{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Pression osmotique et propriétés de transport \n", "## ou comment prendre en compte les effets des interactions colloïdales dans les équations de transport de la matière ?\n", "### Cours M2 Génie des Procédés Avancés\n", "\n", "La présence d'interactions de surface entre colloïdes modifie les propriétés de transport. Ainsi, on peut démontrer que la diffusion collective (transport des colloïdes dans un gradient de concentration) peut s'écrire : \n", "$$D=\\frac{K(\\phi)}{6\\pi\\mu a}V_p\\frac{d\\Pi}{d\\phi}=D_0 K(\\phi)\\frac{V_p}{k_B T}\\frac{d\\Pi}{d\\phi}$$\n", "où $K(\\phi)$ permet de prendre en compte l'effet de la fraction volumique, $\\phi$, sur la mobilité d'une sphère en régime concentré et $\\frac{d\\Pi}{d\\phi}$ permet de prendre en compte l'effet des interactions de surface. La variation de pression osmotique en fonction de la fraction volumique, $\\Pi=f(\\phi)$, represente l'équation d'état de la dispersion colloïdale et prend en compte l'effet des interactions colloïdales multi-corps.\n", "\n", "Lorsque on utilise cette expression pour décrire un bilan de masse différentiel, il est possible de montrer qu'en régime stationnaire, le profil de concentration peut s'écrire en fonction de la pression osmotique :\n", "- près d'une membrane fonctionnant en filtration tangentielle :\n", "$$Pe=\\frac{J\\delta}{D_O}=\\frac{V_p}{k_B T}\\int_{\\Pi_b}^{\\Pi_m} \\frac{K(\\phi)}{\\phi} \\, \\mathrm{d}\\Pi=\\int_{\\phi_b}^{\\phi_m} \\frac{D(\\phi)}{D_0} \\, \\frac{\\mathrm{d}\\phi}{\\phi}$$\n", "où $\\delta$ est l'épaisseur de la couche limite induite par la vitesse tangentielle au dessus de la membrane\n", "- lors d'un équilibre entre sédimentation et diffusion :\n", "$$Pe=\\frac{u_{sed}(r_1-r_2)}{D_O}=\\frac{V_p}{k_B T}\\int_{\\Pi_1}^{\\Pi_2} \\frac{1}{\\phi} \\, \\mathrm{d}\\Pi$$\n", "où les indices 1 et 2 représentent deux positions dans la hauteur du fluide qui sédimente\n", "\n", "On peut noter qu'il est possible de retrouver les équations d'équilibre advection-diffusion classique pour le régime dilué \n", "$K(\\phi)\\rightarrow1$ et $\\Pi \\rightarrow \\frac{k_B T \\phi}{V_p}$\n", "\n", "*Données* : On utilisera la loi suivante pour la pression osmotique présentant un écart à l'idéalité positive qui peut prendre en compte la présence de répulsion. \n", "\n", "$$\\Pi = \\frac{k_B T \\phi}{V_p}+0.05 (\\rho_p \\phi)^2$$\n", "\n", "Cette expression à l'avantage de pouvoir être intégrée analytiquement suivant :\n", "\n", "$$\\frac{V_p}{k_B T}\\int_{\\Pi_1}^{\\Pi_2} \\frac{1}{\\phi} \\, \\mathrm{d}\\Pi=\\frac{V_p}{k_B T}\\int_{\\phi_1}^{\\phi_2} \\frac{1}{\\phi}\\frac{d\\Pi}{d\\phi} \\, \\mathrm{d}\\phi=ln(\\frac{\\phi_2}{\\phi_1})+\\frac{V_p}{k_B T}2*0.01\\rho_p^2 (\\phi_2-\\phi_1)$$\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "En régime concentré, la pression osmotique prenant en compte les interactions s'écarte de la loi de Van't Hoff (dispersions idéales) \n" ] }, { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Le coefficient de diffusion en régime dilué est 1.0908479799518506e-11 m.s-2\n", "En régime concentré, la diffusion devient plus importante : les répulsions entre colloïdes augmentent la diffusion (effet de ressorts comprimés entre colloïdes) \n" ] } ], "source": [ "#Calcul des propriétés de la dispersion concentrée\n", "from scipy.misc import derivative\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import quad\n", "from scipy.optimize import fsolve\n", "\n", "#constant\n", "kT= 1.38e-23*298.\n", "#dispersion\n", "a=20.e-9\n", "mu=0.001\n", "rho_p=1350 #kg m-3\n", "vp=4*np.pi*(a**3)/3\n", "D0=kT/(6*np.pi*mu*a)\n", "viriel2=0.01\n", "\n", "\n", "def K(phi):\n", " return (6.-9.*(abs(phi)**(1./3.))+9.*(abs(phi)**(5./3.))-6.*(abs(phi)**2.))/(6.+4.*(abs(phi)**(5./3.)))