example_interactive.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "00897fc8-e8d9-4531-b339-ddcf756b0be0",
   "metadata": {},
   "source": [
    "# An interactive evaluation of the Mason-Weaver concentration profile\n",
    "\n",
    "This Notebook enables to conveniently set the nanoparticle solution parameters using physical quantities and units typically used in real-life laboratory situations and directly obtain a concentration profile. At present, we do not provide any interactive sliders with real-time graph redrawing. For now, set the physical quantities defining the systems in Cell #5 and then re-evaluate the Notebook.\n",
    "\n",
    "A very nice HTML5/JavaScript app for plotting the Mason-Weaver concentration profiles has been developed by Steven Abbott:\n",
    "\n",
    "https://www.stevenabbott.co.uk/practical-solubility/Gravitational-Sedimentation.php"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cd1169ed-aca4-472b-bcb3-fffb10b6b5b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import pi\n",
    "from scipy.constants import Boltzmann as k_B\n",
    "from scipy.constants import g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6c15872f-cb4f-4b33-b5e9-fe5840efc0e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d7ccf32d-ab45-4630-8947-f01d6cda1967",
   "metadata": {},
   "outputs": [],
   "source": [
    "from masonweaver_analytic import MW_c_profile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "656538f2-0f8e-4e61-bc22-8f8b52f8c2b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# User-interface unit (UI units)\n",
    "_r_p = 41. # nm\n",
    "_rho_p = 10.41 # g/cc\n",
    "_rho_l = 1.01 # g/cc\n",
    "_eta = 2.2 # cP\n",
    "_h = 2.6 # mm\n",
    "_t = 6 # h\n",
    "_T = 25. # °C\n",
    "_relmax = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d67f051a-0099-436f-874f-ed0f21169b8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# conversion from UI units to SI\n",
    "# Incidentally, this also ensures that all variables are floating point.\n",
    "r_p = _r_p * 1e-9 # m\n",
    "rho_p = _rho_p * 1000. # kg m3\n",
    "rho_l = _rho_l * 1000. # kg m3\n",
    "eta = _eta * 1e-3 # Pa.s\n",
    "h = _h * 1e-3 # m\n",
    "t = _t * 3600. # s\n",
    "T = _T + 273.15 # K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1604f046-b298-4a48-ae3a-6eb809cd1a8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rename variables to be compatible with expression from the PPSC 2017 paper\n",
    "a = r_p\n",
    "z_max = h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2a4aedbd-1b46-40b0-8b78-c9b9456aaec3",
   "metadata": {},
   "outputs": [],
   "source": [
    "D = (k_B*T)/(6*pi*eta*a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d891fee9-a1fb-4fd3-9e66-cd521700ceae",
   "metadata": {},
   "outputs": [],
   "source": [
    "s = 2/9 * (a**2 * (rho_p - rho_l))/eta\n",
    "sg = s*g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "567f80f0-e34d-49d4-ab19-b3f81dc1355d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.4210872227778505e-12 m2 s-1\n",
      "1.5961010101010104e-09 s-1\n",
      "1.5652403970707073e-08 m s-1\n"
     ]
    }
   ],
   "source": [
    "print(D, 'm2 s-1')\n",
    "print(s, 's-1')\n",
    "print(sg, 'm s-1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "97758b7a-c871-49ab-8062-29bc754cba25",
   "metadata": {},
   "outputs": [],
   "source": [
    "solnz, solnc = MW_c_profile(t, z_max, D, sg, Nz = 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "99eac0af-6bfc-4728-84de-5a1031403b0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'rel. height (% of z_max)')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(solnc, solnz/z_max * 100)\n",
    "plt.grid(visible = True)\n",
    "plt.ylim(0,100)\n",
    "plt.xlim(0,_relmax)\n",
    "plt.xlabel('rel. concentration')\n",
    "plt.ylabel('rel. height (% of z_max)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "246a3ded-3a30-4d80-97fb-ad6620456a31",
   "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": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}