# Orders of magnitude

## Boiling delay

This delay depends somewhat on the liquid-phase temperature. The following table provides the values according to the weight ratio X of sugar in the liquid. A more complete treatment is given by Bubnik et al. [BUB 95].

 X% 35 50 60 70 80 90 Re°C 1 2 3 5 9 17

Table 3.3. Boiling delay RE

## Diffusivity

Austmeyer [AUS 81] proposed an algorithm and curve network from which we have taken the following approximate values (in 10-12 m2.s-1).

 ' t°C 50 70 90 X % 30 0.5 0.75 1.1 60 0.2 0.30 0.40 70 0.15 0.20 0.25

Table 3.4. Diffusivity

Further details are available in Austmeyer’s thesis [AUS 81] or in the work of Bartens [BAR 98].

## Viscosity

### I. Liquid viscosity

This applies for:

• - the transfer of matter through the diffusion layer;
• - the calculation of thermal transfer;
• - centrifugal filtration (this can be divided by 2 per reheating).

Purity influences the liquid’s viscosity, diminishing it by 10-20% when it goes from 100 to 60%.

Schliephake et al. [SCH 83] provided a network of curves for the viscosity of pure solutions and technical solutions according to the weight ratio in dry material, temperature and purity.

Referring to the table of approximate values relative to T and of M.S.%, we see that purity has some influence:

 ' °C M.S.% 40 60 80 [SCH 83] 40 3.5 2 1 60 25 10 5.5 80 1 050 300 80

Table 3.5. Solution viscosity (centipoises)

### Magma viscosity

This applies to the agitation power. At 1,500 Pa.s, the impeller rotation speed is reduced to 0.5 rev.mn-1. Magma viscosity can be divided by 10 per heating or dilution.

(The crystal content and liquid viscosity are involved separately for the thermal exchange calculation.)

 ' °C M.S.% 40 60 80 90 138 30 10 92 300 70 14 95 1 400 300 103

Table 3.6. Magma apparent viscosity (Pa.s)

## Properties of crystallized sugar

Superficial energy у = 0.224 J.m-2

Density ps = 1590 kg.m-3

Molar mass M = 342.2 kg.kmol-1

Thermal conductivity X = 0.58 W.m-1 .K-1

Water conductivity A,e = 0.45 W.m-1 K-1

Melting temperature Tf = 186°C

Molar heat capacity Cs = 425.8.10 J.kmol-1 .K-1

Fusion enthalpy AH^ = 46.41.106 J.kmol-1

Dissolution (in water) is athermal.