Page 201 - Instrumentation Reference Book 3E

Doppler anemometry 185
coefficient y of a spherical particle of radius a can Small differences between using the computer
be expressed according to the Stokes-Einstein least squares fit and the graphical method were
relation as: reported, with a discrepancy of about 3.5 percent
in determining the mean radius. The computer
(12.24) curve-fitting method was likely to be the more
accurate, although the graphical method is much
where k is Boltzman's constant, Tis the absolute simpler.
temperature, and 17 is the absolute viscosity of Experiments using syton particles of approxi-
the fluid medium. For a particle distribution with mately 46nm radius over a 1:2048 dilution
a diffusion coefficient ofy( y). the autocorrelation range from undiluted syton over 12 subsequent
function of scattered light amplitude C(T) result- dilutions, each diluted with an equal volume of
ing from a suspension of particles undergoing distilled water, have been reported. Good COI-
Brownian motion is given by: relation was observed for the mean radius
1: (46.5 nm) and the standard deviation (20.8 nm)
c(t) = p(y)e-@J" dv (12.25) over the spread of radii, although particle clamp-
where Q is the Bragg wavenumber (Q = 47rdX). ing in the undiluted specimen was believed to
have distorted the result for this initial sample.
By using the power spectrum of the scattered
light with an amplitude of: 12.4.3 Fluid flow
C(t) COSW~ dt
S(W) = 2 6 (12.26) The extension of the FODA type technique to
it can be shown that the expression for the nor- fluid flow measurement has met with some suc-
cess, although problems have been found in that
malized modified Lorentzian power spectrum is: the fiber disturbs the flow about its end face. This
problem stems from the fact that a stagnation
S(w) = region exists within a few hundred micrometers
of the fiber end face. Since the depth of penetra-
tion of the radiation from the fiber into the fluid
medium ranges from about 100pm to about
1 mm, a range of velocities will generally be
where wo = Q' kT16ii17a for particles with a mean observed in the Doppler shifted backscattered
radius n with a standard distribution of the radius radiation, depending on the absorbency of the
ofa; for oa < a. fluid suspension. FODA has been applied to the
The particle radii and the radii standard devi- measurement of blood flow (Kilpatrick et al.
ation were determined by a computer least squares 1982), where the penetration depth of HeNe laser
fit, and good correlation was found for the calcu- radiation at 632.8nm is of the order of 30Qpm
lated Lorentzian with the measured power spec- from the fiber tip. Here, the fiber probe was
trum (Ross etal. 1978). A second and more introduced into a simulated blood flow stream
convenient method of determining a and cra from and the backscattered power spectrum recorded
the integrated Lorentzian power spectrum with a spectrum analyzer. A frequency spectrum
expressed ir, equation (12.27) is to plot the inverse of the form shown in Figure 12.19 was obtained,
Lorentzian as a function of w2 from the data "tail" showing an exponential type decrease with
in Figure 12.18 and use the high frequency linear increased frequency. The free flow velocity was
asymptotic expansion: identified as the maximum observed frequency; it
was assumed that the depth of penetration of the
radiation extended beyond the disturbed flow
region. In order to identify the maxlmuni fre-
quency more precisely, a second power spectrum
+ was recorded. this time with the probe in blood at
11 + (ao/fl>?] a zero flow velocity, thus giving the noise asso-
The mean particle radius N and standard devi- ciated spectl-urn of the system (Figure 12.19). The
ation CT~! were thefi obtained graphically from point at which the signal power spectrum over-
the slope and intercept, respectively, as: lapped with the noise spectrum was assigned to be
the free flow Doppler frequency indicated by the
1lW; point vf,.,, flow. Due to the noise of the system
Slope =
1 -t (a"/?$ (12.29) this point contains some degree of uncertainty.
1 + 6(a,/Cr)' Another interesting feature of these measure-
Intercept = do ments was a series of readings of blood flow
1 + (CTa,/8)' velocity taken in vivo as the fiber probe was