g | | Accélération de la pesanteur | Gravity | | m/s2 |
\dot{\gamma } | | Cisaillement local | Local shear | | s-1 |
{D}_{m} | [1] | Coefficient de diffusion | Diffusion coefficient | | m2/s |
{C}_{D} | | Coefficient de traînée | Drag coefficient or Stokes friction factor | | - |
u{\mathrm{'}}_{L} | | Composante fluctuante de la vitesse du liquide | Velocity fluctuating component | u{\mathrm{'}}_{L}={u}_{L}-{U}_{L} | m/s |
{U}_{L} | [2] | Composante moyenne de la vitesse du liquide | Average velocity | | m/s |
c\mathrm{'} | | Concentration fluctuante | Fluctuating concentration | c\mathrm{'}=c-C | mol/m3 |
c\mathrm{'} | | Concentration fluctuante | Fluctuating concentration | c\mathrm{'}=c-C | mol/m3 |
{C}_{\mathrm{A0}} | | concentration initiale en soluté | initial solute concentration | | mol.m-3 |
C | [3] | Concentration moyenne | Average concentration | | mol/m3 |
C | [4] | Concentration moyenne | Average concentration | | mol/m3 |
K | [5] | Constante | Constant | | - |
\alpha | [6] | Constante | Constant | | - |
{k}_{c} | [7] | constante de consolidation | consolidation constant | | s-1 |
{k}_{d} | [8] | Constante de de transfert de matière | Mass transfert coefficient | | m/s |
{k}_{r} | [9] | constante de rupture | disruption constant | | s-1 |
{k}_{\mathrm{col}} | | constante de vitesse de collision | collision rate constant | | m3.s-1 |
{Q}_{E} | | débit volumique d'entrée | feed flow rate | | m3.s-1 |
{Q}_{S} | | débit volumique de sortie | exit flow rate | | m3.s-1 |
{d}_{p} | [10] | Diamètre de particule | Particle diameter | | m |
{D}_{t} | | Diamètre de tube | Tube diameter | | m |
| | Diamètre moyen en masse | Average mass diameter | {d}_{43}=\frac{{\int }_{0}^{\infty }{d}_{p}^{4}n\left({d}_{p}\right){{dd}}_{p}}{{\int }_{0}^{\infty }{d}_{p}^{3}n\left({d}_{p}\right){{dd}}_{p}} | m |
| | Diffusivité thermique | Thermal diffusivity | \alpha =\lambda /\left({\rho }_{S}{c}_{\mathrm{pS}}\right) | m2/s |
n\left({d}_{p},t\right) | [11] | distribution des tailles de particules | particles size distribution | | m-4 |
{n}_{v}\left({v}_{p},t\right) | [12] | distribution des volumes de particules | particle volume distribution | | m-6 |
{\sigma }^{\mathrm{*}} | | dureté du pont cristallin | hardness of the crystalline bridge | | Pa |
{l}_{B} | | Échelle de Batchelor | Batchelor microscale | {l}_{B}={\left(\frac{\nu {D}_{m}^{2}}{{\epsilon }_{M}}\right)}^{1/4} | m |
{l}_{K} | | Échelle de Kolmogoroff | Kolmogoroff microscale | {l}_{K}={\left(\frac{{\nu }^{3}}{{\epsilon }_{M}}\right)}^{1/4} | m |
{l}_{K} | | Échelle de Kolmogoroff | Kolmogoroff microscale | {l}_{K}={\left(\frac{{\nu }^{3}}{{\epsilon }_{M}}\right)}^{1/4} | m |
{\eta }_{\mathrm{AG}} | [13] | efficacité d'agglomération | agglomeration efficiency | | - |
