Microfluidics Module Glossary

absorption (gas)

Uptake of a gas into the bulk of a liquid. Gas absorption takes place, for example, in the liquid of a scrubber tower where an up-streaming gas is washed by a down-going flow of a scrubber solution.

adsorption (molecule)

Attachment of a molecule or atom to a solid surface. Adsorption involves a chemical bond between the adsorbed species and the surface.

ALE

See arbitrary Lagrangian-Eulerian method.

arbitrary Lagrangian-Eulerian (ALE) method

A technique to formulate equations in a mixed kinematical description. An ALE referential coordinate system is typically a mix between the material (Lagrangian) and spatial (Eulerian) coordinate systems.

biosensor

A general term for sensor devices that either detect biological substances or use antibodies, enzymes, or other biological molecules in their operation. Biosensors are a subcategory of chemical sensors.

Bond number

A dimensionless number given by the ratio of surface tension forces to body forces (usually gravity) for a two-phase flow. It is also known as the Eötvös number, Eo. At high Bond numbers surface tension has a minimal effect on the flow; at low Bond numbers, surface tension dominates. The Bond number, Bo, is given by:

where ρ is the density, g is the body force acceleration, L is the characteristic length, and σ is the surface tension coefficient. The density can refer to a density difference when considering buoyancy.

Brinkman equations

A set of equations extending Darcy’s law in order to include the transport of momentum through shear in porous media flow.

Capillary number

A dimensionless number given by the ratio of viscous forces to surface tension for a two phase flow. At low capillary numbers flow in porous media is dominated by surface tension. The capillary number, Ca, is given by:

where μ is the viscosity, v is the characteristic velocity of the problem, and σ is the surface tension coefficient.

continuum Flow

Fluid flow which is well described by approximating the liquid as a continuum with the Navier-Stokes equations.

convection

Transport of molecules or heat due to the movement of the surrounding medium.

crosswind diffusion

A numerical technique for stabilization of the numeric solution to a convection-dominated PDE by artificially adding diffusion perpendicular to the direction of the streamlines.

Darcy’s Law

Equation that gives the velocity vector as proportional to the pressure gradient. Often used to describe flow in porous media.

Debye Layer

See electric double layer.

dielectrophoresis

Migration of polarizable particles in an electrolyte in a nonuniform applied electric field.

diffusion

Transport of material resulting from the random motion of molecules in the presence of a concentration gradient.

Direct simulation Monte Carlo (DSMC)

The DSMC method uses probabilistic (Monte Carlo) simulation to solve the Boltzmann equation for finite Knudsen number fluid flows. The approach models the trajectories of large numbers of molecules through the system, taking account of collisions between the molecules and the walls.

Dukhin number

A dimensionless number given by the ratio of the surface conductivity contribution to the fluid bulk electrical conductivity contribution in electrokinetic phenomena. The Dukhin number, Du, is given by:

where Kσ is the surface conductivity and KB is the bulk conductivity. For low Dukhin numbers, surface conductivities can be neglected when modeling electrokinetic flows.

electric double layer (EDL)

Sometimes referred to as the Debye layer. At the contact of a solid and a polar fluid (such as water), the solid acquires an electric charge. This charge attracts ions within the fluid, and a narrow fluid layer of opposite charge, the Stern layer, forms on the boundary. In addition, adjacent to the Stern layer, a wider layer with the same charge as in the Stern layer forms in the fluid. Together, the Stern layer and the wider layer (called the diffuse or Gouy-Chapman layer) form the electric double layer. Due to the close distance between the charges, the Stern layer is fixed on the surface, but the more distant diffuse layer can move.

electrokinetics

Study of the motion of charged particles under an applied electric field in moving substances such as water.

electrokinetic flow

Transport of fluid or charged particles within a fluid by means of electric fields. See also electroosmosis, electrophoresis, electrothermal flow, and dielectrophoresis.

electrolyte

A solution that can carry an electric current through the motion of ions.

electroosmosis

Fluid flow in a narrow channel produced by the movement of the electric double layer (EDL) along the channel boundary under the influence of an applied electric field. Also, fluid flow through a membrane under the influence of an applied electric field. See also electric double layer.

electroosmotic flow

See electroosmosis.

electrophoresis

Migration of charged electrolyte ions or particles in an applied electric field.

electrothermal flow

Fluid flow resulting from an applied nonuniform AC electric field on a fluid. The Joule heating changes the fluid’s electrical properties locally, and that effect, together with the power gradient of the AC electric field, results in fluid motion.

electrowetting

The electrowetting effect describes the change in solid-electrolyte contact angle that occurs when a potential difference is applied between the solid and the electrolyte.

electrowetting-on-dielectric (EWOD)

A form of electrowetting in which a thin insulating layer separates the conducting solid surface from the electrolyte.

Eötvös number

See Bond number.

Eulerian frame

A frame of reference with its coordinate axes fixed in space.

Fick’s laws

The first law relates the concentration gradients to the diffusive flux of low concentration solute diluted in a solvent. The second law introduces the first law into a differential material balance for the solute.

free molecular flow

The flow of gas molecules through a geometry which is much smaller than the mean free path (Knudsen number, Kn>10). In the free molecular flow regime the gas molecules collide with the walls of the geometry much more frequently than they collide with themselves.

fully developed laminar flow

Laminar flow along a channel or pipe that has velocity components only in the main direction of the flow. The velocity profile perpendicular to the flow does not change downstream in the flow.

Gouy-Chapman layer

See electric double layer (EDL).

