The name is absent



Chapter3


1             T f

Mxy(2τ^T) = -M^xp(--~-)


[3.11]


This procedure allows increasing the diffusion time while reducing the effect


of extended relaxation which will reduce the SNR. Eq. 3.8 can also be used to


calculated spin echo signal attenuation for stimulated spin-echo PGSE sequence.


3.3.2. Drop size determination from PGSE measurement


Eq. [3.9] is limited to bulk fluids. But in many cases, the fluids are confined in


small geometries such as pores or droplets and cannot diffuse freely, which is


referred as restricted diffusion. In these cases, Murday and Cotts [15] developed


the equation for the PGSE sequence. For restricted diffusion within a sphere of


radius a, the attenuation ratio Rsp is:


Rsb = exp<-2χ2g27  7 7       ,

sp pl z s ^a2m(a2ma2-2)[a2mD


(⅛D)jj


[3.12]


Here Ψ = 2 + e~a2-D(&~S) - 2e~a^ - 2e~a-


+ e-a^lD(Δ+δ)


[3.13]


am is the mth positive root of the equation:

ota ∙ Jr5z2(Qa)-Z372 (ota) = 0    [3.14]


Jk is the Bessel function of the first kind, order k.

If Δ » a2∕2D, Δ » δ, Eq. [3.8] can be simplified as1:

Rsp = exp(-y2g2δ2a2 /5)

[3.15]


Figure 3.4 shows the predicted attenuation of emulsified water droplets with
different drop diameters from 5 to 50 μm. Here the diffusion time Δ is 500 ms,

46



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