Microfluidics Effects of Surface Tension

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MicrofluidicsEffects of Surface Tension

• Schuyler Vowell
• Physics 486
• March 12, 2009

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Microfluidics

• Microfluidics refers to the behavior and control
  of liquids constrained to volumes near the µL
  range.
• Behavior of liquids in the micro domain differs
  greatly from macroscopic fluids.
• Surface tension.
• Laminar flow.
• Fast thermal relaxation.
• Diffusion.
• Microfluidics was developed in the 1980s, mainly
  for use in inkjet printers.
• Microfluidics is an multidisciplinary field with
  a wide variety of applications.

3
Interface

• An interface is a smooth surface separating two
  materials.
• Real interfaces are not smooth, molecules from
  each material mingle at an interface.

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Surface Tension

• Molecules in any medium experience an attractive
  force with other molecules.
• Mainly hydrogen bonds for polar molecules
• Van der Waals forces for other molecules

• Imbalance of this attractive force at an
  interface leads to surface tension

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Surface Tension

• Let U be the average total cohesive energy of a
  molecule, and d be a characteristic dimension of
  a molecule such that d2 represents the effective
  surface area of a molecule, then surface tension
  is approximately
• Surface tension has units of J/m2 N/m, and is
  usually given in mN/m. If S is the total surface
  are of an interface and ? is the surface tension,
  then the total energy stored in the interface is

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Surface Tension Example

• Surface tension can be treated in two ways as
  stored energy per unit area (J/m2) or as a
  tangential force per unit length (N/m)

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Contact Angle Youngs Law

• The contact angle at a triple point (intersection
  of three interfaces) is entirely determined by
  balancing the surface tensions of each interface.
• A more rigorous derivation from minimization of
  free energy yields the same result as a geometric
  argument.

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Capillary Action

• Capillary action refers to the movement of liquid
  through thin tubes, not a specific force.
• Several effects can contribute to capillary
  action, all of which relate to surface tension
• Minimization of surface energy
• Young-Laplace equation pressure difference due
  to curvature of interface.

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Minimization of Surface Energy

• Like any type of energy stored in a system,
  surface energy wants to be minimized.
• Examples include
• Soap films on wire frames form minimal surfaces.
• Water in capillary tubes rises above or falls
  below the surrounding water level.

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Capillary Rise

• Capillary rise is a balance of surface energy and
  gravitational potential energy

For a contact angle less than 90o, the liquid
will rise in the tube, but the liquid can also
fall if the contact angle is greater than 90o.
If the liquid is water, solids with a contact
angle less than 90o are called hydrophilic, the
opposite is hydrophobic.
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Young-Laplace Equation

• The Young-Laplace equation describes the
  relationship between a pressure difference across
  an interface and the curvature of the interface.
• The higher the curvature, the higher the pressure
  difference across the interface.

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Movement of a Liquid Plug
R2 lt R1 for a wetting surface (? lt 90o), hence
P2 gt P1 and the liquid plug moves to the right,
towards the narrower part of the wedge.
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Marangoni Effect

• A gradient in the surface tension along an
  interface causes motion in surface molecules and
  thus motion in the bulk. This is called the
  Marangoni effect.

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Applications of MicrofluidicsBiology (LOC)
Lab on a Chip (LOC) for bacterial culturing and
testing.
Fast PCR using nanodroplets
Kim, H. et al. Nanodroplet real-time PCR system
with laser assisted heating. Optics Express
Vol. 17 No. 1. 5 Jan 2009
Orenstein, D. Microfluidic chips may
accelerate biomedical research. Stanford
Report, 18 Jan 2009. http//news-service.stanfor
d.edu
15
Lab-on-a-Robot
Wireless mobile unit carrying an electrochemical
detection unit and HVPS. After choosing a
location, onboard GPS navigates the robot to the
test site. At test site, a MEMS device diffuses
a gas sample through 50 µL of buffer solution. A
small sample of this solution is injected into a
microfluidic device that electrophoretically
separates the components of the gas. A detector
sends real-time sampling data back to the base
computer running a LabVIEW program, which can be
used to relay new commands to the robot and
analyze the data transmitted from the robot.
Berg, C. et al. Lab-on-a-robot Integrated
microchip CE, power supply, electrochemical
detector, wireless unit, and mobile platform.
Electrophoresis Vol. 29, 2008.