Numerical Simulation of Falling Liquid Film Flow on a Vertical Plane by Two-Phase Lattice Boltzmann Method

<table>Velocity directions <svg height="11.4625" id="M22" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 4.7624998 11.4625" width="4.7624998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.2)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
q16 0 76 48z" id="x1D456"></path></g>
</svg> and velocity vectors <svg height="12.3875" id="M23" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 11.5375 12.3875" width="11.5375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.1)"><path d="M403 126l24 -14q-44 -70 -88.5 -98t-109.5 -28q-90 0 -147 67t-57 171q0 112 57 180q58 69 152 69q83 0 128 -50q53 -59 59 -178h-252q6 -81 25 -128q24 -59 94 -59q32 0 58 15.5t57 52.5zM164 282h134v21q0 73 -9 92q-13 26 -24.5 36.5t-30.5 10.5q-37 0 -53.5 -37
t-16.5 -123z" id="x1D41E"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.613,12.188)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
q16 0 76 48z" id="x1D456"></path></g>
</svg> in D2Q9 lattice.</table>

Journal of Engineering

fig1

Figure 1

Figure 1: Numerical Simulation of Falling Liquid Film Flow on a Vertical Plane by Two-Phase Lattice Boltzmann Method 