{\eta }_{\mathrm{AG}} | [14] | efficacité d'agglomération | agglomeration efficiency | | - |
\alpha | [15] | efficacité de collision | collision efficiency | | - |
{E}_{c} | | Energie cinétique | Kinetic energy | {E}_{c}=\frac{{\rho }_{L}I{U}_{p}^{2}}{2} | J |
{\varepsilon }_{M} | | énergie dissipée | energy dissipation rate | \begin{array}{ccc}{\varepsilon }_{M}&=&\frac{{N}_{P}{N}^{3}{D}^{5}}{{V}_{T}}\\ &\textrm{et}&\\ {\varepsilon }_{M}&=&\frac{f}{2}\frac{{V}^{3}}{{D}_{T}}\end{array} | m-2.s-3 (W.kg) |
F\left({d}_{\mathrm{pi}},{d}_{\mathrm{pj}}\right) | [16] | facteur de forme de Marchal | Marchal's shape factor | | - |
{\phi }_{v} | | facteur de forme volumique des particules | volumetric shape factor | {v}_{p}={\phi }_{v}{d}_{p}^{3} | - |
f | | Facteur de frottement (tube) | Tube friction factor | {dp}=\frac{\frac{f}{2}\cdot \rho {U}_{L}^{2}}{{D}_{T}}\cdot {dL} | - |
Z | | facteur de Zeldovich | | | - |
{F}_{\mathrm{AG}} | [17] | flux d'accroissement de volume cristallin par agglomération | agglomeration growth flux | | s-1 |
{F}_{G} | [18] | flux d'accroissement de volume cristallin par croissance | crystalline growth flux | | s-1 |
{f}_{\mathrm{col}} | [19] | fonction de collision | particle size function | | - |
{F}_{\mathrm{Ce}} | [20] | Force centrifuge | Centrifugal force | | N |
{F}_{B} | [21] | Force de Basset | Basset force | | N |
{F}_{C} | [22] | Force de Coriolis | Coriolis force | | N |
{F}_{A} | [23] | Force de masse ajoutée ou trainée aditionnelle | Added weight force | | N |
{F}_{G} | [24] | Force de pesanteur ou poids apparent | Gravity force | | N |
{F}_{\mathrm{Rubinow}} | | Force de Rubinow | Rubinow force | {F}_{\mathrm{Rubinow}}=\frac{\pi }{16}\rho u{d}_{p}^{3}\dot{\gamma } | N |
{F}_{\mathrm{Saffman}} | | Force de Saffman | Saffman force | {F}_{\mathrm{Saffman}}=1,61{\rho }_{L}{\nu }^{1/2}u{d}_{p}^{2}{\dot{\gamma }}^{1/2} | N |
{F}_{D} | [25] | Force de traînée ou force de frottement visqueux | Force | | N |
{\phi }_{S} | [26] | Fraction volumique de phase solide | Volumetric solid phase fraction | | - |
{K}^{-1} | [27] | longueur de Debye-Hückel | | {K}^{-1}={\left(\frac{\varepsilon {k}_{B}T}{{2N}_{A}{e}^{2}I}\right)}^{1/2} | - |
{M}_{a} | [28] | Masse ajoutée | Added weight | | kg |
{\rho }_{L} | | Masse volumique du liquide | Liquid density | | kg/m3 |
{\rho }_{S} | | Masse volumique du solide | Solid density | | kg/m3 |
{m}_{\mathrm{vk}} | | moment d'ordre k variable volume | kth-order moment-volume variable | {m}_{\mathrm{vk}}={\int }_{0}^{\infty }{n}_{v}\left({v}_{p}\right){v}_{p}^{k}{{dv}}_{p} | m3k-3 |
\mathrm{Ar} | | Nombre d'Archimède | Archimides Number | \mathrm{Ar}=\frac{{d}_{p}^{3}g\mid {\rho }_{S}-{\rho }_{L}\mid }{{\rho }_{L}{\nu }^{2}} | - |
