Aerosol-Diffusion.ipynb

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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import useful packages\n",
    "import numpy as np\n",
    "from time import sleep\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display\n",
    "from bokeh.io import show, output_notebook, push_notebook\n",
    "from bokeh.models import LinearColorMapper, ColorBar\n",
    "from bokeh.palettes import Spectral10\n",
    "import matplotlib as mpl\n",
    "from bokeh.plotting import figure \n",
    "output_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "This notebook simulates diffusion of microscopic particles (by solving the Langevin equation). You can interact with the simulation using the various sliders that will appear after you run the last cell. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defines a class for the Langevin simulation\n",
    "class Langevin2D:\n",
    "    \n",
    "    # Initializing variables\n",
    "    def __init__(self, particle_size, mass_density_of_particle, \n",
    "                 fluid_viscosity, temperature, initial_velocity):\n",
    "        self.numparts = 50\n",
    "        self.meanrad = particle_size * 0.5 * 1e-6\n",
    "        self.dt = 5e-3\n",
    "        self.boxsize = np.array([2.2, 1.2])\n",
    "        self.center = self.boxsize / 2\n",
    "        self.partden = mass_density_of_particle\n",
    "        self.flvisc = fluid_viscosity * 1e-5\n",
    "        self.initvel = initial_velocity\n",
    "        self.temp = temperature\n",
    "        self.calc_params()\n",
    "        self.reset()\n",
    "        \n",
    "    # Reseting positions and velocities to zero\n",
    "    def reset(self):\n",
    "        self.x = np.ones([self.numparts, 2]) * np.array([0, 1])\n",
    "        self.p = np.zeros([self.numparts, 2]) \n",
    "        self.pmid = np.zeros([self.numparts, 2])\n",
    "        \n",
    "    # Calculating useful parameters used in solving the Langevin equation\n",
    "    def calc_params(self):\n",
    "        self.partrad = np.random.exponential(self.meanrad, self.numparts)\n",
    "        self.partmass = self.partden * 1.333 * np.pi * self.partrad**3\n",
    "        self.stokes = 6.0 * np.pi * self.flvisc * self.partrad\n",
    "        self.gamma = self.stokes / self.partmass\n",
    "        self.gravity = self.partmass * 9.81\n",
    "        self.c1 = np.exp(-self.gamma * self.dt)\n",
    "        self.c2 = np.sqrt(kb * self.temp * (1 - self.c1**2))\n",
    "        \n",
    "    # Run the Langevin update\n",
    "    def run(self):\n",
    "        for n in range(self.numparts): \n",
    "            self.pmid[n, :] = self.p[n, :] + np.array([0, -self.dt * self.gravity[n] * 0.5])\n",
    "            self.x[n, :] = self.x[n, :] + self.dt * (self.pmid[n, :] / 2 / self.partmass[n] + [self.initvel, 0])\n",
    "            self.pmid[n, :] = (self.c1[n] * self.pmid[n, :] + self.c2[n] * \n",
    "                               np.random.randn(2) * np.sqrt(self.partmass[n]))\n",
    "            self.x[n, :] = self.x[n, :] + self.dt * (self.pmid[n, :] / 2 / self.partmass[n] + [self.initvel, 0])\n",
    "            self.p[n, :] = self.pmid[n, :] + np.array([0, -self.dt * self.gravity[n] * 0.5])\n",
    "#             self.check_boundary(n)\n",
    "    \n",
    "    # Apply sticky boundary conditions \n",
    "    def check_boundary(self, n):\n",
    "        # Applying sticky boundaries\n",
    "        for i in range(2):\n",
    "            if self.x[n, i] <  0: \n",
    "                self.x[n, i] = 0\n",
    "            if self.x[n, i] >=  self.boxsize[i]:\n",
    "                self.x[n, i] = self.boxsize[i]"
   ]
  },
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   "execution_count": 3,
   "metadata": {},
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   "source": [
    "kb = 1.380e-23  # Boltzmann constant\n",
    "\n",
    "# Start the Langevin simulation\n",
    "def start_Langevin_sim(particle_size=10e-6, mass_density_of_particle=1000.0, \n",
    "                       fluid_viscosity=9e-4, temperature=300, initial_velocity=1):\n",
    "    \n",
    "    # Update arrays for plotting\n",
    "    def plot_trajectories():\n",
    "        r1.data_source.data['x'] = l2d.x[:, 0]\n",
    "        r1.data_source.data['y'] = l2d.x[:, 1]\n",
    "        push_notebook(handle=target)\n",
    "    \n",
