Thermodynamic Analysis of Irreversibility in Microfluidic Mixing Devices

Abstract

Microfluidic mixing devices must generate species-concentration uniformity within channel lengths of only a few
millimeters, and doing so under laminar, low-Reynolds-number flow necessarily relies on chaotic advection
structures that dissipate mechanical energy and generate entropy through both viscous friction and irreversible
mass diffusion, yet the relative size of these two irreversibility sources across realistic operating conditions is not
always reported quantitatively for a given mixer geometry. We performed a second-law (entropy generation
minimization) analysis of a staggered-herringbone passive micromixer combining computational fluid dynamics with
a scalar transport solver across 40 operating conditions spanning flow rates from 5 to 200 muL/min (Reynolds
number 0.02-0.9, Peclet number 1.2 x 10^3-4.8 x 10^4). Total volumetric entropy generation rate increased from 3.1
x 10^-3 W/(m^3 K) at the lowest flow rate to 2.86 W/(m^3 K) at the highest, a roughly 920-fold increase, with the
balance between viscous and diffusive (concentration-gradient) contributions shifting systematically across this
range: diffusive entropy generation dominated at low flow rate (81% of total at 5 muL/min) while viscous entropy
generation dominated at high flow rate (76% of total at 200 muL/min), crossing over at an intermediate flow rate of
approximately 42 muL/min. The mixing index, defined from the coefficient of variation of outlet concentration,
improved from 0.61 at the lowest flow rate to 0.94 at 80 muL/min but then plateaued, reaching only 0.96 at the
highest flow rate tested, while total entropy generation over the same interval more than quadrupled, indicating
strongly diminishing thermodynamic returns on mixing quality beyond roughly 80 muL/min. A dimensionless Bejan
number, the ratio of diffusive to total entropy generation, decreased monotonically from 0.81 to 0.24 across the
tested flow range (R^2 = 0.97 for a power-law fit against Peclet number), and a geometric parameter sweep varying
herringbone groove depth by ±25% shifted the crossover flow rate by up to 18% while changing peak mixing index
by less than 2 percentage points. These results identify an operating window, approximately 60-90 muL/min for this
geometry, in which near-complete mixing is achieved without incurring the steep entropy-generation penalty of
substantially higher flow rates, providing a quantitative second-law basis for selecting operating conditions in
passive microfluidic mixer design.