\n", "def pi(phi):\n", " return kT*phi/vp+viriel2*((rho_p*phi)**2)\n", "\n", "phi_a=np.logspace(-5,-1,100)\n", "plt.loglog(phi_a,pi(phi_a), label='With interactions')\n", "plt.loglog(phi_a,kT*phi_a/vp,'--', label='Van\\'t Hoff')\n", "plt.xlabel('phi')\n", "plt.ylabel('Pi')\n", "plt.title('Pression osmotique')\n", "plt.legend(loc='best')\n", "plt.show()\n", "print ('En régime concentré, la pression osmotique prenant en compte les interactions s\\'écarte de la loi de Van\\'t Hoff (dispersions idéales) ')\n", "\n", "\n", "D=D0*K(phi_a)*vp*derivative(pi, phi_a)/kT\n", "plt.loglog(phi_a,D/D0, label='With interactions')\n", "plt.loglog(phi_a,np.ones(100),'--', label='Van\\'t Hoff')\n", "plt.xlabel('phi')\n", "plt.ylabel('D/D0')\n", "plt.title('Diffusion collective (Stokes Einstein generalized law)')\n", "plt.show()\n", "print('Le coefficient de diffusion en régime dilué est', D0, 'm.s-2')\n", "print ('En régime concentré, la diffusion devient plus importante : les répulsions entre colloïdes augmentent la diffusion (effet de ressorts comprimés entre colloïdes) ')\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "La vitesse de sédimentation en régime diluée est : 3.0520000000000004e-10\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Pour un même Péclet (condition opératoire fixée), la concentration maximum sera plus grande en l absence de répulsions\n", "Pour obtenir une même concentration maximum, le Péclet devra être plus important en présence de répulsions\n", "\u001b[1mEn présence de répulsions, la dispersion résiste mieux à la sédimentation\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "A la position r= 0.1 la fraction volumique est 0.004265965242888397 et la concentration 5.759053077899336 g/L\n" ] } ], "source": [ "#Données\n", "cb=1 #kg/m3\n", "phi_b=cb/rho_p\n", "pi_b=pi(phi_b)\n", "rho_f=1000 #kg m-3\n", "g=9.81 #m s-2\n", "#Calcul de la vitesse de sédimentation en régime dilué\n", "u_set=vp*(rho_p-rho_f)*g/(6*np.pi*mu*a)\n", "print ('La vitesse de sédimentation en régime diluée est :', u_set)\n", "\n", "phi_m=np.linspace(phi_b, 20*phi_b)\n", "\n", "#fonction à intégrer pour obtenir le nombre de Péclet numériquement\n", "def pe_set(phi):\n", " return vp*derivative(pi, phi)/(kT*phi)\n", "\n", "#calcul du nombre de Péclet avec solutions analogiques\n", "Pe_D0=np.log(phi_m/phi_b)\n", "Pe=np.log(phi_m/phi_b)+2*viriel2*(rho_p**2)*(phi_m-phi_b)*vp/kT\n", "\n", "#calcul par integration numérique\n", "Pe_num=np.zeros(len(phi_m))\n", "for i in range(len(phi_m)):\n", " Pe_num[i]=quad(pe_set,phi_b,phi_m[i])[0]\n", "\n", "plt.plot(Pe,phi_m)\n", "plt.plot(Pe_D0,phi_m,'--')\n", "plt.xlabel('Pe')\n", "plt.ylabel(r'$\\phi_m$')\n", "plt.title('Variation de la concentration maximum en fonction du nombre de Péclet')\n", "plt.show()\n", "print('Pour un même Péclet (condition opératoire fixée), la concentration maximum sera plus grande en l absence de répulsions')\n", "print('Pour obtenir une même concentration maximum, le Péclet devra être plus important en présence de répulsions')\n", "print('\\033[1m'+'En présence de répulsions, la dispersion résiste mieux à la sédimentation')\n", "#Tracé du profil de concentration en fonction de r=Pe D0 / u_set\n", "plt.plot(Pe*D0/u_set,phi_m,label='With interactions')\n", "plt.plot(Pe_D0*D0/u_set,phi_m,'--', label='Van\\'t Hoff')\n", "plt.ylabel(r'$\\phi$')\n", "plt.xlabel('r')\n", "plt.xlim(0., 0.1)\n", "plt.ylim(phi_b, 0.016)\n", "plt.title('Variation de la concentration en fonction de la distance')\n", "plt.legend(loc='best')\n", "plt.show()\n", "\n", "#calcul de la concentration pour une position donnée\n", "r_s=0.1\n", "Pe_s=r_s*u_set/D0\n", "\n", "#fonction à résoudre pour déterminer phi à la membrane pour le Péclet Pe_s correspondant à la position r_s\n", "def solve(phi):\n", " return np.log(phi/phi_b)+2*viriel2*(rho_p**2)*(phi-phi_b)*vp/kT - Pe_s\n", "\n", "phim=fsolve(solve, x0=phi_b)[0]\n", "print ('A la position r=',r_s,'la fraction volumique est', phim, 'et la concentration', phim*rho_p,' g/L')\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Pour un même Péclet (condition opératoire