Microfluidics Module

Single-Phase Flow

The Fluid Flow interfaces use physical quantities, such as pressure and flow rate, and physical properties, such as viscosity and density, to define a fluid flow problem. The Laminar Flow interface covers incompressible and weakly compressible flows. This interface also allows for the simulation of non-Newtonian fluid flow. An interface for creeping flow is used when the Reynolds number is significantly smaller than one. This is often referred to as Stokes flow and is appropriate for use when viscous flow is dominant. It is usually applicable to microfluidic devices.

Three-Phase Flow

The Laminar Three-Phase Flow, Phase Field multiphysics interface is designed to track the interfaces between three immiscible and incompressible fluids. The flow is assumed to be laminar; that is, the Reynolds number is low to moderate, and the density of each phase is constant. The interface solves the Navier–Stokes equations for the conservation of momentum as well as a continuity equation for the conservation of mass. The interface position is tracked by solving four additional transport equations, two for the phase field variables and two for the generalized chemical potentials. The movement of the surface is determined by the minimization of free energy. A Ternary Phase Field interface is also available for tracking moving interfaces between three immiscible fluids by solving for two phase field variables and two generalized chemical potential variables.

Transport of Species

The Microfluidics Module provides a dedicated interface for transport of diluted species. It is used to simulate chemical species transport through diffusion, convection (when coupled with fluid flow), and migration in electric fields for mixtures where one component — a solvent — is present in excess (90 mol% or greater). It is typically employed to model the performance of mixers. For modeling chemical reactions in microfluidic devices, the Microfluidics Module can be combined with the Chemical Reaction Engineering Module, which also makes available transport of concentrated species with binary diffusion.

Electrokinetic Flow

When modeling the transport of diluted species, the electromigration of ions in a static electric field can be included according to the Nernst–Planck equation. Applications of this functionality include electrophoretic mobility and electroosmotic flow, i.e., electrokinetic flow. The Microfluidics Module can be combined with the Chemical Reaction Engineering Module to access the Nernst–Planck interface and Electrophoretic Transport interface, which are dedicated to the modeling of electrolytes and can include the formulations of Poisson’s equation or the electroneutrality condition for the charge balance. The combination of Nernst–Planck and Poisson's equations can be used for modeling charged double layers and electroosmotic flow.

Two-Phase Flow

Three different methods are available in the Microfluidics Module for modeling two-phase flow: level set, phase field, and moving mesh methods. These are used to model two fluids separated by a moving fluid interface, where the interface is tracked in detail, including surface curvature and surface tension forces. The level set and phase field methods use a fixed background mesh and solve additional equations to track the interface location. The moving mesh method solves the flow equation on a moving mesh, and boundary conditions representing the fluid interface are directly applied at the surface. In this case, additional equations are solved for the mesh deformation by means of the arbitrary Lagrangian–Eulerian (ALE) method. All of these methods and their interfaces support both compressible and incompressible laminar flows, where one or both fluids can be non-Newtonian.

Porous Media Flow

Porous media flow can also occur in microscale geometries. When the pore size is in the micron range, the flow is often friction-dominated; in such cases, Darcy’s law can be used to solve the flow. The Microfluidics Module features a dedicated interface for porous media flow based on Darcy's law. In this case, shear stresses perpendicular to the flow are neglected. For intermediate flows, an interface for the Brinkman equations is available. This interface models flow through a porous medium where shear stresses cannot be neglected. There is support for both the Stokes–Brinkman formulation, suitable for very low flow velocities, and Forchheimer drag, which is used to account for effects at higher velocities. The fluid can either be incompressible or compressible, provided that the Mach number is less than 0.3. The formulation allows for free and porous media models, including porous media using the Brinkman equations or laminar flow.

These interfaces are appropriate for microfluidic porous media flow. Example applications include paper microfluidics and transport in biological tissue.

Rarefied and Slip Flow

Rarefied gas flow occurs when the mean free path of the molecules becomes comparable with the length scale of the flow. The Knudsen number, Kn, characterizes the importance of rarefaction effects on the flow. As the gas becomes more rarefied (corresponding to how high the Knudsen number is), the Knudsen layer — which is present within one mean free path of the wall — begins to have a significant effect on the flow. For Knudsen numbers below 0.01, rarefaction can be neglected, and the laminar flow interfaces of the Microfluidics Module can be used with nonslip boundary conditions. For slightly rarefied gases (0.01 < Kn < 0.1), the Knudsen layer can be modeled by appropriate boundary conditions at the walls together with the continuum Navier–Stokes equations in the domain. In this instance, a Slip Flow interface is available in the Microfluidics Module. To model higher Knudsen numbers, the Molecular Flow Module is required.