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



More intriguing information

1. Equity Markets and Economic Development: What Do We Know
2. How do investors' expectations drive asset prices?
3. DETERMINANTS OF FOOD AWAY FROM HOME AMONG AFRICAN-AMERICANS
4. An Intertemporal Benchmark Model for Turkey’s Current Account
5. DISCUSSION: POLICY CONSIDERATIONS OF EMERGING INFORMATION TECHNOLOGIES
6. The name is absent
7. Errors in recorded security prices and the turn-of-the year effect
8. 101 Proposals to reform the Stability and Growth Pact. Why so many? A Survey
9. Migrating Football Players, Transfer Fees and Migration Controls
10. AGRICULTURAL TRADE IN THE URUGUAY ROUND: INTO FINAL BATTLE