{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fruit juice ultrafiltration \n", "\n", "Concentration of a fruit juice is achieved by ultrafiltration on a 6 mm diameter, 1.2 m long tubular membrane. Nanofiltration is carried out in tangential mode (cross-flow filtration), i.e. with a flow velocity in the tube (parallel to the membrane) and a permeation velocity (perpendicular to the membrane). The fruit juice has a mass concentration of 0.2% and is totally retained by the membrane.\n", "\n", "\n", "*Data :*\n", "- *Fruit juice 0.2% mass : $\\rho$=1200 kg/m3, $\\mu$=0,001 Po, D=7.10-10 m2.s-1*\n", "- *Osmotic pressure (eq. 31 TI J2789) : $\\Pi(bar)=\\frac{133.75c}{100-c}$ with concentration c in mass %*\n", "\n", "\n", "**1. Considering the accumulation of fruit juice at the membrane surface, calculate the fruit juice concentration at the membrane surface, cm, for a permeation flux of 10-6 m/s and 2.10-6 m/s and circulation velocities of 0.05 and 0.1 m/s. Comment on results.**\n", "\n", ">During filtration, there is a coupling between convection due to permeation, J, which brings solutes (or colloids) towards the membrane, and diffusion, D, in the boundary layer, $\\delta$, which generates \"retro\"-transport from the membrane to the solution (or dispersion). It can be demonstrated (see course) by performing a differential balance on a volume element in the boundary layer that the concentration profile is exponential:\n", "$$c=c_b e^{Jx/D}$$\n", ">The concentration at the membrane, $c_m$, is then :\n", "$$c_m=c_b e^{Pe}$$\n", ">where, $Pe=\\frac{J\\delta}{D}$, is the Peclet number characterizing the ratio $\\frac{advective~flux}{diffusive~flux}$. To calculate the Péclet number, we need to estimate the thickness of the boundary layer. This can be estimated from a correlation between dimensionless numbers for transfer in a tube.\n", "$$Sh=1.86(Re~Sc~\\frac{d_H}{L})^{0.33}$$ for Re<2100\n", "$$Sh=0.023Re^{0.8}Sc^{0.33}$$ for Re>2100\n", "> The code allows ro :\n", ">1. calculate the boundary layer thickness\n", ">2. calculate the Peclet number\n", ">3. calculer the concentration at the membrane" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The boundary layer thickness is 256.7 micrometers for a tangential velocity of 0.05 m/s\n", "The boundary layer thickness is 204.2 micrometers for a tangential velocity of 0.1 m/s\n", "\n", " J \\ u | 0.05 0.1\n", "------------------------------------------------------------------------------\n", " | Pe= 0.367 0.292\n", " 1.00e-06 | \n", " | cm= 0.289 0.268\n", "------------------------------------------------------------------------------\n", " | Pe= 0.733 0.583\n", " 2.00e-06 | \n", " | cm= 0.416 0.358\n" ] }, { "data": { "image/png": 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rlJLs7OzbynJrefLKAlrtacCAAYB2vbdu3cpvv/3G448/zquvvsoTTzxhtpaqzvWc67y69VW2Rm7ludbPMbb1WKsOYVaGQ1HpqVWrFjExMcTHx+Pq6sqvv/6a/8IqrsYxePBgHnnkESZMmEBUVBRnz56lQ4cOBcZbtWoVkyZNYtWqVQwZMgSA2NhYvLy8sLe3Jzw8nLNnzxISElKqcpi+aNPS0rh+/Tr33nsvnTp1omHDhmbnU1Y1jqCgIPbv38/w4cP5+eefycnJKVH6jRs35l/7ixcvUrduXcaMGUN6ejoHDhxQhsNMEjMTeWHjCxyLP8Z/O/2X4U2GW1uSMhyKyo+joyNvvPEGHTt2JDg4mKZNm5qdtkWLFgwfPpzmzZvj4ODA4sWLsbfXqv+jR49m7NixhIWFMWnSJIYPH86KFSuoV68e33//PQBbt27ljTfewMHBAXt7e5YsWVJsp3NhrFu3joULFwKQmprKkCFDyMzMRErJvHnzikybm5t7Uy2gOB5++GE2b95MXFwcAQEBvPnmm4waNeqmOGPGjGHIkCF06NCBPn36UKNGDbPzj42NxdnZOb/JbvPmzbz//vs4Ojri6urK559/bnZeVZkraVcYu2EsUWlRfNDjA/rU72NtSQCIgtp4KythYWFSLeRU/pw8eZJmzZpZW0alJisriy5dupR6IbIFCxZw5coVZs+eXcbKSseXX35JZGQkkyZNMjuNeo5u5lTCKZ776zkyDZks6r2IdrXaWeQ8Qoj9Usrb21aLQNU4FIoKQLVq1UptNEaNGsWxY8f47rvvylhV6XnsscesLaFSszt6N+M3jcfV0ZXPB3xOQ0/zmyrLA2U4FIpKzooVK6wtQVGG/B7+O69vf50g9yA+7vsxtWvUtrak21CGQ6FQKCoAUkpWHV/F3P1zaefXjg97f4hHNQ9ryyoQi84cF0IMEEKcFkKcE0IU2tgphLhLCGEQQjxY0rQKhUJR2TEYDczaO4u5++dyT/17WHbPsgprNKCENQ4hhDPgJKUsdmqwEMIeWAz0AyKBvUKItVLKEwXEmwX8WdK0CoVCUdnJzM1kyj9T2HBxA481e4xX73oVO1GxvUGZrU4IMRrt5f6bEOI9M5J0AM5JKcOllNnAamBIAfFeBNYAMaVIq1AoFJWWpMwkxqwfw4aLG3gl7BUmdphY4Y0GFGE4hBD333Kor5Syh5SyGzDIjLzrApdN9iP1Y6bnqAsMA251KVpsWpM8nhZC7BNC7IuNjTVDlkJxM+a4Vf/+++9p0aIFdnZ2pR79ZEpZuBufPn06c+bMMStufHw8vXr1wtXVlRdeeOGOzlsc33zzDe+++65Fz2ELXE69zON/PM6J+BPM6TGHES1GWFuS2RRl2loLIX4WQrTW948IIb4SQnwJHDcj74Lmw986aWQ+MFFKeasfa3PSagelXCalDJNShvn6+pohS6G4gblu1Vu2bMkPP/xA9+7dy+S85e1u3NnZmbfffttsQ3MnrFu3Ln8GvKJgjsUd47HfHyMhM4FP7vmE/kGVy/V8oYZDSvkO8AzwvBBiGfApMA2YLaV8xIy8I4FAk/0AIOqWOGHAaiFEBPAg8JEQYqiZaRUKoHzcqjdr1owmTZoUmVdFdjdeo0YNunbtirOzc5HxgoKCiIuLA2Dfvn35Lt6nT5/OiBEjuOeeewgKCuKHH37gtddeIzQ0lAEDBuS7I5FScujQIdq1a8eWLVvyF7hq27YtqampFilbZWPTpU089edTuDi48MW9X1hsYp8lKa5zPB14CWgELAP2Au+bmfdeoJEQIhi4AjwE3GRwpJTBedtCiJXAr1LKn4QQDsWlVVRQ/pgEV4+WbZ61Q2HgzOLjFUBZuVU3F2u5Gy+unGXB+fPn2bRpEydOnKBz586sWbOG2bNnM2zYMH777TeGDh3KwYMHad26NUII5syZw+LFi+nSpQtpaWnFGq2qwOpTq5mxZwbNvZqzsM/Ccl9Ho6wo1HAIId4BugOOwLdSysFCiMFoneMrpZRfFJWxlDJXCPECWoe6PfCplPK4EGKsHl7oUmmFpS1p4RQKS7tVvxVruRsvrpxlwcCBA3F0dCQ0NBSDwZDfHBUaGkpERARwoyYF0KVLFyZMmMCjjz7Kv/71LwICAiyqryJjlEY+2PcBq06somdAT2Z1n1WuK/aVNUXVOO6TUrYR2n/RfmC+lHKtEOJ34HlzMpdS/g78fsuxAg2GlHJkcWkVlYBS1gzuhPJwq24u1nI3XlY1DtNraXod4Wa38I6OjvkG1rRs69evZ82aNYC2guGgQYP4/fff6dSpE3/99VeJHFDaCqbDbR9u+jAT75potXU0yoqiDMcxIcQXgAuwJe+glDIXWGBpYQqFuZSHW/WyxBLuxsuqxpHnSn3gwIH5BsBckpOTyc3NxdvbG9CatkJDQwkNDWXnzp2cOnWqyhmO+Ix4xm0ax9HYo7x212s81uwxq66jUVYUajiklI8JIUKBHCnlqXLUpFCUiPJwq/7jjz/y4osvEhsby6BBg2jTpk2hQ3eLoizdjZfUlXpQUBApKSlkZ2fz008/sX79epo3b35