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Annu. Rev. Fluid Mech. 1998. 30:579–612
Copyright
c
1998 by Annual Reviews Inc. All rights reserved
MICRO-ELECTRO-MECHANICAL-
SYSTEMS (MEMS) AND FLUID
FLOWS
Chih-Ming Ho
Mechanical and Aerospace Engineering Department, University of California at Los
Angeles, Los Angeles, California 90095; e-mail: chihming@seas.ucla.edu
Yu-Chong Tai
Electrical Engineering Department, California Institute of Technology, Pasadena,
California 91125; e-mail: yctai@touch.caltech.edu
KEY WORDS: flow control, MEMS, micro transducers, size effect, surface force
ABSTRACT
The micromachining technology that emerged in the late 1980s can provide
micron-sized sensors and actuators. These micro transducers are able to be inte-
grated with signal conditioning and processing circuitry to form micro-electro-
mechanical-systems(MEMS)thatcanperformreal-timedistributedcontrol. This
capability opens up a new territory for flow control research. On the other hand,
surface effects dominate the fluid flowing through these miniature mechanical
devices because of the large surface-to-volume ratio in micron-scale configura-
tions. Weneedtoreexaminethesurfaceforcesin themomentum equation. Owing
to their smallness, gas flows experience large Knudsen numbers, and therefore
boundary conditions need to be modified. Besides being an enabling technology,
MEMS also provide many challenges for fundamental flow-science research.
1. INTRODUCTION
During the past decade, micromachining technology has become available to
fabricate micron-sized mechanical parts. Micromachines have had a major
impact on many disciplines (e.g. biology, medicine, optics, aerospace, and
mechanical and electrical engineering). In this article, we limit our discussion
to transport phenomena, specifically emphasizing fluid-dynamics issues. This
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emerging field not only provides miniature transducers for sensing and actua-
tion in a domain that we could not examine in the past, but also allows us to
venture into a research area in which the surface effects dominate most of the
phenomena.
Figure 1 shows a scanning-electronic-microscope (SEM) picture of an elec-
trostatically driven motor (Fan et al 1988a). This device signifies the beginning
of the micromachine field. A comb structure (Tang et al 1989) derived from
the micro motor concept eventually evolved into the airbag sensor, which re-
duces the damage caused by automobile collisions and is used now on almost
all American-made cars. During the development of the micro motor, it was
found that the frictional force between the rotor and the substrate is a function
of the contact area. This result departs from the traditional frictional law (i.e.
f = µN), which says that the frictional force is linearly proportional to the
normal force, N, only. In the micro motor case, the surface forces between the
rotor and the substrate contribute to most of the frictional force. However, the
traditional frictional law describes situations with a dominating body force that
do not depend on the contact area. Deviations from the conventional wisdom
are commonly found in the micro world. This makes the micromachine field a
new technology as well as a new scientific frontier.
The micromachining process uses lithography to expose the designed photo-
resist patterns; the unwanted portion is then selectively etched away. These
proceduresaresimilarto those usedinintegratedcircuit(IC) fabricationbutwith
Figure 1 A micro motor (Fan et al 1988a). A piece of human hair is shown in front of the motor
to illustrate its minute size.
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a difference: 3-D and freestanding structures are common features, because of
thenatureofmechanical parts. Severalmanufacturingtechnologiessuchasbulk
micromachining, surfacemicromachining, and LIGA (acronym forthe German
phrase LIthographe, Galvanoformung, und Abformung) have been developed
to make various micromachines. A brief introduction of these technologies can
be found in a paper by Ho & Tai (1996). For detailed information, readers are
referred to Petersen 1982, Seidel 1987, and Ristic 1994.
Micromachines have several unique features. First, typical micromachined
transducersizesareontheorderof100microns,whichcanbeoneormoreorders
of magnitude smaller than traditional sensors and actuators. The drastic reduc-
tion in inertia resulting from these smaller sizes means a substantial increase in
the frequency response. Second, batch processing—which is characteristic of
IC fabrication—can be used to make many transducers for distributed sensing
and actuation over a wide area. This capability enables us to sense certain flow
characteristics in a 2-D domain and to perform control at the proper locations.
Potentialapplication areasinclude themanipulationof separationovera smooth
contour or the reduction of surface shear stress in a turbulent boundary layer.
Third, micromachine manufacturing technology is derived from, although not
completely compatible with, IC fabrication so it is possible to integrate the IC
with micro transducers to provide logic capability. Integrated microelectronics
and micromachines constitute the micro-electro-mechanical-system (MEMS),
which can execute sense–decision–actuation on a monolithic level.
In biomedical applications, fluid transport is commonly required in drug
delivery and in chemical and DNA analyses. When dealing with flow in con-
figurations of microns or less, we have observed many unexpected phenomena
that are similar to the aforementioned experience of frictional force between
solid surfaces. Sir Eddington (1928) once said “We used to think that if we
know one, we know two, because one and one are two. We are finding that we
must learna greatdeal moreabout ‘and’.” Indeed, theflows in macro and micro
configurations are not quite the same. The unique features in micromechanics
are perhaps the most intriguing ones for researchers in basic fluid mechanics.
