Hari Sriram
Multiscale Mechanics and Nanotechnology Laboratory
Advisor: Sumit Sinha Ray, Dr. Suman Sinha Ray, Dr. A.L. Yarin
August 2, 2012
 Carbon Nanotubes (CNTs) are group of carbon
molecules rolled up into cylindrical structure and are
used in different parts of science such as
microelectronics, biomedical applications etc.
 We are using CNTs as carriers of phase change
materials (PCM), like wax, which will serve as a
coolant in microelectronic devices
Transmission Electronic
Microscopy (TEM) image
of PCM intercalated CNTs
Sinha-Ray, S., R. P. Sahu, and A. L. Yarin. "Nano-encapsulated Smart Tunable Phase Change Materials." Soft Matter 7.19 (2011): 8823-827
 Find a surfactant that will create a stable suspension as
well as to optimize the CNT and surfactant
concentration
 Find the highest weight percentage of CNTs in
suspension that can flow through microchannels
 Find the flow characteristics of CNT suspensions with
and without wax
 Using the flow characteristics of the wax intercalated
CNTs to see how the suspension absorbs heat in a
microelectronic system by making a prototype of it
with a constant heat flux condition
 Pressure from the air line
two way valve
pushes the plunger down
 The plunger pushes the oil
down through the pipe
which in turn pushes the
CNT suspension through
the microchannel
 The valve is used to release
the oil into the syringe
.
Q exp erimental 
Air Line
Air
Plunger
Oil Chamber
Pressure Gauge
Valve Assembly
Suspension Chamber
V
t
three way valve
Microchannel
The connected line is the theoretical flow rate and the scattered points are the
experimental flow rate
 We have found sodium dodecylbenzenesulfonate (NaDDBS) to
be the surfactant that creates the most stable suspension
 The ratio of CNT concentration to NaDDBS concentration was
found to be 1:10
(a)
(b)
CNT Suspension after
16hrs of sonication and
left to settle for 1 hour
with:
(a) 1mL of NaDDBS
(b) No added surfactant
M. F. Islam, E. Rojas, D. M. Bergey, A. T. Johnson and A. G. Yodh: Nano Letters., 2003, 3, 269-273
 We have varied CNT weight percentage for CNT
suspensions as well as wax intercalated CNTs
 Experimental flow rate was observed to be 1.2-1.4 times
greater than theory
 The experimental flow rate was greater for higher
concentrations of CNTs
Flow Rate of different concentrations of CNT suspension: (a) 0.1% (b) 0.3% (c)
0.6% (d) 1%. The connected line is the theoretical flow rate and the scattered
points are the experimental flow rate
Flow Rate of different concentrations of wax intercalated CNT suspensions: (a)
0.15% (b) 0.2% (c) 0.5% (d) 0.7%. The connected line is the theoretical flow rate
and the scattered points are the experimental flow rate
 Formation of nanobubbles caused by the surfactant
 Desolubilization of gas in the suspension causes
the formation of the nanobubbles
 λ is referred to as the slip length, which is defined
as the fictitious distance below the surface where
the no-slip boundary condition would be satisfied.
.
Q exp erim ental
.
Q theoretical
 1
4
No Slip
Partial Slip
Perfect Slip
a
λ=0
λ
0<λ<∞
λ=∞
C. Tropea, A. L. Yarin, and J. F. Foss: ‘Springer Handbook of Experimental Fluid Mechanics’, 1219-1240; 2007, Berlin, Springer.
As the concentration of CNT increased, the concentration of surfactant
increased and therefore created more slip along the walls of the channel
 As constant heat flux is added to system, the fluid
absorbs the heat and through convection the heat is
dissipated in the wax
 We assume that the flow is at steady state and that all
the heat that is put in the system should be taken out
 The heat transfer coefficient will tell us how much of
the heat is taken out of the system
𝒒
𝒉=
𝑨(𝑻𝒆 − 𝑻𝒊
q is the heat put into the system
A is the surface area of the channel
Te-Ti is the change in overall
temperature
J. P. Holman: ‘Heat Transfer’, 253-257; 2010, New York, McGraw-Hill.
 Flow characteristics for suspensions of CNT as high
as 1%/wt without wax and 0.7%/wt for wax
intercalated CNT has been seen
 The surfactant NaDDBS produces slip along the
walls of the microchannel, producing a higher flow
rate
 Vary concentrations of wax intercalated CNTs and
measure the heat transfer coefficient
The financial support from the National Science
Foundation, EEC-NSF Grant # 1062943 is gratefully
acknowledged
Special Thanks to Dr. Christos Takoudis, Dr. Gregory
Jursich
 The Poiseuille equations gives the flow profile of a fluid through a
cylindrical pipe with a circular cross sections
 Assumptions that are made are that the flow is laminar, fully
developed and at steady state
 The fluid is assumed to be viscous and incompressible
 The Poiseuille equation is derived from the Navier-Stokes equations
which are the basis the describe the velocity profile of fluids
dz
vz 
1 dP
4  dz
R (1 
2
r
2
R
2
)
r is the radius of the
fluid
dP/dz is the change
in pressure
R
r
dr
Flow through a cylindrical
channel with circular cross
section
Munson, Bruce Roy, T. H. Okiishi, and Wade W. Huebsch. Fundamentals of Fluid Mechanics. Hoboken, NJ: J. Wiley &
Sons, 2009.
Velocity at the walls are zero
due to friction and the
maximum velocity is at the
center (No-slip boundary
condition)
Q theoretica
R  P
4
.
l

8L
Q is the volumetric flow rate
R is that radius of the channel
P is the pressure at the exit valve
μ is the viscosity of the carbon
nanotubes
L is the length of the microchannel
Munson, Bruce Roy, T. H. Okiishi, and Wade W. Huebsch. Fundamentals of Fluid Mechanics. Hoboken, NJ: J. Wiley &
Sons, 2009.