Active micromixers - Micromixers Fundamentals Design and Fabrication - page 244

on the size and the bulk polymer. Using packed small particles instead of a bulk material would
improve the response of the actuator. Common hydrogels are polymethacrylic acid tri-ethyleneglycol
(pMAA-g-EG), polyacrylic acid-2-hydroxymethylmethacrylate (pAA-2-HEMA), and polyacryl-
amide-3-methaacrylamidophenylboronic acid (pAAm-3-MPBA).
Electrocapillary actuators rely on the change in interfacial tension between two immiscible,
conductive liquids, or between a solid surface and a liquid, caused by a potential difference. The effect
is also called electrowetting and is caused by the adsorption characteristics of ions at the electric
double layer between the two phases. This layer is typically 1 to 10 nm thick and works as an electrical
insulator between the two conductive liquids. By changing the electrical potential across this double
layer, the surface tension s between the two liquids becomes:

C
2 DF

2

s ¼ s 0 (7.14)

where s 0 is the maximum value of surface tension at V V 0 , C is the capacitance per unit area of the

double layer, and V is the voltage applied across the liquid interface. Electrowetting can be used for
moving a droplet that leads to improved mixing either inside the droplet or in the surrounding liquid.
Readers may refer to Chapter 5 for chaotic mixing in a droplet.
Thermocapillary actuator is another actuation concept suitable a multiphase system. The ther-
mocapillary effect is caused by the temperature dependence of the interfacial tension between two
immiscible phases. At a higher temperature, the molecules in the bulk liquid move faster and their
attractive force decreases. The smaller attractive force causes lower viscosity and lower interfacial
tension. Thermocapillary forces cause a liquid droplet to run away from a heat source and make
a bubble to run toward the heat source. Since the rate of change of surface tension with temperature is
not large, the effect requires considerable heating power to get the desired force. Thermocapillary
actuators are suitable for droplet-based systems.
Centrifugal/Coriolis actuator is based on the rotational motion of a unique device platform, also
called “lab-on-a-disc.” For the flow in this platform, the Navier-Stokes equation has two additional
terms for the centrifugal force f cf the Coriolis force f C [2] :
r D v

¼

2 v

Dt ¼V

p þ m V þ f cf þ f C : (7.15)

For the model depicted in Fig. 7.2 , the expression for the centrifugal force and the Coriolis force
are:

(7.16)
where u indicates the vector of the angular velocity. The Coriolis force acting on the liquid plug
depicted in Fig. 7.2 can be estimated as:

f cf ¼ru ðu rÞf C ¼ 2 ru v;

rRW 2 u 3
8 m

f C ¼ : (7.17)

The Coriolis force is perpendicular to the radial direction and consequently improves transversal
transport in the liquid plug. The ratio between the Coriolis force and the driving centrifugal force is:

rW 2 u
8 m :

f C
f cf ¼

(7.18)