (IRBF)-based multiscale method is used to simulate the rheological properties of dilute fibre suspensions. For the approach, a fusion of the IRBF computation scheme, the Discrete Adaptive Viscoelastic Stress Splitting (DAVSS) technique and the Fibre Configuration Field has been developed to investigate the evolution of the flow and the fibre configurations through two separate computational processes. Indeed, the flow conservation equations, which are expressed in vorticity-stream function formulation, are solved using IRBF-based numerical schemes while the evolution of fibre configuration fields governed by the Jeffery’s equation is captured using the principle of Brownian Configuration Fields. The two procedures are coupled together by the Lipscomb expression which is used to determine the fibre stress of dilute fibre suspensions. Owing to advantages of the IRBF scheme and the DAVSS technique, the present method yields a more accurate solution and faster convergence rate. The simulation method is verified and its capability is demonstrated with the fibre suspension flows through two parallel plates, a circular tube and the 4:1 and 4.5:1 axisymmetric contraction geometries which are usually chosen to test a numerical method because of the challenging nature of these problems.

A new approach based on the Adomian decomposition and the Fourier transform is introduced. The method suggests a solution for the well-known magneto-hydrodynamic (MHD) Jeffery-Hamel equation. Results of Adomian decomposition method combined with Fourier transform are compared with exact and numerical methods. The FTADM as an exclusive and new method satisfies all boundary and initial conditions over the entire spatial and temporal domains. Moreover, using the FTADM leads to rapid approach of approximate results toward the exact solutions is demonstrated. The second derivative of Jeffery-Hamel solution related to the similar number of items of recursive terms under a vast spatial domain shows the maximum error in the order of 10 − 5 comparing to exact and numerical solutions. The results also imply that the FTADM can be considered as a precise approximation for solving the third-order nonlinear Jeffery-Hamel equations.

A numerical method based on the one-way coupling using the Jeffery equation is presented. The influence of the inlet velocity and the initial orientation on the evolution of fiber orientation is investigated. It is observed that the rotation mainly contributes to the pressure rise, and the flow structure is not obviously altered. Due to the one-way coupling, the effects of the inlet velocity and the rotating rate are insignificant. nema

In this article, we developed the new functional matrix of integration using the Bernoulli wavelet and proposed a novel technique called the Bernoulli wavelet collocation method (BWCM). The main intention of this study is to present a consistent methodology to compute an imprecise solution of Jeffery–Hamel flow and heat transfer in Eyring–Powell fluid in the presence of a magnetic field by using the BWCM. Jeffery–Hamel flows occur in different realistic situations connecting flow between two non-parallel walls. Applications of such fluids in biological and industrial sciences brought great concern to the investigation of flow characteristics in converging and diverging channels. Here, we transform the nonlinear partial differential equations into coupled ordinary differential equations (ODEs) via similarity transformation. Using the BWCM, coupled ODEs are converted into a system of a nonlinear algebraic equation. This technique finds the numerical solution without any restrictive assumptions and avoids round-off errors. The numerical solutions attained by the proposed scheme point out that the approach is easy to implement and computationally very beautiful. The validity of the BWCM is ascertained by comparing our results with the Haar wavelet method and numerical differentiation Solver in Mathematica results. The influence of several emerging dimensionless parameters, namely the Eyring–Powell parameter, Hartman number, Eckert number, local Reynolds number, and the angle between the two walls on velocity and temperature evolution in the boundary layer regime, is examined in detail.