Table 1.

Dimensionless parameters of fluid dynamics in droplet-based microfluidics

Dimensionless parameter	Mathematical definition	Physical implication
Reynolds number (Re)	$\frac{\rho LV}{\mu }$	The ratio of inertia forces to viscous forces
Capillary number (Ca)	$\frac{\mu V}{\sigma }$	The ratio of viscous force to surface or interfacial tension
Weber number (We)	$\frac{\rho L{V}^2}{\sigma }$	The ratio of inertia forces to surface or interfacial tension
Flow rate ratio (Ψ )	$\frac{Q_1}{Q_2}$	The flow rate ratio between dispersed and carrier phases
Viscosity ratio (Ω )	$\frac{{\mu }_1}{{\mu }_2}$	The viscosity ratio between dispersed and carrier fluids

Symbol ρ : fluid density; L : characteristic length; V : characteristic velocity; μ : dynamic viscosity of fluids; σ : surface tension or interfacial tension between two fluid phases; Q : flow rate. Subscript 1: dispersed phase; 2: carrier phase.