We still have a great deal of difficulty in understanding these features, because
not much is known about the complex surface effects that play major roles in
these events. The search for their answers will excite researchers for years to
come. In this paper, we first report and discuss the fundamental micro-fluid-
mechanics issues and then review flow sensing and control using MEMS.
2. SIZE EFFECTS
2.1 Ratio Between Surface Force and Body Force
Length scale is a fundamental quantity that dictates the type of forces governing
physical phenomena. Body forces are scaled to the third power of the length
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scale. Surface forces depend on the first power or the second power of the
characteristic length. Because of the difference in slopes, the body force must
intersect with the surface force. In biological studies (Went 1968), empirical
observations indicated that a millimeter length is the approximate order of the
demarcation. Experiences gathered in MEMS also show that surface forces
dominate in sizes smaller than a millimeter. For example, the friction expe-
rienced by the 100-micron-diameter micro motor (Fan et al 1988a,b) must be
caused mainly by the surface force, because the rotor started to move when
the contact area between the rotor and the substrate was reduced by placing
dimples on the lower surface of the rotor.
2.2 Ratio Between Device and Intrinsic Length Scales
Besides the large surface force, the large surface-to-volume ratio is another
characteristic inherent in small devices. This ratio is typically inversely pro-
portional to the smaller length scale of the cross section of the device and is
about one micron in surface micromachined devices. Therefore, the surface-
to-volume ratio is much larger in a micro device than in a macro device,
which accentuates the role of surface force as well as other surface effects in
general.
In micro flows, the Reynolds number is typically very small and shows the
ratio between the viscous force and the inertial force. However, in the case
when gas is the working fluid, the size can be small enough to further modify
the viscous effect when the device length scale is on the order of the mean free
path. For large Knudsen-number flows, the flow velocity at the surface starts
to slip (Knudsen 1909, Kennard 1938); therefore, the viscous shear stress is
much reduced. For liquid flows, the distance between molecules is on the order
of angstroms. The non-slip condition has always been used as an empirical
result. By using a molecular dynamics approach (Koplik et al 1989, Koplik
& Banavar 1995), the non-slip condition at the solid surface is established in
Couette and Poiseuille liquid flows. On the other hand, molecular ordering has
been observed and results in oscillatory density profiles in the vicinity of the
wall, which are a few molecular spacings thick. In the case of a moving contact
line at the fluid/fluid/solid interface, the non-slip condition needs to be relaxed
(Dussan & Davis 1974). Typical micromachined devices have a length scale
much larger than the molecular spacing of simple liquids. Hence, the non-slip
boundary condition should hold in the absence of a moving contact line.
In other situations, the bulk flow instead of the boundary condition is mod-
ified. For example, most solid surfaces have electrostatic surface charges,
which can attract ions in liquid flows to form an electric double layer (EDL)
(see Section 3.2). The thickness of the EDL varies from a few nm to 100s of
nm (Hunter 1981), which can be comparable to the order of micro-flow length
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MEMS & FLUID FLOWS 583
scale. In these cases, the bulk flow can be affected by this electrically charged
layer (Mohiuddin Mala et al 1996).
3. SURFACE FORCES
For fluid flows in MEMS, new phenomena arise because of certain surface
forces that are usually ignored in macro scales. Here, a brief survey is given on
several kinds of surface forces (Israelachvili 1991). Before the discussion of
someseeminglydifferentsurfaceforces, it isimportanttoknowthattheseforces
originate from intermolecular forces. Moreover, even though basic intermolec-
ular forcesare short range (<1 nm) in nature, theycan cumulativelylead to very
long-range (>0.1 µm) effects (e.g. surface-tension effects in liquids). Another
important point is that all intermolecular forces are fundamentally electrostatic
(coulombic). This is established by the Hellman-Feynman theorem that states
that once the spatial electron distribution is determined from the Schr¨odinger
equation, all intermolecular forces can then be calculated using classical elec-
trostatics. However, in practice this cannot always be done, and empirical or
semiempirical laws of forces are still useful. In the following, we then treat
the following surface forces differently even though they are the same in origin
from the point of view of quantum mechanics.
3.1 Van der Waals Forces
The van der Waals forces are the weakest among all the forces, but they are
important because they are always present. The van der Waals forces are short
range in nature but, in cases where large molecules or surfaces are involved,
they can produce an effect longer than 0.1 µm. In general, van der Waals forces
have three parts: orientation force, induction force, and dispersion force. All
have an interaction free energy that varies with the inverse sixth power of the
distance (1/r
6
) and are, hence, short range. The orientation force is the dipole–
dipole interaction force between polar molecules. The induction force arises
from the interaction between a polar molecule and a nonpolar molecule. The
permanent dipole of the polar molecule induces a weak dipole in the nonpolar
molecule and then produces a dipole-induced dipole-interaction force. The
dispersion force is then the induced-dipole–induced-dipole interaction force.
Interestingly, the dispersion forces act on all atoms and molecules even when
they are totally neutral, as are those of helium and oxygen. The source of the
dispersion force between two nonpolar molecules is the following: Although
the averaged dipole moment of a nonpolar molecule is zero, at any instant there
exists a finite dipole moment depending on the exact position of the electrons
around its nucleus. This instantaneous dipole moment can then generate an
interaction force with nearby molecules.
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