Bidisperse gravity-current deposition ($f_1(x)$)

In a bidisperse particle suspension transported by a steady depositing gravity current, species with concentrations $c_i$ and downward settling velocity magnitudes $v_i$ satisfy $c_i(x)=c_{i0}{e}^{-v_{i}x/q}$. Their local particle deposition fluxes are $v_i{c}_i$. The local deposited particle-volume fraction belonging to species one isFor $v_1>v_2>0$ and both species present, $f_1$ decreases strictly downstream, since $f_1^{\prime }=(v_2-v_1)f_1(1-f_1)/q$. If $g_i^{\prime }=g_{0i}{c}_i$, use $c_i=g_i^{\prime }/g_{0i}$ rather than buoyancy ratios unless $g_{01}=g_{02}$. A number fraction additionally divides each species volume flux by its single-particle volume. Integrating deposition over $[0,x]$ instead gives cumulative weights $q{c}_{i0}(1-e^{-v_{i}x/q})$.