\mathrm{Fr}{\mathrm{'}}_{\left(p\right)} | | Nombre de Froude modifié | Particle Froude number | \mathrm{Fr}{\mathrm{'}}_{p}=\frac{{\rho }_{L}{U}_{L}^{2}}{\mid {\rho }_{S}-{\rho }_{L}\mid {d}_{p}g} | - |
\mathrm{Nu} | | Nombre de Nusselt | Nusselt Number | \mathrm{Nu}=\left({k}_{T}{d}_{p}\right)/\alpha | - |
\mathrm{Pr} | | Nombre de Prandtl | Prandtl number | \mathrm{Pr}=\nu /\alpha | - |
{N}_{p} | | Nombre de puissance | Power number | {\epsilon }_{M}=\frac{{N}_{p}{N}^{3}{D}^{5}}{{V}_{T}} | - |
| | Nombre de Reynolds (tube) | Reynolds number (tube) | \mathrm{Re}={\mathrm{VD}}_{T}/\nu | - |
{\mathrm{Re}}_{A} | | Nombre de Reynolds agitateur | Reynolds stirrer number | {\mathrm{Re}}_{A}=\frac{{\mathrm{ND}}^{2}}{\nu } | - |
{\mathrm{Re}}_{p} | | Nombre de Reynolds particulaire | Reynold's Number of particle | {\mathrm{Re}}_{p}=\frac{{\rho }_{L}U{d}_{p}}{\mu } | - |
{\mathrm{Re}}_{\mathrm{pc}} | | Nombre de Reynolds particulaire dans l'écoulement cisaillé | Reynolds number in | | - |
{\beta }_{\mathrm{AG}} | | noyau d'agglomération | agglomeration kernel | {R}_{\mathrm{AG}}={r}_{\mathrm{col}}\alpha {\eta }_{\mathrm{AG}}={\beta }_{\mathrm{AG}}{N}_{i}{N}_{j} | m3.s-1 |
n | | ordre de nucléation | | | - |
k | | ordre du moment | moment order | | - |
{S}_{Z} | | Paramètre de Zwietering | Zwietering's constant | {N}_{\mathrm{JS}}={S}_{Z}\frac{{\nu }^{0,1}{d}_{p}^{0,2}}{{D}^{0,85}}{\left(g\frac{\left({\rho }_{S}-{\rho }_{L}\right)}{{\rho }_{L}}\right)}^{0,45}{\left(\frac{{\rho }_{S}{\phi }_{S}}{{\rho }_{L}\left(1-{\phi }_{S}\right)}\right)}^{0,13} | - |
k | [29] | Perméabilité | Permeability | | m2 |
{\epsilon }_{M} | [30] | Puissance dissipée | Energy dissipation rate | | m2/s3 (=W/kg) |
{N}_{\mathrm{AG}} | | rapport des flux d'agglomération et de croissance | agglomeration flux to growth flux ratio | {N}_{\mathrm{AG}}=\frac{{F}_{\mathrm{AG}}}{{F}_{G}}=\frac{{d}_{\mathrm{pj}}^{3}{\beta }_{\mathrm{AG}}N\left({d}_{\mathrm{pj}}\right)}{{3d}_{\mathrm{pi}}^{2}G} | - |
{S}_{p} | [31] | Section | Section | | m2 |
a | [32] | Surface spécifique | Specific surface | | m2/m3 |
{d}_{\mathrm{pi}} | | taille de particule i | i-particle size | | m |
t | | temps | time | | s |
{t}_{m} | [33] | Temps de mélange | Mixing time | | s |
\sigma | [34] | tension interfaciale | | \sigma ={\left(\frac{\partial G}{\partial \Omega }\right)}_{T,P,{n}_{i}} | J/m2 |
\sigma | [35] | tension interfaciale | | \sigma ={\left(\frac{\partial G}{\partial \Omega }\right)}_{T,P,{n}_{i}} | J/m2 |
\tau | [36] | Tortuosité | Tortuosity | | - |
{M}_{k,\mathrm{AG}} | | transformée de vitesse d'agglomération | agglomeration rate transform | \begin{array}{rcl}
{M}_{k,\mathrm{AG}}&=&{\beta }_{\mathrm{AG}}{\int }_{0}^{\infty }\frac{1}{2}\left[{\int }_{0}^{{v}_{p}}{n}_{v}\left({v}_{\mathrm{p1}}\right){n}_{v}\left({v}_{\mathrm{p2}}\right)
{{dv}}_{\mathrm{p1}}\right. \\
&-& \left.
