nPIV Velocimetry

**Effect of**

**Non-Uniform Out-of Plane Illumination and Shear rates on nPIV Velocimetry**

**Objectives**

To identify the effects of hindered Brownian motion, shear and non-uniform light illumination on nPIV velocity measurements using simulated particle images at the near wall region.

**Problem Definition**

Tracer particles immersed in
a fluid are assumed to follow the fluid flow with fidelity, which in
turn enables velocimetry measurements. However, at the near-wall
region, *O*(10-8 m), hindered Brownian motion occurs due to the
presence of the wall which violates the assumption and in turn biases
the velocimetry measurements. Nano-PIV uses evanescent-wave
illumination produced by Total Internal Reflection (TIR) (see Fig. 1)
which can also bias measurements therefore these effects, as well as
effects of varying shear rates, are studied to identify fluid
characteristics that are required for the design of nano-scale systems
in industries such as medicine and electronics.

**General procedure**

Monte Carlo simulations and
the Langevin equation are used to generate images that simulate the
flow of naturally buoyant fluorescent tracers in Poiseuille flow at the
near-wall region. The effects of hindered Brownian motion, linear
velocity profiles and exponential light decay are studied, over time by
introducing these parameters, individually and collectively, to
uniform flow. Standard cross-correlation PIV techniques are then used
to process the images, identifying any velocimetry bias that may occur.

**Conclusions and Future Direction**

It is clear from our results that hindered Brownian motion can lead to overestimation of near-wall velocities for time intervals ∆t ~ zv/D∞, where zv is the visible region defined by the objective lens, and D∞ is the Brownian diffusion coefficient. The results also show that the type of illumination used affects the bias in velocimetry measurements, largely underestimating the flow when using exponentially decaying illumination such as that generated using TIR. The combined effects of hindered Brownian motion and varying shear rates can be seen for the 3 different light illumination profiles in Figure 4 below. It is clear from the figure that shear rate is also a dominant factor in the measurements bias.

Future work will be carried out to address further the effects of
surface forces on nPIV velocimtery, in combination with shear rates,
uniform and exponentially decaying light illumination and hindered
Brownian motion.

**Supervisor:** Dr. Reza Sadr

**Acknowledgements:** Dr. Anoop Kanjirakat

**Publication **

Khader, R. and Sadr, R., 2010,
“Effect Of Non Uniform Out-Of-Plane Illumination And Shear Rate On The
Accuracy Of Npiv Velocity Measurements,” ASME Paper no.
FEDSM-ICNMM2010-30567.** **

Figure 1.** **Light illumination schematic in an nPIV set up

*a*= particle radius

*z _{v} = *depth in which the particles can be seen

*z*=(

_{c}*z*/2 +

_{v}*a*)

*θ*= incident angle

Figure 2.** **Actual convected velocity of the particle tracers in a shear flow in this study compared with the suggested model by Sadr *et al*., 2007, JFM.

*G* = shear rate, s^{-1}

*U _{c}* = average center position (

*U*=

_{c}*z*×

_{c }*G)*

Figure 3.** **Effects of lighting profile on shear flow
velocity measurement. Each line contains all the shear rates study in
this work, i.e. *G* = 1000, 1500, 2000, and 3000 *s*^{-1}

Figure 4.** **Calculated nPIV velocity for Brownian particle tracers in shear flow with different illumination profile *a)* uniform light, *b) *linear light profile *c) *exponential light profile.