In general, as the length scale (L) of the fluid flow is reduced, properties that scale with the surface area of the system become comparatively more important than those that scale with the volume of the flow (see Table 2-1). This is apparent in the fluid flow itself as the viscous forces, which are generated by shear over the isovelocity surfaces (scaling as L2), dominate over the inertial forces (which scale volumetrically as L3). The Reynolds number (Re), which characterizes the ratio of these two forces, is typically low, so the flow is laminar. In many cases the creeping (Stokes) flow regime applies (). The section Single-Phase Flow describes microfluidic fluid flows in greater detail.

When multiple phases are present surface tension effects become important relative to gravity and inertia at small length scales. The Laplace pressure, capillary force, and Marangoni forces all scale as 1/L. The section Multiphase Flow gives more information on modeling flows involving several phases.

Flow through porous media can also occur on microscale geometries. Because the permeability of a porous media scales as L2 (where L is the average pore radius) the flow is often friction dominated when the pore size is in the micron range and Darcy’s law can be used. For intermediate flows this module also provides a physics interface to model flows where Brinkman equation is appropriate. For more information see Porous Media Flow.

At the microscale, a range of electrohydrodynamic effects can be used to influence the fluid flow. The electric field strength for a given applied voltage scales as 1/L, making it easier to apply relatively large fields to the fluid with moderate voltages. In electroosmosis the uncompensated ions in the charged electric double layer (EDL) present on the fluid surfaces are moved by an electric field, causing a net fluid flow. Electrophoretic and dielectrophoretic forces on charged or polarized particles in the fluid can be used to induce particle motion, as can diamagnetic forces in the case of magnetophoresis. The manipulation of contact angles by the electrowetting phenomena is also easy in microscale devices. The section Electrohydrodynamics explains how to model these phenomena in detail.

Laminar flows make mixing particularly difficult, so mass transport is often diffusion limited. The diffusion time scales as L2, but even in microfluidic systems diffusion is often a slow process. This has implications for chemical transport and hence reactions within microfluidic systems. Chemical Transport and Reactions describes how to model diffusion-based transport and chemical reactions in microfluidics.

As the length scale of the flow becomes comparable to intermolecular length scale, more complex kinetic effects become important. For gases the ratio of the molecular mean free path to the flow geometry size is given by the Knudsen number (Kn). Clearly, Kn scales as 1/L. For Kn < 0.01, fluid flow is usually well described by the Navier–Stokes equations with no-slip boundary conditions. In the slip-flow regime (0.01 < Kn < 0.1) appropriate slip boundary conditions can be used with the Navier–Stokes equations to describe the flow away from the boundary (see Slip Flow). At Knudsen numbers above 0.1 a fully kinetic approach is required. Flows in this regime can be modeled using tools from the Molecular Flow Module.

The next section describes the importance of Dimensionless Numbers in Microfluidics, which are frequently used in transport equations.