TnGnTpjFq1Cjee++9/OY0c9mwYQN9+/bN358/fz6bNm3C3t6e5s2b5zdhVRXCk8J5buNzxGfEM6/nvArjEr0sUG7VFXeMcodtPqVxN14Yw4YNY8yYMdx7771loOzOGT16NKNHj75psEFJsKXnaE/0Hl7a/BKOdo4s6r2IUN9Qa0sqFOVWXaGo4JSVu/HQ0FAaN258x5MIy5Lly5dbW0KF4OdzPzN953Tqu9Vncd/F1HUtcO5ypUYZDoWiEnL0aBkPeVbcMUZpZNHBRXxy9BM6+nfkg54f4O7kbm1ZFqFYpyhCiC5CiBr69mNCiA+EEPUtL02hUCgqB5m5mby29TU+OfoJDzR6gI/7fmyzRgPMc3L4MXBddz3yGnARUAsGKxQKBRCXEceoP0exPmI9E9pPYFrnaTjaOVpblkUxp6kqV0ophRBDgAVSyhVCiMrjjUuhUCgsxJnEM7yw8QUSMxNtbuRUUZhjOFKFEJOBx4Du+loZtm1OFQqFohi2RW7j1a2vUt2hOisHrKSFTwtrSyo3zGmq+jeQBYySUl5Fc29urr8qhaLCY45b9YSEBPr160ejRo3o168fiYmJgOZg0cXFJd+Z39ixY+9Yz4ABA0rsL2vz5s3cd999ZsW9fPkyvXr1olmzZrRo0YIFCyw3n7cs3MdXNKSUfHXyK174+wUCXAP4etDXVcpogJk1DrQmKoMQojHQFPjGsrIUivLB1K16VFQUffv25cyZM/mTAPOYOXMmffr0YdKkScycOZOZM2cya9YsQPNJdejQoTLRk5GRQUJCAnXrWm4Ip4ODA3PnzqVdu3akpqbSvn17+vXrd9tkwLKgvN3HW5ocYw4zd8/kuzPf0SuwFzO7zazUPqdKizk1jq1ANX3RpY3Ak8BKS4pSKEpCebhV//nnnxkxQuvaGzFiBD/99FOJNAYFBTFlyhQ6d+5MWFgYBw4coH///jRo0IAlS264b9u8eXO+K/NJkybRvHlzWrVqxSuvvFKi8xWFv78/7dpprrzd3Nxo1qxZgTWckSNH8r///S9/39XVNV9jRXUfb0mSs5J59q9n+e7MdzzZ8knm95pfJY0GmFfjEFLK60KIUcBCKeVsIcQhC+tSVFJm7ZnFqYSy9VDT1KspEztMLFXasnKrfu3atXyvt/7+/sTE3Fjp+MKFC7Rt2xZ3d3feeecdunXrVqCWwMBAdu7cycsvv8zIkSPZvn07mZmZtGjRIr+J648//mDo0KEkJCTw448/curUKYQQJCUlmV3mTZs28fLLL992vHr16uzYseOmYxERERw8eLDE7kWs5T7eWkQkR/Di3y8SmRbJW3e/xbBGw6wtyaqYZTiEEJ2BR4FR+rHK7dpRUWWwtFt1f39/Ll26hLe3N/v372fo0KEcP3483xeVKYMHDwa0Wd9paWm4ubnh5uaGs7MzSUlJ1KxZk+3btzNnzhzs7OxwdnZm9OjRDBo0yOz+C4BevXqZ1XSWlpbGAw88wPz58wvUWxTWch9vDXZF72LC5gk4CAeW37Oc9rXaW1uS1THHcIwHJgM/6utphACbLCtLUVkpbc3gTigPt+q1atUiOjoaf39/oqOj8fPzAzRX43mOBtu3b0+DBg04c+YMYWG3u/4xdUt+q/v13NxcwsPDCQwMxMnJCYA9e/awceNGVq9ezaJFi/j777/Nuh7m1DhycnJ44IEH8tfKKAjT6yqlJDs7+7ay3FoeS7uPL29Wn1rNzD0zCfYIZmHvhQS4Vd01RUwp1nBIKbei9XPk7YcD4ywpSqEoCeXhVn3w4MGsWrWKSZMmsWrVKoYMGQJo3m69vLywt7cnPDycs2fPEhISUqpymL5o09LSuH79Ovfeey+dOnWiYcOGZudTXI1DSsmoUaNo1qwZEyZMKDRenov14cOH8/PPP+cvD2sulnAfX17kGHOYtWcW357+lh4BPZjZbSauTq7WllVhKNZwCCF80WaMtwDy136UUva2oC6FwmzKw636pEmTGD58OCtWrKBevXp8//33AGzdupU33ngDBwcH7O3tWbJkCV5eXqUqx7p161i4cCEAqampDBkyhMzMTKSUzJs3r8i0JXGxvn37dr744gtCQ0Pzm4zee++927zsjhkzhiFDhtChQwf69OlDjRo1zC5LWbqPL2+SMpN4Zcsr7L66mydbPMn4duMr/cJLZU2xbtWFEOuBb4FXgLHACCBWSln+bRLFoNyqWwdbcodtLbKysujSpQulfX4XLFjAlStXmD17dhkrKx2lcR9fEZ6j80nnefHvF7mafpVpnacxpOEQq+opDyzlVt1bdzMyXkq5BdgihNhSbCqFQmE21apVK7XRGDVqFMeOHeO7774rY1Wlp6zcx5cnWy5vYeK2iTjbO/PZgM9o7dva2pIqLOYYjryGzWghxCAgClA9RApFBWHFihXWllCpkVKy4tgKPjzwIU29mvJh7w+pXaO2tWVVaMwxHO8IITyA/wALAXfg9iEbCoVCUcnIyM1g2o5p/HHhDwYGDeTNLm/i4uBibVkVHnNGVf2qbyYDvSwrR6FQKMqH6LRoxm8az6mEU4xvN55RLUeVaA5PVcacUVXBwItAkGl8KeVgy8lSKBQKy7H/2n4mbJ5AliGLhb0X0iOwh7UlVSrMaar6CVgB/AIYi46qUCgUFZvvTn/HjN0zCHALYEHvBYR4lG7eTVXGHCeHmVLKD6WUm6SUW/J+FlemUJQT5rhV//7772nRogV2dnalHv1kSlm4G58+fTpz5swxK+6GDRto3749oaGhtG/f3uxZ6KXhm2++4d1337VY/qUlx5DDmzvf5O1db9OpTie+GvSVMhqlxJwaxwIhxDRgPdq6HABIKQ9YTJVCUU6Y61a9ZcuW/PDDDzzzzDNlct7ydjfu4+PDL7/8Qp06dTh27Bj9+/cv8Zof5rJu3TrGjatYziVir8cyYfMEDsUeYnToaF5o84Ka1HcHmFPjCAXGADOBufrPvM8chaIcKA+36s2aNaNJkyZF5lWR3Y23bds23wdXixYtyMzMJCsr67Z4QUFBxMXFAbBv3758F+/Tp09nxIgR3HPPPQQFBfHDDz/w2muvERoayoABA/LdkUgpOXToEO3atWPLli35C1y1bduW1NRUi5StOI7EHuGhXx/idOJp3u/xvpoJXgaYU+MYBoRIKbOLjamo8lx97z2yTpatW/VqzZpSe8qUUqUtK7fq5mItd+PFldOUNWvW0LZtW7NdlORx/vx5Nm3axIkTJ+jcuTNr1qxh9uzZDBs2jN9++42hQ4dy8OBBWrdujRCCOXPmsHjxYrp06UJaWhrOzs7Fn6SM+eHsD7yz6x38qvvxRd8vaOJVtPFXmIc5huMwUBOIKSaeQlHhsLRb9Vuxlrvx4sqZx/Hjx5k4cSLr168v8TkGDhyIo6MjoaGhGAyGfIeMoaGhREREADdqUgBdunRhwoQJ+R54AwLKb95wjiGHWXs1J4Wd/Tszu/tsajrXLLfz2zrmGI5awCkhxF5u7uNQw3EVt1HamsGdUB5u1c3FWu7GzalxREZGMmzYMD7//HMaNGhQYD6m19L0OpqWzc7ODkdHx3wDa1q29evXs2bNGkBbwXDQoEH8/vvvdOrUib/++qtEDihLS8z1GCZsnsDh2MM82eJJxrUbh4OdOa86hbmYczWnWVyFQnEHlIdb9bLEEu7GiytnUlISgwYNYsaMGXTp0qXQeHmu1AcOHJhvAMwlOTmZ3NxcvL29Aa1pKzQ0lNDQUHbu3MmpU6csbjgOxhxkwuYJpOek836P9xkQNMCi56uqFNs5bjoEVw3HVVRETN2q33fffaV2qz5gwIDb3KrnDb398ccfCQgIYOfOnQwaNKjUI6IKcjee13m8Zs0axo8fb3ZeJXGlvmjRIs6dO8fbb7+d32FtuvxtHtOmTWP8+PF069bttpFlxbFhwwb69u2bvz9//nxatmxJ69atcXFxyW/CsgRSSr459Q1PrXuK6g7V+erer6qM0UjftZvYxYvL96RSSpv5tW/fXirKnxMnTlhbQqXhiy++kDNmzCiTvIYOHSp/++23MsmrLBg1apTcuXNnqdOX9jnKyMmQU7ZNkS1XtpTP//W8TM5KLrWGyoTRaJRxKz6VJ5q3kOcG3isNaWmlygfYJ0v4rlUNfwpFOVJW7sZDQ0Np3LjxHU8iLEuWL19e7ue8nHqZCZsncDrhNM+1eY5nWj2DnTBnlkHlxpieTtTUqaT+sQ63e+7B/733sCvBQlt3ijIcCkUl5OjRo9aWYHW2Rm5l8rbJSCSL+iyie0B3a0sqF7LCLxA57kWywy/g+58JeI8eXe7OGc1xctgFmA7U1+MLQEop1Vx9RT5SSuVZVFFqZDErkZpilEaWHl7Kx4c/prFnY+b1mkegW6AF1VUcUjZsIHrSZISTE/U+XUENkzlI5Yk5NY4VaOtv7AcMlpWjqIw4OzsTHx+Pt7e3Mh6KEiOlJD4+3qwJgslZyUzaNol/rvzD4AaDmdppapVYP0Pm5hIzbx4JKz7FuVUrAhbMx1GfL2QNzDEcyVLKP0qTuRBiALAAsAeWSyln3hI+BHgbzetuLvCSlPIfPSwCSEUzVrmyhGviKsqPgIAAIiMjiY2NtbYURSXF2dm52AmCx+OPM2HTBGIzYpnacSrDmwyvEh8qubGxXPnPK1zfswfPRx7Gb9Ik7JycrKrJHMOxSQjxPvADJXByKISwBxYD/YBIYK8QYq2U8oRJtI3AWimlFEK0Ar4DTMdS9pJSxplXFIW1cHR0JDg42NoyFDaKlJI1Z9cwY/cMvFy8WDVgFaG+odaWVS5c37+fKy+9jCE1lTqzZuIxZIi1JQHmGY6O+l/TL34J9C4mXQfgnJQyHEAIsRoYAuQbDillmkn8Gnq+CoVCAWhLu76z6x3Wnl9LZ//OzOo+C09nT2vLsjhSShJWriJmzhwcA+oStHw5zk0aW1tWPuYsHVva5WLrApdN9iO5YYTyEUIMA2YAfsAg01MD64UQElgqpVxW0EmEEE8DTwPUq1evlFIVCkVF42LKRSZsnsDZxLM82/pZnmn1TJXwamtITSV6yuukbtiAa98+1JkxA3s3N2vLuolCDYcQ4jEp5ZdCiAkFhUspPygm74IaH2+rUUgpfwR+FEJ0R+vvyJt62kVKGSWE8AM2CCFOSSm3FpB+GbAMICwsTNVYFAobYMPFDfx3+39xsHPgo74f0bVuV2tLKhcyT5/myrjxZEdG4vfaa3g9ObJC9uMUVePIm01SWlMXCZiOkQsAogqLLKXcKoRoIITwkVLGSSmj9OMxQogf0Zq+bjMcCoXCdsgx5jBv/zy+OPEFrXxaMafHHPxdrTd6qDxJWvMDV996C3t3d+qvWkn1sIo7HqhQwyGlXKr/fbOUee8FGgkhgoErwEPAI6YRhBANgfN653g7wAmIF0LUAOyklKn69j3AW6XUoVAoKgFX06/yypZXOBx7mEebPcp/2v8HR3tHa8uyOMaMDK6+9TbJP/5I9c6dqDtnDg66o8iKisVmjkspc4UQLwB/og3H/VRKeVwIMVYPXwI8ADwhhMgBMoB/60akFlrzVZ7Gr6WU6yylVaFQWJdtkduY8s8Ucow5zOkxh/5B5besrjXJCr/AlfHjyTp3Dp/nnsXn+ecRJXQuaQ1ESWZsVnTCwsJknjdThUJR8ck15vLRoY/45OgnNPZszNwecwnyCLK2rHIh+ZdfiZ42Dbtq1agzezau3azTjyOE2F/SeXLKV5VCobAKMddjeG3ra+y/tp9/NfoXkztMxtmh/JeXLW+MWVlcmzGDpNXf4tKuHXU/mItj7drWllUizPFVVQ2tSSnINL6UUvU5KBSKUrEjageTt00mIzeD97q+x/0N7re2pHIhOyKCyJcnkHXyJF6jnsLvpZcQjpWvH8ecGsfPQDKar6qsYuIqFApFoeQ1TS0/upwGNRswt8dcQmpWDX+pKb//TvR/30A4OBCw5GPceva0tqRSY47hCJBSVo2ltBQKhcW4ln6Nidsmsv/afoY1HMbkjpOrhINCY2Ym196bQdJ33+HSpg11531gVQeFZYE5hmOHECJUSqkWAFAoFKViW+Q2Xv/ndTINmVWqaSorPJwrL08g6/RpvEePwnf8+ErZNHUr5hiOrsBIIcQFtKaqvPU4WllUmUKhqPTkGHNYeGAhnx3/jEaejZjTYw4hHlWjaSr555+JfvMt7JycCFy6BNcePawtqcwwx3BYboV5hUJhs1xJu8JrW1/jSOwRhjcezqt3vVo1Rk2lp3P17XdI/uknqoeFUWfuHBxr1bK2rDLFHCeHF4UQrYFu+qFtUsrDlpWlUCgqMxsubmDa9mlIJO/3eJ8BQVWjmzTz1CmuvDyB7IgIbULfc88hHGxv1oM5w3HHA2PQ1uMA+FIIsUxKudCiyhQKRaUjMzeTOfvm8O3pbwn1CWV299kEuBW9QJMtIKUk8euviZk1G3sPD+p99hk1Ot3mDNxmMMcUjgI6SinTAYQQs4CdgDIcCoUin/NJ53l166ucTTzLyBYjGdd2XJXwNWVISiJq6lTS/tpIje7dqDNzJg5eXtaWZVHMMRyCm9caN1Cwy3SFQlEFkVLyw9kfmLlnJtUdq/Nx34+rjBv06/v2ceXV18iNi8Nv4kS8RjyBsLOztiyLY47h+AzYrbs2BxgKrLCYIoVCUWlIyU7hzR1vsv7iejr6d2RG1xn4Vve1tiyLI3NziVu6lLjFH+EYGEDQ11/jEtrS2rLKDXM6xz8QQmxGG5YrgCellActLUyhUFRsDsUcYuLWicRcj+Gldi/xZMsnsRO2/7WdExXFlddeI2PfftwH30/tN6Zh71qj+IQ2RFErALpLKVOEEF5AhP7LC/OSUiZYXp5Coaho5Bpz+eToJyw9vBT/Gv58PvBzQn1DrS2rXEhZ9yfR06ZBTg51Zs/CY/Bga0uyCkXVOL4G7kPzUWXqe13o+1VjFo9CocgnOi2aSdsmcSDmAINCBjG141RcnVytLcviGK9f1zzafv8/nENDqTvnfZzq17e2LKtR1AqA9+l/g8tPjkKhqKisi1jHWzvfwiiNVcptSMbx40S98irZERF4P/00vi++YBNuQ+4Ec+ZxbJRS9inumEKhsE3Sc9KZsXsGP5//mVY+rZjZbSaB7oHWlmVxpNFIwmcriZk/HwcvL5ufm1ESiurjcAaqAz5CCE9uDMF1B+qUgzaFQmFljsYeZdK2SUSmRfJ0q6cZ23osjna2/7Wdc+0aUZMmcX3nLtz69aP2W2/i4OlpbVkVhqJqHM8AL6EZif3cMBwpwGLLylIoFNbEYDSw/OhyPj78MX7V/fi0/6e0r9Xe2rLKhZQNG7g69b8Ys7Op/fZb1HzwQYRQU9dMKaqPYwGwQAjxonIvolBUHa6kXWHKtikciDnAwOCBTO00FXcnd2vLsjjG9HSuvvceyWt+wLlFC+rMeZ9qwaqLtyDMmcexUAjREmgOOJsc/9ySwhQKRfkipeTX8F95d/e7AMzoNoP7Qu6zsqryIePQIa5MnEjOpctaB/gLzyOcnKwtq8JiTuf4NKAnmuH4Hc3N+j+AMhwKhY2QnJXMO7veYV3EOtr5teO9bu9R17WutWVZHJmbS9ySpcR9/DEOtfyo//kqqt91l7VlVXjMcTnyINAaOCilfFIIUQtYbllZCoWivNgVvYvX/3mdhIwExrcbz5MtnsTezt7asixO9sWLRL02kYzDh7UZ4P/9L/ZubtaWVSkwx3BkSCmNQohcIYQ7EIOa/KdQVHqyDFnM3z+fL09+SbBHMB/2/pAW3i2sLcviSClJ+v57rs2chXBwoM7cOXgMGmRtWZUKcwzHPiFETeATtNFVacAeS4pSKBSW5WT8SSZvm8z55PM83PRhXm7/Mi4OLtaWZXFy4+KInvpf0jZvpnrnTtSZMQPH2rWtLavSUaThENoYtBlSyiRgiRBiHeAupTxSHuIUCkXZYjAa+Oz4Zyw+tBjPap4s6buELnW7WFtWuZD6119E//cNjOnp1JoyGc/HHqsSLtAtQZGGQ0ophRA/Ae31/Yhy0KRQKCzApZRLvP7P6xyKPcQ99e/hv53+S03nmtaWZXEMaWlce/c9kn/8kWrNm1F39myqNWxobVmVGnOaqnYJIe6SUu61uBqFQlHmSCn5/sz3zNk3BwfhwHtd3+O+kPuqxKS29N17iJ48mZyrV/F+diy+zz6rhtmWAeYYjl7AM0KIi0A6undcKWUriypTKBR3TMz1GKbtmMY/V/6hk38n3u7yNrVr2H6bvjEzk9h580lYtQqn+vWp/9WXVG/b1tqybAZzDMdAi6tQKBRlipSSPy78wbu73yXbkM3kDpN5qOlDVWKhpYyjR4maOIns8HA8H3kEv1f+g1316taWZVOYYzjekVI+bnpACPEF8Hgh8RUKhRVJzEzknV3vsP7ielr5tuLdLu8S5BFkbVkWR2Zna5P5li7FwdeXwBXLce1SNTr+yxtzDMdNA7uFEPboneUKhaJisenSJqbvnE5Kdgrj241nZIuRONiZ829euck8fYaoSZPIOnkSjyFDqPX6FOzdbd+/lrUoyq36ZGAK4CKESMk7DGQDy8pBm0KhMJOU7BRm7ZnF2vNraerVlGX9ltHEq4m1ZVkcmZtL/PIVxC5ejL27OwGLF+HWRy0VZGmK8o47A5ghhJghpZxcjpoUCkUJ2Ba5jek7phOfGa+tmdFqLI72tr9mRtb580RNnkLmkSO49e9P7enT1JoZ5YQ53nEnCyHqAvVN40spt1pSmEKhKJrU7FTm7JvDD2d/oIFHA81liE8VcBliMJCwchWxCxZg5+JC3Q/m4n7vvdaWVaUwxzvuTOAh4ARg0A9LQBkOhcJK7Liygzd2vEFsRixPtXyK59o8RzX7ataWZXGywi8QPWUKGYcO4dq3D/7TpuHg62ttWVUOc3rNhgFNpJRZJc1cCDEAWADYA8ullDNvCR8CvA0YgVzgJSnlP+akVSiqImnZaczZN4c1Z9cQ7BHMFz2/oJWv7U+pkgYDCas+J3bBAoSzM3Xen437fVVjEmNFxBzDEQ44AiUyHProq8VAPyAS2CuEWCulPGESbSOwVndt0gr4DmhqZlqFokqx/cp2pu+cTsz1GJ5s8STPt32+itQywome8rpWy+jdm9rTp+Ho52dtWVUacwzHdeCQEGIjJsZDSjmumHQdgHNSynAAIcRqYAhak1deHmkm8WugNYGZlVahqCqkZKcwd99cfjj7AyEeIXwxsArVMlauJHbBhwgXF+rMnoX7/ferWkYFwBzDsVb/lZS6wGWT/Uig462RhBDDgBmAH5DnFN+stAqFrbM1citv7nyTuIy4qtWXce4cUVNeJ/PIEVz79MF/uurLqEiYM6pqlRDCBagnpTxdgrwL+iyQtx2Q8kfgRyFEd7T+jr7mpgUQQjwNPA1Qr169EshTKCouSZlJzN47m1/Cf6FhzYZ82KuKjJjKySF+xafELV6MXY0a1Jk7B/d771W1jAqGOaOq7gfmAE5AsBCiDfCWlHJwMUkjgUCT/QAgqrDIUsqtQogGQgifkqSVUi5Dn5AYFhZWoHFRKCoTGy5u4J1d75CSlcIzrZ7h6VZP42Rv+x5dM0+eJGrK62SdPInbgAHU/u9UHLy9rS1LUQDmNFVNR+tz2AwgpTwkhAg2I91eoJEe9wrakN5HTCMIIRoC5/XO8XZoxikeSCourUJha8RlxPHe7vfYcHEDzbyaVZnZ38asLOI++pj45cux9/Kk7sIPce/Xz9qyFEVgjuHIlVIm31JVLPbLXkqZK4R4AfgTbUjtp1LK40KIsXr4EuAB4AkhRA6QAfxbSimBAtOWpGAKRWVBSskv4b8wa88sMnMzGdd2HCNbjsTRzvZnf18/cJDoqVPJDg/HY9gwak18DfuaNa0tS1EM5hiOY0KIRwB7IUQjYByww5zMpZS/A7/fcmyJyfYsYJa5aRUKWyMqLYq3dr3F9ivbaePbhje7vEmIR4i1ZVkcY3o6MfPmk/jVVzj41ybwk09w7dbV2rIUZmKO4XgReB1tKO7XaLWAdywpSqGwdQxGA6tPr2bBgQUATOowiYebPlwl1stI27aN6GnTyI2+iuejj+L70kvYu9awtixFCTBnVNV1NMPxuuXlKBS2z7nEc0zfOZ3DsYfpUrcLb3R6gzqudawty+LkJiZybcYMUtb+glNIiLYqX7t21palKAXmjKraAPyflDJJ3/cEVksp+1tYm0JhU2Qbsvnk6CcsP7ocV0fXKrP2t5SSlF9/5dp7MzCkpuLz3LN4jx2LnVr7u9JiTlOVT57RAJBSJgoh1Hx/haIEHLh2gDd3vkl4cjj3hdzHq3e9ipezl7VlWZzsyCtcffNN0rdtw7l1K+q99TbOTRpbW5biDjHHcBiFEPWklJcAhBD1MWNUlUKh0Fyfz98/n+/OfEedGnX4uO/HdK1r+53AMjeXhC++JPbDD0EIak2ZguejjyDs7a0tzWbIMRjZHZ7An8evci0lk2VPhJXbuc0xHK8D/wghtuj73dFnaisUioKRUvLXpb+YsXsG8ZnxPNH8CZ5v8zzVHatbW5rFyTxxguj/vkHm8eO49uhB7Wlv4FjH9vtwyoOMbANbzsSy/sRVNp6MITkjB2dHO3o18SPHYMTRvnwGV5jTOb5On5zXCc0VyMtSyjiLK1MoKilX06/y7q532Ry5maZeTVnYe2GVcBdivH6d2IWLSPj8c+w9Pak77wPcBgyw+T4cS5N0PZu/Tsaw/vhVtp6NJTPHiIeLI32a+dG/RW26N/LFxal8a3LmrmJfDUjQ4zcXQqgVABWKWzAYDXxz6hsWHlyIRPKf9v/hseaP4WBn7r9Z5SVtyxauvvkWOVFR1Py//8Pvlf9g7+FhbVmVlitJGWw4fpX1J66x+0ICBqPE38OZ4WGB9G9Rmw7BXuVWuygIc0ZVzQL+DRxHW3AJ1AqACsVNnIg/wZs73+RE/Am61O3C1I5TCXALsLYsi5MTE8O192aQum4dTg0aaENs27e3tqxKh5SS09dSWX/8GutPXOXYlRQAGvm58kz3EPq3qE2rAI8KU3sz51NoKKVcAVChsHXSc9JZdHARX5/6Gi9nL97v8T796/evMP/glkIaDCR++y2xH8xDZmfjO34c3qNGIdQQW7MxGCX7LyayXq9ZXEq4DkC7ejWZOKAp/VvUIsTX1coqC8ZiKwAqFLaMlJK/L/3NjD0ziLkew/81/j/Gtx+Pu5O7taVZnMyTJ4meNp3MI0eo3rkT/tOm4RQUZG1ZlYKMbAPbzsay4cQ1Np6KISE9Gyd7O+5u6M0zPULo16wWfu7O1pZZLJZcAVChsEmi0qKYsXsGmyM309izMXN7zqW1b2try7I4hrR04hYuJOGLL7D39FTrfptJfFoWG0/GsP7ENf45p3Vuuzk70LupH/c0r02PJr64Vqtc/WCWXAFQobApcow5fH78c5YeWQrAf9r/h0ebP2rzXmyllKRu2MC192aQe/UqNf/9b/wmvKw6v4sgPDaNDSeuseHENfZfSkRKqOPhzL/DAunXvDYdQ6zbuX2nmLsCoBOQN93ztJQyx7KyFIqKxb6r+3h397ucSzpH78DeTOowCX9Xf2vLsjjZkZFcfftt0rdspVqTJtSd9wHV27a1tqwKh8EoOXgpkQ0nNWMRHpsOQHN/d8b1bkS/5rVoUcfdZmpn5oyq6gmsAiLQ5nEECiFGqOG4iqpAQmYCc/fNZe35tdSpUYeFvRfSM7CntWVZHGN2NgkrVhC3ZCnC3h6/SRPxeuwxhEPlalKxJNezc/nnbBwbTlzj71MxxKdn42An6BTizYjOQfRtXou6NV2sLdMimPMUzAXuyVtvXAjRGPgGUGPuFDaLwWhgzdk1zD8wn4zcDEaHjubpVk/j4mCbLwJT0nfs4Opbb5MdEYFb//7UmjwJx9q1rS2rQnAtJZONJ2P46+Q1tp+LIytX66/o1cSPPs386NnEDw8X2266BPMMh2Oe0QCQUp4RQtj+lVFUWY7HHeedXe9wLP4YHWp34PWOrxNS0/YXV8q5FkPMrJmk/P4HjvXqEfjJMly7dbO2LKsipeREdAobT8aw8eQ1DkcmAxDg6cIjHevRt1ktq0/GswbmGI59QogVwBf6/qPAfstJUiisQ3JWMh8e+JDvz3yPt4s3M7vN5N7ge22mXbowZE4OCV9+RdzChcjcXHxefAHv0aOxq1bN2tKsQmaOgV3h8fnGIio5EyGgTWBNXu3fhD7N/GhSy83mn4uiMMdwPAs8j7ZkrECbMf6RJUUpFOWJURr5+dzPzNs/j+TsZB5t9ijPtXkONyc3a0uzOOl79nDt7bfJOnsO1x49qDX1dZwCA60tq9yJS8vi71Oaodh2No7r2QZcHO3p1siHl/o2pldTP3zdqqYhLQhzDIcDsEBK+QGAEMIezXeVQlHpORF/gnd3v8uR2CO08W3D1E5TaeLVxNqyLE5OTAwx788h5ZdfcKxTh4DFi3Dt3bvKfEVLKTl1NZWNJ6/x18kYDkcmISXUdndmWNu69G1Wi84NvHF2VG7gC8Icw7ER6Auk6fsuwHrgbkuJUigsjWmzlKezJ+90eYf7G9xv82t+y5wcEr74krhFi7RmqeeexXvMGOxcbL/TPzPHwM7weP4+GcPfp2K4kpQBQKsAD17q05g+zfxsasisJTHHcDhLKfOMBlLKNCGE7S8qoLBJDEYDP5z7gQ8PfEhqdiqPNHuE59o8VyVchaTv3MnVd98l+9x5avToTu0pU3CqX9/asizKtZRMNp2K4a+TMWw/F0dGjtYE1bWRD+P6NKRXE79K4eKjomGO4UgXQrSTUh4AEEK0BzIsK0uhKHsOxx5mxu4ZHI8/Tvta7ZncYXLVaJaKjubarNmkrluHY2AgAR99hFvvXtaWZRGMRsmRK8n8fSqGTadiOHpFGwVVt6YLD7YPoE8zPzqFqCaoO8Ucw/ES8L0QIkrf90dzs65QVAriMuKYt38ea8+vxc/Fr8qMljJmZZHw6afELV0GgO/4cXg99ZTNjZZKzczhn7NxbDwVw+bTscSlZWEnoG09T14b0ITeTW10FJQhBy7thDN/Qto1eGB5uZ3aHJcje4UQTYEmaKOqTimXI4rKQI4hh69Pfc2Sw0vINGTyVMuneLrV09RwrGFtaRZFSknaxo1cmzmLnMhI3AYMoNarr+BYt661pZUZ4bFp/H1K66vYG5FAjkHi7uxA98a+9GnmR4/GfnjVsEEX72kxcHYDnP0Tzm+CrBSwd4Lg7mDIBfvymdlv1ll0Q3HMwloUijJjx5UdzNw7kwvJF+hatysT75pIkEeQtWVZnKzz57n23gzSt2+nWqOG1Fv5GTU6dbK2rDsmK9fA7vAE/j4Vw+bTMUTEa2tXNK7lylNdg+ndxI/29T1xsLWJeEYjRB+EM+s1YxF1UDvu5g8thkLjARDcA6qV77odyvGMwqa4lHKJ9/e+z+bIzdRzq8fiPovpHtDd2rIsjiElhbjFi0n46mvsXFyoNWUKno88XKl9S0UnZ7DpVCx/n4phx3ltbkU1BzvubuDNqK7B9GziR6CXDY7TyUyG83/rNYsNkB4DCAgIg15TofE9ULsVWLHprfI+VQqFCek56Sw7sozPT3yOk50TL7V7icebP46TvQ02V5ggDQaS/reG2PnzMSQlUXP4cHzHj8PBy8va0kpMrsHIgUtJbDqtdWyfupoKaB3bD7QLoFdTXzqH+ODiZGMd21JCzEk4u14zFJd2gjSAc01o2Bca94cGfaCGt7WV5mOOd1yB5mYkREr5lhCiHlBbSrnH4uoUimIwSiNrz69lwYEFxGXEMbjBYF5q9xK+1X2tLc3ipO/Zw7UZM8k6eRKXsPbUnjIF5+bNrS2rRMSkZrLldCybz8Sy9UwsqZm5ONgJwoI8mXJvU3o18aOhn6vtdWxnpcGFrTeMRUqkdrxWKHQZD43ugYC7yq3PoqSYo+ojwAj0Bt4CUoE1wF0W1KVQFMuhmEPM3DOT4/HHaeXbig97fUiob6i1ZVmc7MgrxLz/Pql//omDvz91P5iL28CBleLlajBKDl1OYvNpbQRU3nBZP7dqDGxZm15N/OjSyAd3ZxvzoyolxJ3RjMS5DXBxBxiywckVQnpCj9egUT9wr2NtpWZhjuHoKKVsJ4Q4CCClTNQXdlIorEJ0WjTz9s/jj4g/8HPxY0a3GdwbfK/Nz/o2pKUTv2wZCStXgr09PuNexPupp7BzrtgT2GJTs9h6RqtVbDsbS9L1nPzhsq/2b0LPJr4097fBGdvZ6XBhm2Yozq6HpEvacd+m0OFprQkqsBM4VL7XqTmGI0f3TyUBhBC+aDUQhaJcuZ5znRXHVrDq+CoAnmn1DE+1fIrqjjbYQWqCNBpJ/vEnYubPwxAbh/vg+/GbMKHCrpGh1SoS2Xw69qZahY+rE72b+tGriR/dGvlQs3rle2EWSV6t4txfWs3i4g4wZIFjDQjpAV1e0vosPCv/bH1zDMeHwI+AnxDiXeBBYKpFVSkUJhilkV/O/8KCAwuIzYhlYNBAXmr/EnVcK0e1/k64vncvV2fMIOvESZxbtyJw4UJc2rSxtqzbyOur2HImlm1n40jOuFGr+E+/xvRsovmBsrOzsVpFVqpJreIvSNZrFT5NoMMYzVDUvxscbGvSpTkTAL8SQuwH+qBNABwqpTxpcWUKBbD36l7e3/s+JxNO0sqnFR/0/IA2fm2sLcviZF+6RMz7c0jdsAEHf3/qvP8+7vcNqjDNOTkGIwcv3eirOBGdAoCvWzX6Na9Fj8a+tluriDlxo1ZxaRcYc7S+iuAe0O1lzVjUrGdtpRbFnFFVnYDjUsrF+r6bEKKjlHK3xdUpqiyXUi7xwf4P2HhpI7Vr1K46/RjJycQtWUrCl18iHB01NyEjR1YI77VXkjL0WkUMO87Fk5qljYBqV1/rq+jRWOursLlaRUYihG/WjMW5jZAarR2v1RI6Pat1alfSvorSYk5T1cdAO5P99AKOKRRlQnJWMksOL2H16dU42jnyYtsXeaL5Ezg7VOwO4DtF5uSQuPpb4hYvxpCcjMe/huE7bjyOtfyspikzx8DuCwlsPaM1QZ2L0Zxk1/Fw5r7W/vRo7MvdDW1wBJTRAFGHdEPxF1zZB9IIzh4Q0gsa9tFqFZVkBJQlMMdwCCmlzNuRUhqFEBVzcLGi0pJjyGH16dUsObyEtJw0hjUcxgttX8DHxcfa0iyKlJK0v/8m5v05ZEdEUL1TJ2pNfA3nZs2souV8bBpbzsSx9Uwsu8Ljyco14uRgR8dgLx66K5DujX1pZIvzKlKitdna5zdqPqAyEgABddpCt1c0Q1G3fYWdV1HemHMVwoUQ49BqGQDPAeHmZC6EGAAsAOyB5VLKmbeEPwpM1HfTgGellIf1sAi0OSMGIFdKGWbOORWVCyklGy5uYP6B+VxOvUwn/068EvZKlXB3nnH0GDGzZnF93z6cQkII+PgjXHv2LNeXcvL1HLaf1wzFtrNx+YsbhfjW4JGO9eje2JdOwd62N1s7N0uboX3uLzj3N8Qc14671tL8PzXso9UuKtBs7YqEOYZjLNrIqqloQ3I3Ak8Xl0gfwrsY6AdEAnuFEGullCdMol0AeuhzQwYCy4COJuG9pJRxZpVEUek4FHOIufvmcij2EA1rNuTjvh/TpU4X2/uavYXsyCvEzp9Pyq+/Yu/lRe1pb1DzwQcRjpZv8jEYJYcjk9iqz9Q+dDkJowS3ag7c3dCb53s1pHtjHwI8bWyIs5QQd1arUZzbCBH/QG4G2DlCvU7Qd7rm1qN2qFV9QFUWzBlVFQM8VIq8OwDnpJThAEKI1cAQIN9wSCl3mMTfBQSU4jyKSsallEvMPzCfDRc34OPiw7TO0xjacCgOdrbdDGBISSFu6VISv/gShMD76afxfnoM9q6W9WwamXidbWfj2HY2ln/OxpGSmYsQ0Cqgpm4ofGkTWBNHW/Msm5EI4VtuND8lX9aOezeEdo9rhiKoa7l7lrUFCv1PFUK8JqWcLYRYiD75zxQp5bhi8q4LXDbZj+Tm2sStjAL+MD0FsF4IIYGlUsplheh8Gr0GVK+ebQ+Bq+wkZCaw7Mgyvj39LY52jjzX+jlGtBhh8xP4jNnZJH79NfEfL8GQkoLHkCH4jh+Ho7+/Rc6XnpXLrvB4tp2NY+vZWMJj0wGo7e7MgJa16dbIl64NffC0tfUqDDkQuU/vq/gbog5ondrV3LX1KrpNgAa9wTPI2korPUV94uXN1dhXyrwLqu/dZoAAhBC90AxHV5PDXaSUUUIIP2CDEOKUlHLrbRlqBmUZQFhYWIH5K6xLRm4GX574kk+PfUpGbgbDGg3judbP2bwjQmk0kvL7H8TOm0fOlSvU6NIFv1dfwblp0zI9j8EoOR6VrBmKM7EcuJRIjkHi7GhHx2BvHu1Yn26NfGyvU1tKSAjXDcUmzWlgdioIO60ju/urWq1CdWqXOYVeTSnlL/rfVaXMOxIINNkPAKJujSSEaAUsBwZKKeNNzh+l/40RQvyI1vR1m+FQVFwMRgM/n/+ZxQcXE5MRQ8/Anrzc7mVCaoZYW5rFSd+5k5g5c8k8fpxqTZsSuHw5rl27lFn+V5Iy+OdsLFvPxrHjXByJ17VFOZv5u/NU12C6N/KlfX1P21tbOyNRMxB5xiLponbcox6EPqDVKIK7g4undXXaOOZMANxEwU1VvYtJuhdoJIQIBq6g9ZM8ckve9YAfgMellGdMjtcA7KSUqfr2PWieeRWVACklWyK3sODAAs4lnaOVbytm95hN+1rtrS3N4mSeOkXMnLmk//MPDnX8qTNrJu7334+wu7P+g9TMHHaFJ/DPWW30U3ic1vxUy70avZvWontjH+5u4IOvm225tiA3GyL3QvgmzVDkNT85uWkG4u4XNWPhFaI6tcsRc+pvr5hsOwMPALnFJZJS5gohXgD+RBuO+6mU8rgQYqwevgR4A/AGPtKr0HnDbmsBP+rHHICvpZTrzC6VwmocijnEvP3zOBBzgCD3ID7o+QF96/W1rSaSAsiOvELshwtI+eVX7Nzd8XvtNTwffQS7aqV7kecYjByJTGLb2Tj+ORvHwctJGIwSF0d7OoZ45Q+Vtcnmp9hT2kzt85vg4nbITgNhf6P5KaSXthqevY1NPKxECJO5feYnEmKLlLKHBfTcEWFhYXLfvtJ2ySjuhHOJ51hwcAGbL2/Gx8WHZ1s/y7BGw3C0s+1/7tyEBOKWLCHxm9UIOzu8nngC7zGjsXd3L1E+UkrC49L552wc287GsSs8nrQsbfRTaF0Pujb0oWsjH9rX96Sag401P6Ve1UY/hW/SDEaeSw+vBtpaFQ16Q3A3bea2oswRQuwv6Tw5c5qqTNegtAPaAxXTn7Oi3IlOi+ajwx+x9vxaqjtU58W2L/JYs8dsfqSUIS2dhFUrSfj0M4wZGdR84F/4PP98iVydx6ZmseO8Zii2n4sjOjkTgEAvF+5vXYdujXzoHOJte6OfstK0mkT4Zu0Xo4/Qd/HS3I+H9NIMhg24H7dVzGmq2o/WxyHQmqguoI2AUlRhEjMTWX50OatPrUYiebTZo4wJHYOns213Shqzs0la/S1xS5ZgSEjArV8/fF8aT7UGDYpNm56Vy54LCfxzTjMUeWtqe7g40qWhNy829KVLQ2/qe9ewdDHKF0MOXDlww1BE7gFjLjg4Q73O0Gq4Zixqt4I77AtSlA/mTAAMLg8hispBek46n5/4nFXHV5GRm8HgBoN5rvVz+LtaZk5CRUEaDCSv/YW4hQvJiYqieseO+E14GZfWrQtNk2MwcvhyEv+ci2PHuXgOXEok1yhxcrDjriBPJg5oSteGPjSv4469LXmUlRJiTsKFLZqhiPhH66dAgH9rrUM7pCcEdgRH63v9VZScoiYA9pZS/i2E+FcBwRJIAP6RUhospk5RYcgyZPH96e/55OgnJGQm0KdeH15s+yINahb/pV2ZkVKS+tdfxC5YQPa58zg3b07tt9+ixt1339YpbTRKTl9LZfu5OHacj2d3eDzp2Yb8forR3ULopvdT2Nww2aTLmpG4sEUbLpt2TTvuFaLVKIJ7aKOgqnsVmY2iclBUjaMH8DdwfyHh3mj+q/qVtShFxSHXmMva82v5+PDHXE2/Sif/ToxrO45Q31BrS7M46Tt2EDNvPplHj+IUHEzd+fNx63/PTQbjUvx1tp/Xmp52no8nPj0bgBCfGgxrV5cuDXzo3MDb9hY0So+HiK1ap/aFLdpEPIAavpqRCOmp9VfY+IJGVZWiJgBO0/8+WVgcIcQKS4hSWB+jNPJnxJ98dOgjIlIiaOXTire7vE0n/07WlmZxrh88SOz8BVzfvRuHOv74v/sOHkOGIBwc8ju0d5yLZ/v5OCITNW+yvm7V6N7Yl7sbeNOloQ91atpYE0xWmraG9gXdUFw9qh13coOgLnDXGM1Y+DVT8ymqAHc0D19KqTrJbYy8yXsLDy7kTOIZGtZsyIJeC+gV2Mu25gsUQOaJE8Qu+JC0LVuw9/am1pTJ2A15gD2Rqez4/TQ7zsdx5pq2mJG7swOdQrwZ0y2Euxt409DW5lPkZukT73RDcWW/1qFt76T1TfSaqtUo6rRV8ymqIMqBiwLQDMau6F0sOriII3FHqOdWj5ndZjIgaAD2djbWHn8LWefPE/vhQlL//BM7NzfSHn+azS168U9kGkdnbsYowdnRjruCvBjaVmt+alnXw7Y6tA25EH3oRh/FpV2Qm6n5ffJvo3VoB/fQXJCrDu0qjznzOKpJKbOKO6aovOy/tp9FBxex79o+/Gv4M73zdAY3HGzzk/eyL13i2ocLSf3tNwxO1fin4/0s9etIUqozDnuiaFuvJi/0bsTdDbxpW6+mbU28Mxq1xYsubNV+Eds1B4EAfi2g/UjNUAR1URPvFLdhTo1jJ7evL17QMUUl40jsERYdXMTO6J34uPgwucNkHmz8IE72NtaRa0KuwcjRA6dI+HgJtXduJMfOnl8adGdN417UC6nLvxt4c3cDH8Lqe1Kjmg1VyKWE2NMQsU03FP/oy6OizdAOfVAb9RTUDVxt22ux4s4pajhubbQ1NVyEEG254SbdHbDtacE2zon4E3x06CO2RG7Bs5onr4S9wvAmw3FxsL0mCINRciIqhR3n4zh26Cwh6/9Hn/Bd+Ar4p0UPkoY9Qqe2jRgX7IWHiw3VsPJcjpsairwhsh6B0GSgZiSCu4NHXetqVVQ6ivqk6g+MRHOH/oHJ8VRgigU1KSzE6YTTfHToI/6+/DfuTu6MazuOR5s9alPuQYxGyamrqewMj2fn+Xh2X4jHISmB4Wf+ZszFXdghSe97L8EvvcAzDWxsqGhihGYgLmzTDEbKFe24a23NQOTVKDyD1MgnxR1R1HDcVcAqIcQDUso15ahJUcacSTzDksNL2HBxA26Objzf5nkea/YYrk6Vf8lMo1FyJiaVXefj2Rkez+4LCSTpa1O0rJ7LtMvbaLZnA3ZGAx7DhuIz9lmcAmzkCzvpsmYg8oxF8iXteHUfbUnU4AkQ1B18GilDoShTimqqekxK+SUQJISYcGu4lPKDApIpKhBnE8+y5PAS1l9cj6ujK2Nbj+Xx5o/j7lQyz60VCaNRcjYmjV3h8ezSDUWCPukuwNOFfs1q0dXHjpZb15Lzw/+QOTl4DB6Mz7NjcarsSwsnR2pGIs9YJEZox128NENx94uaF1nfpspQKCxKUU1VeZ7WKv9naRXjXOI5lhxZwvqI9VR3rM6Y0DGMaDECj2qVb3RMUYaibk0XejXxo3MDbzqFeFHbcJ34FZ+S+O43ZGdn43H//ZrBCAqybiFKS2GGwrmmZig6Pqv99WuunAMqypWimqqW6n/fLD85ijvBtEmqhmMNRoeO5onmT1DTuaa1pZmNadPT7gsJtxmKnk186RTiTecQbwK9tL6Z3NhY4pcu5Nzq1cjsbDzuvw/vsWOpFlzJ/HMmXdKGxUb8AxcLMBQdntFqFH4tlKFQWBVz5nF8RsFLxz5lEUWKEnM64TRLjyzNNxhjQsdUGoNhNEpOXk1hd3gCuy/Es+dCQv762Xk1io4hXnQK9ibQy+Wm2dk5MTEkrFhB4upvtSapymQwpNTWyzY1FEl6H4VzTajfBTqO1WsUylAoKhbmDFT/1WTbGRgGRFlGjqIknIg/wdLDS/n78t+4OrrydKuneaL5ExW6SSrXYORkdCq7L2hNT3suJJCSqa1EHOjlQp9mtegU4k3HYK/8GsWt5Fy7RvzyFSR99x0yN1drkhr7TMVuksobHntx+w1jkRKphbl4Qf27odPz2oQ7ZSgUFRxz1uO4aUSVEOIb4C+LKVIUy5HYIyw9spStkVtxc3LjudbP8UizRyqkwcgxGDl6JTm/RrEvIpG0LM1QBHlXZ2BLfzqGeNExxJu6xTgGzImKIu6TT0j+3xqklHgMHYLP009XzE5vKSHujF6b2K45CMxbErWGr2Yo6o/XahS+TZWhUFQqSjM1thFQAf9TbZ8D1w6w9MhSdkTtwKOaBy+2fZGHmz6Mm5ObtaXlk5lj4PDlJPZcSGBPRAL7LyZyPVtbsqWBbw0Gt6lDx2AvOgZ7U9vD2aw8sy9dIm7ZMpJ/+hmEoOa//oX3mDEVa1it0aAtgRqx/YahuB6nhbn5a01PQV2gflc1PFZR6TGnjyOVm/s4rgITLaZIcRNSSnZf3c3Sw0vZd20fXs5evNTuJR5q+hA1HK2/xGh6Vi4HLiWy50ICu8MTOHQ5iWyDEYCmtd34v/YBdAzxpkOwFz6u1UqUd9b588QtXUrKr78hHBzw/Pe/8R71FI516liiKCXDkAPRh28YiUs7ITNZC/OoB4366bWKLtpiRspQKGyIIg2H0HoiW0gpL5WTHoWOlJKtkVtZdmQZR+KO4Ofix8S7JvJA4wes6hok6Xo2eyMS2RuhjXg6diUZg1FibydoWcedJzrXp2OIN3cFeZZ68aLMkyeJW7qM1D//RDg74/XEE3g99SSOfn5lXJoSkJOhuRa/uEMzFpf3Qk66FubdCJoPvWEoagZaT6dCUQ4UaTiklFII8SPQvpz0VHkMRgN/XfqL5UeXcyrhFHVq1OG/nf7LkIZDqGZfsi/2suBqciZ7IhLYeyGBPRcSOH1N86DqZG9Hm8CaPNujAXcFe9G+vieud+gU8PrBg8QvWUrali3Yubri/fTTeI0cgYOnZ1kUpWRkJsPlPbqh2AFRB8CQDQio1RLaPqoZifp3g6sVDZpCYQXM+U/fJYS4S0q51+JqqjA5xhx+C/+NFUdXEJESQZB7EG93eZtBIYPKzb25lJKI+OuakYjQDMWlhOsAVHeyp319T+5v7c9dQV60DqxZJutmSym5vnMncUuWcn3PHuw9PPAZ9yJejz2GvXs5znBPi7nR5HRxB1w7BtIIdg7aehSdnoV6d0O9juBiBUOmUFQgzDEcvYCxQogIIB3NS66UUraypLCqQmZuJj+c/YGVx1cSnR5NE88mzOkxh771+lp8ASWDUXIyOoU9FxLYdzGBPRcSiUvTllnxquFEWH1Pnuhcnw7BXjT3d8fBvuxG/kijkbRNm4hbuozMI0dw8PXFb+JEPIf/H3Y1LNx3kzc09tJO3VDshITzWphjdQgIg+6vQf3OEHAXOFm/L0mhqEgU5auqnt63MbAc9VQZUrJT+PbUt3x58ksSMhNo69eWqZ2m0q1uN4stQZqZY+DQ5ST2RSSwJyKRAxdvDI2tW9OFrg296RDsTYdgTxr4WmYpVJmTQ8rvvxP3ySdknzuPY2Agtd98E4+hQ7CrZqGmOKNBq0Fc2qXXKnZB2lUtzLkm1OsM7UdoTU/+rdVSqApFMRRV4/gJaCelvCiEWCOlfKCcNNk0cRlxfHniS749/S1pOWl0qduFMaFjaF+r7LuREtOz2X8xkb0XtT6Ko1eSyTFoA+Sa1HJjSJs6dAj2IizIq9g5FHeKMTOTpDVrSFjxKTlRUVRr1Ig678/GfeBAhEMZL5iU15GdV5u4vOfG6nYegZrbjnqdtZ+aQ6FQlJii/mNNPzdDLC3E1rmccpmVx1fy07mfyDHmcE/QPYxqOYpm3s3KJH8pJZcTMtgbkcC+i4nsi0jgbEwaAI72glYBNRnVNYSw+p6E3cGIp5JiSE4m8ZtvSPj8CwwJCbi0bUutqVNx7dkDUVYv7PR4uLxLb3raBVGHwKi5LcGvObQarq2VXa+zGvGkUJQBRRkOWci2ogScjD/Jp8c+Zf3F9dgLe4Y0HMLIFiOp717/jvLNc92x72IC+/ThsTGpWv+Em7MD7et7MrRtXe4K8qJVgEeZdGSXhJxr10hYuYqkb7/FeP06NXp0x2fMGKqHhd1Zxvn9EyaGIv6sFmbvBHXbQ+fn9RqF6shWKCxBUYajtRAiBa3m4aJvw43O8cq7qIOFkVKy5+oePj32KTuidlDDsQYjmo/g8eaP41u9dOs5p2XlcvBSIvsiEtl3MYGDl5LyZ2TXrelC5wbehNX35K5gLxr7uWFnZ50JZ1nnzxO/4lOSf/kFjEbcBwzAe8xonJs2LV2GudnaRLvLuzQjcXk3pMdqYc41tZpEm0e0YbH+bcDRvNnoCoWi9BTlVr18P1FtAIPRwIZLG/js2GeciD+Bt7M349uNZ3iT4SVePOlKUgb7dJcd+yISOXU1BaMEOwFNarvzYPsAwoK8CKvvSR0L90+Yw/UDB4lfsYK0jRsRzs54Dh+O15MjcQoIKGFGCRC594aRuLIfcjO1MM9gaNgXAjtqBsOnieqfUCisQBn3SlZNMnIz+OncT3x+/HMi0yKp716faZ2ncX+D+82atJdrMHLqair79P6J/RcTiU7WXpbVnexpW68mL/RuRFh9T9rWq4mbc8UY9ZM3pDZ+xadkHDigzcF4/nk8H30EBy8vMzIwaXa6vAsu7Ya401qYnQPUbgVho7Qmp8BO4FbLsgVSKBRmoQzHHRCfEc/q06tZfWo1SVlJtPJpxYSwCfQO7F3kHIzkjBwOXNKGw+6/mMihyzeanep4ONO+vqfeie1F09puZTp/oiwwZmWR/PPPJHy2kuwLF3CsW5daU6dS81/DsKtesCt0AHIyIfqQbij2aDWKPEeAzh5aTSKvI7tOO3AqIi+FQmE1lOEoBRdTLrLq+CrWnl9LliGLngE9GdlyJO382t0290FKyYW4dPZfTOTAJc1QnLmmjXaytxM083djeFgg7ep70r6+p8WHxd4JuYmJJK1eTcKXX2GIj8e5eXPqzJ2De//+BQ+pTb16w0Bc3qMZDYO2mh9eIZojQNXspFBUOpThMBMpJQdjDrLy+Eo2X96Mg50DgxsM5okWTxDicWO0cka2gcORSTfVKPJWtHN3dqBdfU/ua1WHsPqetA6sSY079O9UHmRfuqSNkPrhB2RmJjW6d8P7qVFU79jhhqE05ELMcd1Q6MYi6aIWZl8N6rbTVrSr1wkCOoBr6QYJKBQK61Px31pWJteYy8ZLG/n8+OcciTuCRzUPxrQaw8NNH8bb2ZsrSRmsPRyVbyRORqeQa9RGL4f41KBvs1q0r+9Ju/qeNPR1tdpop5IipSTj4EESPvuM1L82IhwccL//frxGjsC5cWOtE/vs+htG4sqBG95iXWtDYAfo+IxmJPxbg0P5zBtRKBSWR0hpO1M0wsLC5L59+8okr7TsNH489yNfnfyKK2lXCHQL5KEmj9LQpSfHIjM5cFGrVeTNnXBxtKd1oAft6mlNTm3reeJVo/K9LGVuLqkbNhC/ciWZh49g5+GB57+H4zmgA47Xz2ojni7vhvhzWgJhD7VDtSanwA7azyNQrT+hUFQShBD7pZQlmmBlUcMhhBgALADsgeVSypm3hD/KjUWh0oBnpZSHzUlbEGVhOKLSovj65NesObuGtJw06tdoQV0xkKtXQzgRlZrvsiPQyyXfSLSr51khO7FLgiEtjaT//Y/Ez78gJyoKR38fvLoHUzMwEbvYQ5ClT+Op7q3VIgLv0oxFnbbKCaBCUYkpjeGwWFOVEMIeWAz0AyKBvUKItVLKEybRLgA9pJSJQoiBwDKgo5lpy5S90Qf5+OCn7IvdigTsr7ch/VpnjmUGcs7RjlZ1HXiqazDt6mlDYv3cbGOiWfaliyQuW0jSrxswZmbj4m9Hra4JuNaJQtgdg9wWEPqgbiw6qNXsFAqFRfs4OgDnpJThAEKI1cAQIP/lL6XcYRJ/FxBgbtqyIj4jmf7fPE6W/QWkwZmcpK74GHsRFtCAdq01I9HM3x3HSlybKIyox3qTvD8KAPd6GXi1dsClzV2aW/HADtqQ2GquVlapUCgqGpY0HHWByyb7kUDHIuKPAv4oaVohxNPA0wD16tUrsUhvFw88Hf0JrNGLYQ2H0im4Dr5u5b/SnjVwquuPt3t1PIcPxTG0l6pNKBQKs7Ck4SjoDVRgh4oQohea4eha0rRSymVoTVyEhYWVqsNmw+NLS5Os0uMz6ytrS1AoFJUQSxqOSMDUh3UAEHVrJCFEK2A5MFBKGV+StAqFQqEofyzZcL8XaCSECBZCOAEPAWtNIwgh6gE/AI9LKc+UJK1CoVAorIPFahxSylwhxAvAn2hDaj+VUh4XQozVw5cAbwDewEf6DORcKWVYYWktpVWhUCgU5qMmACoUCkUVpjTzOGxvjKlCoVAoLIoyHAqFQqEoEcpwKBQKhaJEKMOhUCgUihJhU53jQohY4KKFsvcB4iyUd0VDldV2qUrlVWU1j/pSyhItkGNThsOSCCH2lXTkQWVFldV2qUrlVWW1HKqpSqFQKBQlQhkOhUKhUJQIZTjMZ5m1BZQjqqy2S1UqryqrhVB9HAqFQqEoEarGoVAoFIoSoQyHQqFQKEpElTAcQggvIcQGIcRZ/a9nIfEGCCFOCyHOCSEmmZNeCDFZj39aCNFfP1ZdCPGbEOKUEOK4EGKmSfyRQohYIcQh/TfahstaTQjxrZ5mtxAiqDKXVT/+rhDishAi7ZZzWPS+VsDy2uK9bS+EOKqHfSiE5rLbUve2MO0m4ULXcU4IcUQI0a48y10kUkqb/wGzgUn69iRgVgFx7IHzQAjgBBwGmheVHmiux6sGBOvp7YHqQC89jhOwDW2hKoCRwKIqUtbngCX69kPAt5W5rHpYJ8AfSLvlPBa9rxWwvLZ4b/cAndFWIP0DC/7PFqXdJM69ug6h34fd5VnuIvVb8kGvKD/gNOCvb/sDpwuI0xn402R/MjC5qPSmcfT9P4HOBeS9ABhjqYewApc1Pw7a2i9x6AMyKntZsY7hqEjltal7q8c5ZXL8YWCppe5tUdpNji0FHr71mpRXuYv6VYmmKqCWlDIaQP/rV0CcusBlk/1I/VhR6YtKA4AQoiZwP7DR5PADetXzf0II0yVyy4KKVNb8NFLKXCAZbeGussJqZS0ES95XqFjltbV7W1ffLigvKPt7a841L0preZW7QCy55ni5IoT4C6hdQNDr5mZRwLHixioXmUYI4QB8A3wopQzXD/8CfCOlzBLaaoirgN5maszLt7KUtTTnufmkFbCshXDH9xUqVXlt7d4WlVeZ3FszdZgTp7zKXSg2YziklH0LCxNCXBNC+Espo4UQ/kBMAdEiAdMviQAgSt8uLH1RaUCblHNWSjnfRGe8SfgnwKyiS3Y7laWsJmkidcPiASQUW0ATKmhZC9J5x/dVz6dSlBfbu7eR+vZteZXVvS2B9uLiOBWRtszKXRRVpalqLTBC3x4B/FxAnL1AIyFEsBDCCa3Db20x6dcCD+kjTIKBRmgdTQgh3kH7Z3rJ9CT6zcxjMHCy9MUqkApT1lvyehD4W+oNqWVEuZe1MMrhvubpqhDlxcburd6skyqE6KSPKnoiL42F7m1R2vNYCzyhj67qBCTrOsul3EVSlh0+FfWH1va6ETir//XSj9cBfjeJdy9wBm3EwevFpdfDXtfjn+bGKIwAtOreSeCQ/huth80AjqONcNgENLXhsjoD3wPn0F5EIZW5rPrx2WhfaUb97/TyuK8VsLy2eG/DgGN62CJueNawyL0tSDswFhirbwtgsR5+FAgrz3IX9VMuRxQKhUJRIqpKU5VCoVAoyghlOBQKhUJRIpThUCgUCkWJUIZDoVAoFCVCGQ6FQqFQlAhlOGwIIYRBaN47jwshDgshJggh7PSwMCHEh0WkDRJCPFJ+am87/zghxEkhxFcWPs9LQojqJvtpRcWvCFQGjUVRHvdWv69PlCC+kxBiqz55UVFC1HBcG0IIkSaldNW3/YCvge1SymlmpO0JvCKlvM+iIgs//ym0seUXbjnuIDVfSGV1ngi08fBx+n7+NauomKOxrK9TWSCEsJdSGgq7t2V4HgfgANCuJNdACDENOCeltOjHik1S1pOU1M96P273YBoCxKNNJOoJ/Kof78GNyXoHATdgF5qjukPAy0AQmov0A/rvbj1tT2Az8D/gFPAVNz5A7gJ2oE2U2qPnaw+8jzbb9QjwTAG6lwDZaJOcXgamo7kwWY9m/OqjTWY6ov+tp6dbCXyMNikrXC/Xp2iTEVcWcJ5xJufZlHfNgHd1zbvQnMQB+AJrdN17gS4F5DcS+AnNl9EF4AVggn5Nd3Fj0loDYB2wX7+mTUuiX9c4V78PGwFf/fhm4D1gC/AfNAeTu/Xz/2VSlul6vpv184wzyfsx/V4dQvPGal9AOWcCJ/TrP8dE+4O3Pntoz8cm/b6dKODedkB7Rg7qf5vo6eyBOXq8I8CL+vH2evn2o3l09S9A3z23XK/NwDxgq34t7wJ+QJsU945JvNaYTCZUvxK8a6wtQP3K8GbeYjj0Y4lALW42HL/kvQgBVzSfZfnh+vHqgLO+3QjYp2/3RDMwAWhNnTuBrmj+c8KBu/R47nq+TwNT9WPVgH1AcAE6IwAffXu6/qJwMdE7Qt9+CvhJ314JrEYzjEOAFCBU17UfaFPUefR9Cdyvb8820fo10FXfrgecLCCvkWgzp93QDE0yN2b9zgNe0rc3Ao307Y5o7jnM1q9rfFTffgPdxTfaC/IjEz2e3DDio4G5Jtdzh379fdA+JhyBZvq1ddTjfQQ8cUsZvdBmGuflW9NEe2GGI930Ht9yb90BB327L7BG334WzVA7mJzXUdedZyj/DXxawH14E93QmFyXvHUoxqP5XvLXyx8JeOth9kCstf9vK+NPte/ZPgV5v9wOfKC3Of8gpYwUty/65QgsEkK0AQxAY5OwPVLKSAAhxCG02kkyEC2l3AsgpUzRw+8BWgkhHtTTeqAZouKaLdZKKTP07c7Av/TtL9Be8Hn8IqWUQoijwDUp5VH9vMd1XYeKOU828Ku+vR/op2/3BZqbXBd3IYSblDL1lvSb9GOpQohktBcxaF/OrYQQrsDdwPcmeVUroX4j8K0e/0u0r+c8vjXZDgC+1X0rOXHzNf5NSpkFZAkhYtA+JvqgfdHv1bW5cLszwRQgE1guhPjN5FoVxR5ZeLOUB7BKCNEIzSA66sf7oi0MlQsgpUwQQrQEWgIbdH32QHQBefpzu/+oPN9NR4HjUnc1LoQIR3P2Fy+1ZrTsQu6rogiU4bBhhBAhaC/9GLSvSwCklDP1l8C9wC4hREFeSl8GrqFV5+3QXh55ZJlsG9CeI0HB7pgF2tfgnyWUn15EmOl58rQYb9FlxLznO0fqn5/cKAtoZe5sYrwK49Zzmupx0PNJklK2KSZ9SfSblt/0Oi0EPpBSrtX7rKYXotP0nq2SUk4u5DxIKXOFEB3QjMxDaM1xvYFc9ME1unM8p0I03crbaMZ2mNCWm92sHy/o+RFoL/3OReQHkIHmO8sUc69rNW5+thVmoEZV2ShCCF+09uVFJi/GvLAGUsqjUspZaE1HTYFUtCaXPDzQahBG4HG0r72iOAXUEULcpZ/DTe+0/BN4VgjhqB9vLISoUcLi7EB7aQE8CvxTwvSm3FrOwliP9pIEQK95lRi95nVBCPF/ej5CCNG6hNnYoXmgBXiEwsvvAVzRt0eYke9G4EF9IEXeetX1TSPoNSYPKeXvaN6P2+hBEWi1FdCa2RwxD1ONI02OrwfG5o1yEkLkNZH5CiE668cchRAtCsjzJNDQzPPnI4TwRmuqyilp2qqOMhy2hUvecFy0ztH1aO2/t/KSEOKYEOIw2tfaH2gdkrn6MN6X0dq7RwghdqE1UxX1FYmUMhutDXqhnu8GtK/A5WidpAeEEMfQOmBLWtMdBzwphDiCZsTGlzC9KcuAP4QQm8w4Z5jQVn07gea1tLQ8CozSr8txtBdtSUgHWggh9qN97b9VSLzpaE1i29CWci0SKeUJYCqwXr+2G9CafUxxA37Vw7eg1URBW5eihxBiD1q/TZHPhwmzgRlCiO3c/DGyHLgEHNGv0yP6M/UgMEs/dgit2e9W/gC6m3l+U3oBv5ciXZVHDcdVKBSVHiHEj8BrUsqzJUjzA9o63Kctp8w2UTUOhUJhC0zi9tpSoQhtAaSflNEoHarGoVAoFIoSoWocCoVCoSgRynAoFAqFokQow6FQKBSKEqEMh0KhUChKhDIcCoVCoSgR/w83eR4Ru1wPyAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import newton\n", "#DATA\n", "#Solution\n", "c0=0.2 #% massique\n", "D=7.e-10 #m2/s\n", "ro=1200 #kg m-3\n", "mu=0.001 #Pa.s\n", "#membrane\n", "d_H=6e-3 #m\n", "L=1.2 #m\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", "cm=np.zeros(len(u)*len(J))\n", "Sc=mu/(ro*D)\n", "\n", "for i in range(len(u)):\n", " Re[i]=ro*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 ('The boundary layer thickness is ', round(deltal[i]*1e6, 1),'micrometers for a tangential velocity of ', u[i],'m/s' )\n", " for j in range(len(J)):\n", " Pe[i+len(u)*j]=J[j]*deltal[i]/D\n", " cm[i+len(u)*j]=c0*np.exp(Pe[i+len(u)*j])\n", "print() \n", "print (' J \\ u | ', round(u[0],3),' ', round(u[1],3))\n", "print ('------------------------------------------------------------------------------')\n", "print (' | Pe= ', round(Pe[0],3), ' ', round(Pe[1],3))\n", "print (' ', \"%.2e\"%J[0],' | ')\n", "print (' | cm= ', round(cm[0],3), ' ', round(cm[1],3))\n", "print ('------------------------------------------------------------------------------')\n", "print (' | Pe= ', round(Pe[2],3), ' ', round(Pe[3],3))\n", "print (' ', \"%.2e\"%J[1],' | ')\n", "print (' | cm= ', round(cm[2],3), ' ', round(cm[3],3))\n", "\n", "#Tracé du profil de concentration près de la membrane\n", "x0=np.linspace(-deltal[0],0,100)\n", "x1=np.linspace(-deltal[1],0,100)\n", "c_0=c0*np.exp(Pe[0]*(1+x0/deltal[0]))\n", "c_1=c0*np.exp(Pe[1]*(1+x1/deltal[1]))\n", "c_2=c0*np.exp(Pe[2]*(1+x0/deltal[0]))\n", "c_3=c0*np.exp(Pe[3]*(1+x1/deltal[1]))\n", "plt.plot(x0,c_0, label='u=0.05 m/s J=1 um/s') \n", "plt.plot(x1,c_1, label='u=0.1 m/s J=1 um/s')\n", "plt.plot(x0,c_2, label='u=0.05 m/s J=2 um/s')\n", "plt.plot(x1,c_3, label='u=0.1 m/s J=2 um/s')\n", "plt.legend(loc='upper center')\n", "plt.title('Evolution of the concentration at the membrane')\n", "plt.xlabel('Distance from the membrane surface (m)')\n", "plt.ylabel('Fruit juice concentration in mass %')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">It can be seen that increasing the permeation flux results in greater accumulation at the membrane. On the other hand, increasing the tangential velocity reduces accumulation at the membrane. This velocity is known as the tangential sweep velocity, as it reduces accumulation at the membrane: the thickness of the boundary layer is smaller, which favors material transfer by diffusion into the solution. It should be noted, however, that increasing tangential velocity requires energy, so a compromise must be found." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solvent flux through the membrane is directly related to the concentration at the filter surface by the following relationship : \t\t\t \n", "$$J=\\frac{\\Delta P-\\Delta\\Pi}{\\mu R_m}$$\n", "where\n", "- $\\Delta P$ is the pression difference through the membrane (transmembrane pressure)\n", "- $\\Delta\\Pi$ is the osmotic pressure difference through the membrane $\\Pi(c_m)-\\Pi(c_p)=\\Pi(c_m)$ if the membrane does not let the solute pass\n", "- $R_m$ is the hydraulic resistance of the membrane = 1.10+14 m-1\n", "\n", "**2. Using the above relationships, how can you calculate the membrane concentration and permeation flux for a given pressure difference?