Swimming velocity of spherical squirmers in a square tube at finite fluid inertia

The three-dimensional lattice Boltzmann method(LBM)is used to simulate the motion of a spherical squirmer in a square tube,and the steady motion velocity of a squirmer with different Reynolds numbers(Re,ranging from 0.1 to 2)and swimming types is investigated and analyzed to better understand the swimming characteristics of microorganisms in different environments.First,as the Reynolds number increases,the effect of the inertial forces becomes significant,disrupting the squirmer's ability to maintain its theoretical velocity.Specifically,as the Reynolds number increases,the structure of the flow field around the squirmer changes,affecting its velocity of motion.Notably,the swimming velocity of the squirmer exhibits a quadratic relationship with the type of swimming and the Reynolds number.Second,the narrow tube exerts a significant inhibitory effect on the squirmer motion.In addition,although chirality does not directly affect the swimming velocity of the squirmer,it can indirectly affect the velocity by changing its motion mode.

A LB-DF/FD Method for Particle Suspensions

In this paper, we propose a lattice Boltzmann (LB) method coupled with adirect-forcing fictitious domain (DF/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and the DF/FD methodsby using two unrelated meshes, namely, an Eulerian mesh for the flow domain and aLagrangian mesh for the solid domain, which avoids the re-meshing procedure anddoes not need to calculate the hydrodynamic forces at each time step. The non-slipboundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation, which preserves all remarkable advantages of the LBM in simulatingfluid flows. The present LB-DF/FD method has been validated by comparing its results with analytical results and previous numerical results for a single circular particleand two circular particles settling under gravity. The interaction between particle andwall, the process of drafting-kissing-tumbling (DKT) of two settling particles will bedemonstrated. As a manifestation of the efficiency of the present method, the settlingof a large number (128) of circular particles is simulated in an enclosure.

New formula for drag coefficient of cylindrical particles

The drag force on a cylindrical particle is calculated using lattice Boltzmann method. The results show that the drag coefficient of a particle with different orientation angles decreases with increasing Reynolds number. When the principal axis of the particle is parallel to flow, the drag coefficient is much larger than that of others and decreases fastest with increasing Reynolds number, which becomes more obvious with increasing particle aspect ratio. When the principal axis of the particle is inclined to flow, the drag coefficient is nearly the same for different particle aspect ratios. In the case of flow with small Reynolds number （Re〈 100）, the drag coefficient decreases with increasing orientation angle at different aspect ratios and Reynolds numbers. The drag coefficient is more sensitive to particle orientation angle when the particle orientation angle is small and the aspect ratio is large. Finally, a new correlation formula for the drag coefficient of cylindrical particle is established, with which the drag force on a cylindrical particle can be directly calculated based on the Reynolds number, particle aspect ratio and orientation angle.

Direct Numerical Simulation of Multiple Particles Sedimentation at an Intermediate Reynolds Number

In this work the previously developed Lattice Boltzmann-Direct Forcing/Fictitious Domain(LB-DF/FD)method is adopted to simulate the sedimentation of eight circular particles under gravity at an intermediate Reynolds number of about 248.The particle clustering and the resulting Drafting-Kissing-Tumbling(DKT)motion which takes place for the first time are explored.The effects of initial particleparticle gap on the DKT motion are found significant.In addition,the trajectories of particles are presented under different initial particle-particle gaps,which display totally three kinds of falling patterns provided that no DKT motion takes place,i.e.the concave-down shape,the shape of letter“M”and“in-line”shape.Furthermore,the lateral and vertical hydrodynamic forces on the particles are investigated.It has been found that the value of Strouhal number for all particles is the same which is about 0.157 when initial particle-particle gap is relatively large.The wall effects on falling patterns and particle expansions are examined in the final.

A fluctuating lattice-Boltzmann model for direct numerical simulation of particle Brownian motion

A single-relaxation-time fluctuating lattice-Boltzmann （LB） model for direct numerical simulation （DNS） of particle Brownian motion is established by adding a fluctuating component to the lattice-Boltzmann equations （LBEs）. The fluctuating term is proved to be the random stress tensor in fluctuating hydrodynamics by recovering Navier-Stokes equations from LBEs through a Chapman-Enskog expansion. A three-dimensional implementation of the model is also presented, along with simulations of a single spherical particle and 125 spherical particles at short times. Numerical results including the meansquare displacement, velocity autocorrelation function and self-diffusion coefficient of particles compare favorably with theoretical results and previous numerical results.

A Lattice Boltzmann-Direct Forcing/Fictitious Domain Model for Brownian Particles in Fluctuating Fluids

The previously developed LB-DF/FD method derived from the lattice Boltzmann method and Direct Forcing/Fictitious Domain method is extended to deal with 3D particle’s Brownian motion.In the model the thermal fluctuations are introduced as random forces and torques acting on the Brownian particle.The hydrodynamic interaction is introduced by directly resolving the fluid motions.A sphere fluctuating in a cubic box with the periodic boundary is considered to validate the present model.By examining the velocity autocorrelation function(VCF)and rotational velocity autocorrelation function(RVCF),it has been found that in addition to the two relaxation times,the mass density ratio should be taken into consideration to check the accuracy and effectiveness of the present model.Furthermore,the fluctuation-dissipation theorem and equipartition theorem have been investigated for a single spherical particle.Finally,a Brownian particle trapped in a harmonic potential has been simulated to further demonstrate the ability of the LB-DF/FD model.