Physical Chemistry of Foods

characteristic length equals drop diameterd, and the velocity is that of the
drop relative to the adjacent liquid. The transition occurs for Redr&1. Some
particulars about the regimes are given in Table 11.2 and the mathematical
expression given are discussed further on.
Which regime can be expected for various systems? This depends in the
first place on the size of the apparatus used. If it is very small, Re is small
and the regime becomes LV.

Note If the dimension of the active zone is so small as to be

comparable to drop or bubble size, as in some laboratory

homogenizers, we have a regime that may be called ‘‘bounded

laminar flow,’’ and different relations hold. It will not be discussed

here.

For larger machines the flow is nearly always turbulent for aqueous systems,
where the viscosity of the continuous liquidZCis small. We expect for

Foams, nearly always regime TI, unless the viscosity of the continuous

phase ZC is very high. The bubbles tend to be relatively large

(virtually always> 10 mm), implying Redr>1.

TABLE11.2 Various Regimes for Emulsification and Foam Bubble

Formation. Valid for Small Volume Fractions

Regime

Laminar, viscous

forces, LV

Turbulent, viscous

forces, TV

Turbulent, inertial

forces, TI

Re, flow <* 2000 >* 2500 >* 2500

Re, drop < 1 < 1 > 1 a

sext& ZCCe^1 =^2 Z^1 C=^2 e^2 =^3 d^2 =^3 r^1 =^3

d&

2 gWecr

ZCC

g

e^1 =^2 Z^1 C=^2

g^3 =^5

e^2 =^5 r^1 =^5

aFord>Z 2

C=grC.

Symbols:

Re¼Reynolds number We¼Weber number

d¼drop diameter r¼mass density

g¼interfacial tension s¼stress

e¼power density C¼velocity gradient

Z¼viscosity

Subscripts:

C¼continuous phase ext¼external

cr¼critical value for breakup