**\n", "\n", "> The mass transfer analysis allow to link the concentration at the membrane, $c_m$ to the operating conditions, Pe :\n", "$$c_m=c_b e^{Pe}$$\n", ">The analysis of the momemtum transfer (fluid mechanic) allow to predict the effet of the concentration at the membrane, $c_m$, on the permeate flux, $J$, via the counter osmotic pressure, $\\Pi(c_m)$) with a modified Darcy law :\n", "$$J=\\frac{\\Delta P-\\Pi(c_m)}{\\mu R_m}$$\n", ">We therefore have a system of two equations with two unknowns. If the trans-membrane pressure is fixed, the unknowns are the permeation flux and the membrane concentration. If the flux through the membrane is known, the unknowns are the trans-membrane pressure and the membrane concentration. There is no analytical solution for these equations, as the system is non-linear. However, it is possible to combine the two equations to obtain a single-unknown equation, for example, as a function of $c_m$ :\n", "$$\\frac{D}{\\delta}ln(\\frac{c_m}{c_0})-\\frac{\\Delta P-10^{+5}\\frac{133.75c_m}{100-c_m}}{\\mu R_m}=0$$\n", "\n", "\n", "**3. Realise this calculus for pressure of 2, 5 and 10 bars and for tangential velocities of 0.05 m/s and 0.1 m/s.**\n", "\n", ">The code allows to solve the system of equation as follows :\n", "1. function for the osmotic pressure calculation\n", "2. definition of the function to solve to determine cm\n", "3. main program with loops to calculate cm for differents values of boundary layers and pressure. Values of $c_m$ and $J$ are save in an array.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "u(m/s) delta(m) PTM(Pa) cm(%) J(m/s) \n", "0.05 2.57e-04 0.0 0.183 -2.45e-07\n", "0.05 2.57e-04 200000.0 0.35 1.53e-06\n", "0.05 2.57e-04 400000.0 0.634 3.15e-06\n", "0.05 2.57e-04 600000.0 1.065 4.56e-06\n", "0.05 2.57e-04 800000.0 1.651 5.76e-06\n", "0.05 2.57e-04 1000000.0 2.374 6.75e-06\n", "0.05 2.57e-04 1200000.0 3.208 7.57e-06\n", "0.05 2.57e-04 1400000.0 4.121 8.25e-06\n", "0.05 2.57e-04 1600000.0 5.09 8.83e-06\n", "0.05 2.57e-04 1800000.0 6.095 9.32e-06\n", "0.05 2.57e-04 2000000.0 7.123 9.74e-06\n", "0.1 2.04e-04 0.0 0.186 -2.49e-07\n", "0.1 2.04e-04 200000.0 0.317 1.58e-06\n", "0.1 2.04e-04 400000.0 0.523 3.30e-06\n", "0.1 2.04e-04 600000.0 0.83 4.88e-06\n", "0.1 2.04e-04 800000.0 1.256 6.30e-06\n", "0.1 2.04e-04 1000000.0 1.805 7.54e-06\n", "0.1 2.04e-04 1200000.0 2.469 8.61e-06\n", "0.1 2.04e-04 1400000.0 3.23 9.54e-06\n", "0.1 2.04e-04 1600000.0 4.069 1.03e-05\n", "0.1 2.04e-04 1800000.0 4.966 1.10e-05\n", "0.1 2.04e-04 2000000.0 5.906 1.16e-05\n" ] } ], "source": [ "Rm=1e14\n", "#Fonction pour le calcul de la pression osmotique en Pa\n", "def PI(c):\n", " PI=1.e5*(133.75*c/(100.-c))\n", " return PI\n", "#Foncion à résoudre pour déterminer la concentration à la membrane\n", "def f(cm):\n", " f=(D/delta)*np.log(cm/c0)-(DP-PI(cm))/(mu*Rm)\n", " return f\n", "#creation des tableaux de valeurs\n", "DPl=np.linspace(0,20.e5,21)\n", "cm=np.zeros(len(deltal)*len(DPl))\n", "J=np.zeros(len(deltal)*len(DPl))\n", "print ('u(m/s) delta(m) PTM(Pa) cm(%) J(m/s) ')\n", "for i in range(len(deltal)):\n", " for j in range(len(DPl)):\n", " delta=deltal[i]\n", " DP=DPl[j]\n", " cm[j+len(DPl)*i]=newton(f,c0)\n", " J[j+len(DPl)*i]=(D/delta)*np.log(cm[j+len(DPl)*i]/c0) \n", " if j%2 ==0:\n", " print (u[i],' ', \"%.2e\"%delta,' ', DP,' ',round(cm[j+len(DPl)*i],3),' ', \"%.2e\"%J[j+len(DPl)*i]) \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**4. Plot permeation flux versus pressure difference for both speeds and conclude.**" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Tracé de la concentration à la membrane\n", "plt.plot(DPl/1e5,cm[:j+1], label='u=0.05 m/s') \n", "plt.plot(DPl/1e5,cm[j+1:], label='u=0.1 m/s') \n", "plt.legend(loc='upper center')\n", "#plt.title('Evolution de la concentration au voisinage de la membrane en fonction de pression trans-membranaire')\n", "plt.xlabel('Transmembrane pressure (bar)')\n", "plt.ylabel('Fruit juice concentration at the membrane (w%)')\n", "plt.show() \n", " \n", "#Tracé du flux de perméation\n", "plt.plot(DPl/1e5,J[:j+1], label='u=0.05 m/s') \n", "plt.plot(DPl/1e5,J[j+1:], label='u=0.1 m/s')\n", "plt.plot(DPl/1e5,DPl/(mu*Rm), 'r--', label='pure water')\n", "plt.legend(loc='upper center')\n", "#plt.title('Evolution du flux de perméation en fonction de pression trans-membranaire')\n", "plt.xlabel('Transmembrane pressure (bar)')\n", "plt.ylabel('Permeate flux (m/s)')\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">Note that **increasing pressure** always leads to an increase in permeation flux. However, this increase becomes less significant at higher pressures, as the increase in membrane concentration generates an osmotic counter-pressure which limits permeation. At pressures below the osmotic pressure of the dispersion, permeation fluxes are negative: this is a regime of osmosis, and permeation flux is directed towards higher concentrations (i.e. from the permeate to the concentrate). At higher pressures, the fluid is forced to flow from the concentrate to the filtrate: this is the reverse osmosis regime. All you have to do is modify the membrane properties, $R_m$, and the variation in osmotic pressure, $\\Pi$, as a function of concentration (the osmotic pressure of salts will be very high: seawater has an osmotic pressure of 25 bar). We will therefore also need to examine higher pressure ranges (>25 bar) to describe reverse osmosis. \n", ">\n", "> We note that the **increase in tangential velocity** leads to a reduction in membrane concentration (effect of tangential scavenging, which reduces the thickness of the boundary layer) and thus increases permeation flux (osmotic back pressure is lower)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 2 }