

Article
Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow
Authors: 
Rosén, T., Lundell, F., Aidun, C. K. 
Document Type: 
Article 
Pubstate: 
Published 
Journal: 
Journal of Fluid Mechanics 
Volume: 
738
563590 
Year: 
2013 
AbstractThe basic dynamics of a prolate spheroidal particle suspended in shear flow is studied using lattice Boltzmann simulations. The spheroid motion is determined by the particle Reynolds number (Re
_{p}) and Stokes number (St), estimating the effects of fluid and particle inertia, respectively, compared with viscous forces on the particle. The particle Reynolds number is defined by Re_p=4Ga^2/ν, where G is the shear rate, a is the length of the spheroid major semiaxis and ν is the kinematic viscosity. The Stokes number is defined as St=α⋅Re
_{p}, where α is the solidtofluid density ratio. Here, a neutrally buoyant prolate spheroidal particle (St=Re
_{p}) of aspect ratio (major axis/minor axis) r
_{p}=4 is considered. The longterm rotational motion for different initial orientations and Re
_{p} is explained by the dominant inertial effect on the particle. The transitions between rotational states are subsequently studied in detail in terms of nonlinear dynamics. Fluid inertia is seen to cause several bifurcations typical for a nonlinear system with odd symmetry around a double zero eigenvalue. Particle inertia gives rise to centrifugal forces which drives the particle to rotate with the symmetry axis in the flowgradient plane (tumbling). At high Rep, the motion is constrained to this planar motion regardless of initial orientation. At a certain critical Reynolds number, Re
_{p}=Re
_{c}, a motionless (steady) state is created through an infiniteperiod saddlenode bifurcation and consequently the tumbling period near the transition is scaled as Re
_{p}Re
_{c}
^{1/2}. Analyses in this paper show that if a transition from tumbling to steady state occurs at Re
_{p}=Re
_{c}, then any parameter β (e.g. confinement or particle spacing) that influences the value of Re
_{c}, such that Re
_{p}=Re
_{c} as β=β
_{c}, will lead to a period that scales as ββ
_{c}
^{1/2} and is independent of particle shape or any geometric aspect ratio in the flow.