Hagen-Poiseuille equation

See Poiseuille’s law.

Helmholtz-Smoluchowski equation

Gives the velocity of a parallel electroosmotic flow for an applied electric field.

Knudsen number

A dimensionless number that provides a measure of how rarefied a gas flow is, in other words, the mean free path of the gas molecules compared to the length scale of the flow. The following equation defines the Knudsen number Kn where λ is the mean free path of the molecules and L is a length scale characteristic to the flow.

Knudsen layer

A layer of rarefied fluid flow that occurs within a few mean free paths of the walls in a gas flow. The continuum Navier-Stokes equations break down in this layer.

Laplace number

The Laplace number, La, (also known as the Surataman number, Su) relates the inertial and surface tension forces to the viscous forces. It is used to describe the breakup of liquid jets and sheets: at high Laplace and low Reynolds numbers the Rayleigh Instability occurs, at low Laplace and high Reynolds numbers atomization occurs. The Laplace number is given by:

where ρ is the fluid density, σ is the surface tension coefficient, L is the characteristic length scale of the problem, and μ is the viscosity. The Laplace number is directly related to the Ohnesorge number, Oh, through the equation La=1/Oh2.

Lagrangian frame

A frame of reference with its coordinate axes fixed in a reference configuration of a deforming material. As the material deforms, the Lagrangian frame deforms with it.

Mach number

Ratio of the convective speed, v, to the speed of sound in the medium, a. The Mach number, Ma, is defined by the equation:

magnetophoresis

Migration of magnetic or paramagnetic particles suspended in a fluid as a result of an applied magnetic field. The field must be non-uniform in the case of paramagnetic particles.

Marangoni effect

Fluid flow parallel to an interface induced by surface tension gradients.

Marangoni number

Ratio of thermal surface tension forces to viscous forces. The Marangoni number, Mg, is given by:

where σ is the surface tension coefficient, T is the absolute temperature (ΔT is the characteristic temperature difference), L is the characteristic length, and α is the thermal diffusivity (α=κ/(ρcp)), where cp is the heat capacity at constant pressure, κ is the thermal conductivity, and ρ is the density of the fluid.

microfluidics

Study of the behavior of fluids at the microscale. Also refers to MEMS fluidic devices.

migration

The nonrandom movement of particles under an external force.

mobility

The relation between the drift velocity of a molecule within a fluid and the applied electric field.

Newtonian Flow

Flow characterized by a constant viscosity or a viscosity that is independent of the shear rate in the fluid.

Nernst-Plank Equation

Flow equation that describes the flux of an ion through diffusion, convection, and migration in an electric field. The equation is valid for diluted electrolytes.

Ohnesorge number

A dimensionless number relating the inertial and surface tension forces to the viscous forces. Used to describe the breakup of liquid jets and sheets: at low Ohnesorge and Reynolds numbers the Rayleigh instability occurs; at high Ohnesorge and Reynolds numbers atomization occurs. The Ohnesorge number, Oh, is given by:

where ρ is the fluid density, σ is the surface tension coefficient, L is the characteristic length scale of the problem, and μ is the viscosity. The Ohnesorge number is directly related to the Laplace number, La, through the equation Oh=1/La1/2.

Peclet number

A dimensionless number describing the ratio of convection to diffusion in a fluid flow. The Peclet number, Pe, can be used to describe concentration diffusion or heat diffusion. It is given by:

where v is the convective velocity, L is the flow length scale, and D is the diffusion constant.

Poiseuille’s law

Equation that relates the mass rate of flow in a tube as proportional to the pressure difference per unit length and to the fourth power of the tube radius. The law is valid for fully developed laminar flow.

Reynolds number

A dimensionless number classifying how laminar or turbulent a flow is. The Reynolds number Re is a measure of the relative magnitude of the flow’s viscous and inertial forces. It is defined by the following equation where ρ is the fluid density, μ is the dynamic viscosity, ν is its kinematic viscosity, v is a velocity characteristic to the flow, and L is a length scale characteristic to the flow.

slip flow

Fluid flow that occurs when the Knudsen number, Kn, is in the range 0.01<Kn<0.1. As a result of rarefaction effects in the Knudsen layer the no slip boundary condition fails. The flow outside the Knudsen layer can be represented by the continuum Navier-Stokes equations provided that an appropriate slip boundary condition is used for the fluid flow and the correct temperature jump boundary condition is applied at the interface.

streamline diffusion

A numerical technique for stabilization of the numeric solution to a convection-dominated PDE by artificially adding diffusion in the direction of the streamlines.

Stern layer

A layer of immobile ions and associated solvent molecules present at the solid-liquid interface in an electric double layer (EDL).

surface tension

Surface tension is a property of the surface of a liquid that allows it to resist an external force. Equivalently it can be through of as the energy per unit area of the liquid surface. It is caused by asymmetries in the cohesive forces between molecules at the surface of the liquid.

Surataman number

See Laplace number.

transitional flow

Fluid flow that occurs when the Knudsen number, Kn, is in the range 0.1<Kn<10. In this regime the flow is so rarefied that continuum equations break down completely. However collisions between the molecules are still important, so free molecular flow is not applicable.

Weber number

A dimensionless number describing the ratio of inertial forces to surface tension forces. The Weber number is given by:

where ρ is the density of the fluid, v is the characteristic velocity of the flow, L is the characteristic length scale, and σ is the surface tension coefficient.

zeta potential

The potential of at the interface between the electric double layer and a solid surface in an electrolyte.