Dimensionless Numbers in Microfluidics - Microfluidics for Biotechnology - page 9

Figure1.7 Dimensionless numbers and characteristic times for non-Newtonian fluids.

The Bond number is defined by

2

Bo g R (1.20)
where ∆ρ is the volumic mass difference between the two liquids, g is the gravity
acceleration, γ is the surface tension, and R is a characteristic dimension (radius or
contact radius).
The capillary length is a characteristic length for fluid subject to gravity and
surface tension

= D ρ γ

i

γ

λ =

D g ρ

The Bond number compares the characteristic dimension of the fluid element to the
capillary length Bo = R 2 / l 2 (Figure 1.9). For clean water at standard temperature
and pressure, the capillary length is ~2 mm. Note that the definition of the Bond
number can be extended to other forces acting on the droplet. When an electrically

Figure1.8 Numerical simulations of a microdrop ( Bo <<) and a larger drop ( Bo >>) obtained with

Surface Evolver software (not to scale) [9].