    "    # Create langevin class object\n",
    "    l2d = Langevin2D(particle_size, mass_density_of_particle, fluid_viscosity, temperature, initial_velocity)\n",
    "    # Initialize figure for plotting trajectories\n",
    "    p1 = figure(plot_width=800, plot_height=500, tools='',\n",
    "                x_range=(-0.1, l2d.boxsize[0]), \n",
    "                y_range=(0, l2d.boxsize[1]))\n",
    "    p1.xaxis.axis_label = 'x (m)'\n",
    "    p1.yaxis.axis_label = 'y (m)'\n",
    "    p1.toolbar.logo = None\n",
    "    runtime = 0.25 \n",
    "    \n",
    "    # Hack for getting colors dependent on particle size\n",
    "    colors = [\"#%02x%02x%02x\" % (int(b), int(g), int(r)) \n",
    "              for r, g, b, _ in 255*mpl.cm.Spectral(mpl.colors.Normalize()(l2d.partrad))]\n",
    "    color_mapper = LinearColorMapper(palette=\"Spectral10\", low=min(l2d.partrad*1e6), high=max(l2d.partrad*1e6))\n",
    "    color_bar = ColorBar(color_mapper=color_mapper, label_standoff=12, border_line_color=None, location=(0,0))\n",
    "    \n",
    "    r1 = p1.scatter(l2d.x[:, 0], l2d.x[:, 1], radius=0.01, fill_color=colors, \n",
    "                    fill_alpha=0.4, line_color=colors)\n",
    "    p1.add_layout(color_bar, 'right')\n",
    "    target = show(p1, notebook_handle=True)\n",
    "    # Langevin time-steping loop\n",
    "    for t in range(int(runtime/l2d.dt)):\n",
    "        sleep(0.2)\n",
    "        for n in range(l2d.numparts):\n",
    "            l2d.run()\n",
    "            plot_trajectories()"
   ]
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   "source": [
    "# Interactive controls\n",
    "style = {'description_width': 'initial'}    \n",
    "particle_size = widgets.FloatSlider(description='Mean particle diameter (um)', \n",
    "                                    style=style, min=0.05, max=5,\n",
    "                                    step=0.2, value=0.5, continuous_update=False)\n",
    "mass_density_of_particle = widgets.IntSlider(description='Particle mass density (kg/m^3)', \n",
    "                                              style=style, min=500, max=2000, \n",
    "                                              step=100, value=1000, continuous_update=False)\n",
    "fluid_viscosity = widgets.FloatSlider(description='Dynamic viscosity (x10^5 kg/ms)', \n",
    "                                      style=style, min=1.8, max=1.9, \n",
    "                                      step=0.05, value=1.85, continuous_update=False)\n",
    "temperature = widgets.IntSlider(description='Temperature (K)', \n",
    "                                style=style, min=50, max=600, \n",
    "                                step=50, value=300, continuous_update=False)\n",
    "initial_velocity = widgets.FloatSlider(description='Fluid velocity (m/s)', \n",
    "                                       style=style, min=0, max=0.1, \n",
    "                                       step=0.01, value=0.05, continuous_update=False)\n",
    "\n",
    "# Creating the interactive controls ui\n",
    "widget_ui = widgets.VBox([widgets.HBox([particle_size, mass_density_of_particle]), \n",
    "                         widgets.HBox([fluid_viscosity, temperature]), initial_velocity])\n",
    "widget_out = widgets.interactive_output(start_Langevin_sim, \n",
    "                                        {'particle_size': particle_size,\n",
    "                                         'mass_density_of_particle': mass_density_of_particle,\n",
    "                                         'fluid_viscosity': fluid_viscosity,\n",
    "                                         'temperature': temperature,\n",
    "                                         'initial_velocity': initial_velocity})"
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       "model_id": "f273401e00ef4d33a34057cecea2809d",
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      "text/plain": [
       "VBox(children=(HBox(children=(FloatSlider(value=0.5, continuous_update=False, description='Mean particle diame…"
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      "text/plain": [
       "Output()"
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     },
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   ],
   "source": [
    "# Display the controls and output\n",
    "display(widget_ui, widget_out)"
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