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Fouling and its mitigation in silicon microchannels used for IC chip cooling

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Abstract

Particulate fouling studies with alumina dispersions in water were performed in rectangular, silicon microchannels having hydraulic diameters between 220 and 225 μm with Reynolds numbers of 17–41. Data show for the most part the absence of particle deposition within the microchannels. The primary reason for this is the relatively high wall shear stress at the microchannel walls of 2.3–3.5 Pa compared to conventional size passageways. In contrast, the headers for the microchannels are quite susceptible to particulate fouling under the same conditions. This is because the shear stress in the header region is lower. Proper adjustment of pH has been identified to effectively mitigate the fouling by controlling the electrostatic forces of repulsion between particle–particle interactions.

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Notes

  1. Velocity magnitude is defined as: \( V_{{{\text{mag}}}} = {\sqrt {V^{2}_{x} + V^{2}_{y} } }, \) V x and V y are the velocities in the x and y directions respectively. V x and V y are perpendicular and parallel respectively to the channel entrances in the header region.

  2. The gravitational force was based on the bulk density of the alumina particles. When aggregates grow there is a decrease in the aggregate density. Even if the density was reduced by a factor of 2 the gravitational force would still be eight times greater than the lift force in the header region.

  3. An approximate value for the energy barrier is given because the scaled separation distance, κa, for the 248-nm particles is only 1.04 at pH 9.0 and 1.69 at pH 9.5. At such a low value of κa the curvature of the surface elements will become important between the two interacting particles and Derjaguin’s approximation loses its accuracy, which was used in the derivation of Eqs. 14 and 15.

Abbreviations

a :

particle radius (m)

A 132 :

Hamaker constant (J)

b :

half channel width (m)

c :

half channel height (m)

d, d p :

particle diameter (m)

D h :

hydraulic diameter (m)

e :

elementary electric charge (coulomb)

E el :

electrostatic interaction energy (J)

E t :

total interaction energy (J)

E vdw :

van der Waals interaction energy (J)

F el :

electrostatic force (N)

F g :

gravitational force (N)

F L :

lift force (N)

F T :

total force (N)

F vdw :

Van der Waals force (N)

g :

acceleration due to gravity (m/s2)

H :

minimum separation distance (m)

J B :

collision rate due to Brownian motion (1/s)

J S :

collision rate due to shear (1/s)

k :

Boltzmann constant (J/K)

m, n :

exponents (unitless)

n*:

electrolyte concentration (atom or molecule per m3)

Re :

Reynolds number (unitless)

R ij :

collision radius of particles i and j (m)

R p :

particle radius (m)

s :

half fin width (m)

T :

absolute temperature (K)

u, U :

velocity (m/s)

u m :

mean velocity (m/s)

u max :

maximum velocity (m/s)

y, z :

distance from surface (m)

z*:

electrolyte valance charge (unitless)

αc*:

channel aspect ratio (unitless)

δ*:

parameter in determining zeta potential (unitless)

εo :

dielectric permittivity of vacuum (F/m)

εr :

relative dielectric constant of medium (unitless)

κ:

Debye–Hückel parameter (1/m)

1/κ:

Debye length or diffuse layer thickness (m)

λ:

wavelength (m)

λc :

characteristic wavelength of interaction (m)

μE :

electrophoretic mobility (m2/V s)

μf :

viscosity of fluid (kg/m s)

ρf :

density of fluid (kg/m3)

ρp :

density of particle (kg/m3)

τw :

Shear stress at wall (Pa)

ψs :

surface potential (V)

ζ:

zeta potential (V)

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Acknowledgments

The authors are thankful for the support of the Microsystems program and Thermal Analysis and Microfluidics Laboratory at the Rochester Institute of Technology. The second author acknowledges the IBM Faculty Award in support of this work.

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Authors and Affiliations

  1. Microsystems Engineering, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Jeffrey L. Perry

  2. Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Satish G. Kandlikar

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  1. Jeffrey L. Perry
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  2. Satish G. Kandlikar
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Correspondence to Satish G. Kandlikar.

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Perry, J.L., Kandlikar, S.G. Fouling and its mitigation in silicon microchannels used for IC chip cooling. Microfluid Nanofluid 5, 357–371 (2008). https://doi.org/10.1007/s10404-007-0254-4

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