Biomedical Engineering Reference
In-Depth Information
FIGURE 2.27
Streamlines of flow inside a spherical droplet; the flow direction of the surrounding fluid is in z-axis: (a) external
uniform flow; (b) external shear flow; (c) superposition flow with a ¼ 0, b ¼ 1; (d) superposition flow with a ¼ 0.2,
b
¼
1; (e) superposition flow with a
¼
0.4, b
¼
1; and (f) superposition flow with a
1.
(Reprinted with permission from [34] .)
¼
0.6, b
¼
z p is the radial variable in the spherical coordinate system. Superposition of
(2.119) and (2.121) results in the equations of motions of a fluid particle inside a droplet immersed in
a combined shear and uniform flow as shown in Fig. 2.27 .
x 2
where r
¼
þ
y 2
þ
2.5 VISCOELASTIC EFFECTS
In most analysis and design considerations of micromixers, the solute and solvent are assumed to be
Newtonian fluids. In these fluids, the viscosities do not depend on the velocity gradient or the shear
stress. This means at a given temperature and pressure, the viscosity is a constant and the velocity
gradient is linearly proportional to the shear stress. The Newtonian assumption is true for solvents and
solutes with small molecules. However, if they contain large molecules such as long polymers, the
viscosity is also a function of the shear stress. Since the shear stress and viscosity gradient in microscale
increase with miniaturization, nonlinear effects can be expected and exploited for mixing applications.
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