Abstract
Inertial particle microfluidics (IPMF) is an emerging technology for the manipulation and separation of microparticles and biological cells. Since the flow physics of IPMF is complex and experimental studies are often time-consuming or costly, computer simulations can offer complementary insights. In this tutorial review, we provide a guide for researchers who are exploring the potential of the lattice-Boltzmann (LB) method for simulating IPMF applications. We first review the existing literature to establish the state of the art of LB-based IPMF modelling. After summarising the physics of IPMF, we then present related methods used in LB models for IPMF and show several case studies of LB simulations for a range of IPMF scenarios. Finally, we conclude with an outlook and several proposed research directions.
Competing Interest Statement
The authors have declared no competing interest.
Nomenclature
Latin Letters
- A
- Surface area of a particle
- A(0)
- Surface area of an undeformed particle
- Area of undeformed mesh element
- b
- Body force density
- f (x, v, t)
- Probability distribution function
- cs
- Lattice speed of sound
- fi(x, t)
- Discretised probability distribution function
- ci
- Discretised lattice velocities
- E
- Total energy of the membrane
- EB
- Bending energy of the membrane
- ES
- Strain energy of the membrane
- EA
- Surface area energy of the membrane
- EV
- Volume energy of the membrane
- Discretised equilibrium distributions function
- F
- Total force acting on a particle
- g
- Gravitational acceleration
- H0
- Spontaneous curvature of the membrane
- H
- Trace of the surface curvature tensor
- I
- Inertia tensor of a particle
- I1, I2
- Strain invariants
- l
- Characteristic length scale of the system
- Average distance between neighbouring mesh vertices
- Discretised non-equilibrium distribution function
- n
- Surface normal vector pointing into the surrounding fluid
- p
- Fluid pressure
- mi
- Discretised moments of distribution functions
- x
- Position vector of a point on the particle surface a Particle radius
- Rij
- Relaxation matrix
- Si
- Forcing source terms
- t
- Time
- Δt
- Length of the time step
- T
- Total torque acting on a particle
- 1
- Unit matrix
- U
- Characteristic velocity of the system
- u
- Macroscopic fluid velocity
- ueq
- Equilibrium fluid velocity
- v
- Linear particle velocity
- V
- Volume of a particle
- V(0)
- Volume of an undeformed particle
Greek Letters
- θij
- Angle between two neighbouring normal vectors of the deformed mesh
- Angle between two neighbouring normal vectors of the undeformed mesh
- ω
- Angular velocity of a particle
- Ωi
- Collision operator
- ϕl
- Particle line fraction
- ϕ
- Volumetric particle concentration
- ρp
- Particle density
- ρ
- Fluid density
- σαβ
- Fluid stress tensor
- λ1, λ2
- Principal stretch ratios
- κb
- Bending modulus
- κα
- Dilation modulus
- κs
- Shear modulus
- κS
- Area constraint modulus
- κV
- Volume constraint modulus
- τ
- Relaxation time
- ωj
- Relaxation frequency
- Fluid shear rate
- Strain energy density
- µ
- Dynamic fluid viscosity
- ηin
- Cytoplasmic viscosity
- ηm
- Membrane viscosity
- wi
- Lattice weights
Superscripts
- Ca
- Capillary number
- χ
- Particle-to-channel confinement Re Reynolds number
- Rep
- Particle Reynolds number St Stokes number