{n}_{v}\left({v}_{p}\right)
{\int }_{0}^{\infty }{n}_{v}\left(v{\textrm{'}}_{p}\right){dv}
{\textrm{'}}_{p}
\right]
{v}_{p}^{k}{{dv}}_{p}\end{array}
| m3k-3.s-1 |
\mu | | viscosité dynamique | dynamic viscosity | | kg.m-1.s-1 |
{u}_{\Omega } | | Vitesse angulaire | Angular velocity | | rad/s |
N | [37] | Vitesse d'agitation | Stirring rate | | s-1 |
{N}_{\mathrm{min}} | | Vitesse d'agitation minimale pour éviter la redéposition du solide ou son décollage du fond | Minimum stirring speed | {N}_{\mathrm{min}}=5,1{N}_{p}^{-7/18}\cdot {\left(\frac{T}{D}\right)}^{3/2}\cdot {\left(\frac{{d}_{p}g\mid {\rho }_{S}-{\rho }_{L}\mid }{{D}^{2}{\rho }_{L}}\right)}^{1/2} | s-1 |
{N}_{\mathrm{JS}} | | Vitesse d'agitation minimum de Zwietering | Just suspended stirring speed (Zwietering's correlation) | {N}_{\mathrm{JS}}={S}_{Z}\frac{{\nu }^{0,1}{d}_{p}^{0,2}}{{D}^{0,85}}{\left(g\frac{\left({\rho }_{S}-{\rho }_{L}\right)}{{\rho }_{L}}\right)}^{0,45}{\left(\frac{{\rho }_{S}{\phi }_{S}}{{\rho }_{L}\left(1-{\phi }_{S}\right)}\right)}^{0,13} | s-1 |
{r}_{\mathrm{col}} | [38] | vitesse de collision | collision rate | {r}_{\mathrm{col}}={k}_{\mathrm{col}}{f}_{\mathrm{col}}\left({d}_{\mathrm{pi}},{d}_{\mathrm{pj}}\right){N}_{i}{N}_{j} | m-3.s-1 |
G | [39] | vitesse de croissance cristalline | crystalline growth rate | | m.s-1 |
{r}_{N} | [40] | vitesse de nucléation | nucleation rate | | m-3.s-1 |
{u}_{\mathrm{te},\phi } | [41] | Vitesse de terminale de chute corrigée | Corrected terminal fall velocity | | m/s |
{u}_{L} | [42] | Vitesse du liquide | Fluid velocity | | m/s |
{u}_{\mathrm{tip}} | | Vitesse en bout de pale | Tip speed | {u}_{\mathrm{tip}}=\pi ND | m/s |
u\mathrm{'} | | Vitesse fluctuante | Velocity | | m/s |
u | | Vitesse relative entre une particule et le fluide | Relative particle velocity | u={u}_{p}-{u}_{L} | m/s |
{R}_{\mathrm{AG}} | [43] | vitesse spécifique d'agglomération | specific agglomeration rate | {R}_{\mathrm{AG}}={r}_{\mathrm{col}}\alpha {\eta }_{\mathrm{AG}}={\beta }_{\mathrm{AG}}{N}_{i}{N}_{j} | m-3.s-1 |
{u}_{\mathrm{te}} | [44] | Vitesse terminale de chute libre | Terminal fall velocity | | m/s |
{v}_{\mathrm{pc}} | | volume critique | criticle volume | {v}_{\mathrm{pc}}={\phi }_{v}{d}_{\mathrm{pc}}^{3} | m3 |
{V}_{p} | | Volume de particule | Particle volume | | m3 |
{v}_{p} | | volume de particule | particle volume | {v}_{p}={\phi }_{v}{d}_{p}^{3} | m3 |