fixée), la concentration maximum sera plus grande en l absence de répulsions\n", "\u001b[1mEn présence de répulsions, la dispersion résiste mieux à la compression induite par la force de traînée liée à la filtration : l accumlation est moins importante\n" ] } ], "source": [ "#calcul pour la filtration\n", "phi_m=np.linspace(phi_b, 300*phi_b)\n", "#fonction à intégrer pour la filtration\n", "def pe_filt(phi):\n", " return vp*derivative(pi, phi)*K(phi)/(kT*phi)\n", "\n", "#calcul par integration numérique\n", "Pe_fil=np.zeros(len(phi_m))\n", "for i in range(len(phi_m)):\n", " Pe_fil[i]=quad(pe_filt,phi_b,phi_m[i])[0]\n", "\n", "plt.plot(Pe_fil,phi_m,label='With interactions')\n", "plt.plot(Pe_D0,phi_m,'--', label='Van\\'t Hoff')\n", "plt.xlabel('Pe')\n", "plt.ylabel(r'$\\phi_m$')\n", "plt.title('Variation de la concentration à la membrane en fonction du nombre de Péclet')\n", "plt.legend(loc='best')\n", "plt.show()\n", "\n", "print('Pour un même Péclet (condition opératoire fixée), la concentration maximum sera plus grande en l absence de répulsions')\n", "print('\\033[1m'+'En présence de répulsions, la dispersion résiste mieux à la compression induite par la force de traînée liée à la filtration : l accumlation est moins importante')\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sc= 91671.80197227294\n", "L'épaisseur de couche limite est de 65.0 micromètres pour une vitesse tangentielle de 0.05 m/s\n", "L'épaisseur de couche limite est de 51.7 micromètres pour une vitesse tangentielle de 0.1 m/s\n", "\n", " J \\ u | 0.05 0.1\n", "------------------------------------------------------------------------------\n", " 1.00e-06 | Pe = 5.96 4.741\n", " | phim VH = 0.287 0.085\n", " | phim int= 0.018 0.013\n", "------------------------------------------------------------------------------\n", " 2.00e-06 | Pe = 11.919 9.482\n", " | phim VH = 111.229 9.723\n", " | phim int= 0.053 0.037\n" ] } ], "source": [ "#SUITE EN CONSTRUCTION\n", "\n", "#membrane\n", "d_H=6e-3 #m\n", "L=1.2 #m\n", "#Dispersion\n", "mu=0.001 #Pa.s\n", "# conditions hydrodynamiques\n", "u=[0.05, 0.1] #m/s\n", "J=[1.e-6,2.e-6] #m/s\n", "\n", "#Calcul de l'épaisseur de couche limite, du nombre de Péclet et de la concentration à la membrane\n", "deltal=np.zeros(len(u))\n", "Re=np.zeros(len(u))\n", "Sh=np.zeros(len(u))\n", "Pe=np.zeros(len(u)*len(J))\n", "phi_mVH=np.zeros(len(u)*len(J))\n", "phi_mint=np.zeros(len(u)*len(J))\n", "Sc=mu/(rho_f*D0)\n", "print ('Sc=',Sc)\n", "\n", "#Function à résoudre, f_int=0, pour connaître phi m pour un Pe donné\n", "def f_int(phi_m,Pe):\n", " return quad(pe_filt,phi_b,phi_m)[0]-Pe\n", "\n", "\n", "for i in range(len(u)):\n", " Re[i]=rho_f*u[i]*d_H/mu\n", " if Re[i]<2100:\n", " Sh[i]=1.86*(Re[i]*Sc*d_H/L)**0.33\n", " else:\n", " Sh[i]=0.023*Re[i]**0.8*Sc**0.33\n", " deltal[i]=d_H/Sh[i]\n", " print ('L\\'épaisseur de couche limite est de', round(deltal[i]*1e6, 1),'micromètres pour une vitesse tangentielle de ', u[i],'m/s' )\n", " for j in range(len(J)):\n", " Pe[i+len(u)*j]=J[j]*deltal[i]/D0\n", " phi_mVH[i+len(u)*j]=phi_b*np.exp(Pe[i+len(u)*j])\n", " phi_mint[i+len(u)*j]=fsolve(f_int, x0=phi_b,args=(Pe[i+len(u)*j]))[0]\n", "print() \n", "print (' J \\ u | ', round(u[0],3),' ', round(u[1],3))\n", "print ('------------------------------------------------------------------------------')\n", "print (' ', \"%.2e\"%J[0],' | Pe = ', round(Pe[0],3), ' ', round(Pe[1],3))\n", "print (' | phim VH = ', round(phi_mVH[0],3), ' ', round(phi_mVH[1],3))\n", "print (' | phim int= ', round(phi_mint[0],3), ' ', round(phi_mint[1],3))\n", "print ('------------------------------------------------------------------------------')\n", "print (' ', \"%.2e\"%J[1],' | Pe = ', round(Pe[2],3), ' ', round(Pe[3],3))\n", "print (' | phim VH = ', round(phi_mVH[2],3), ' ', round(phi_mVH[3],3))\n", "print (' | phim int= ', round(phi_mint[2],3), ' ', round(phi_mint[3],3))\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }