 Bidisperse gravity-current deposition

ID: bidisperse-gravity-current-deposition

c_{i}

and downward settling velocity magnitudes

v_{i}

satisfy

c_{i} (x) = c_{i 0} e^{- v_{i} x / q}

v_{i} c_{i}

. The local deposited particle-volume fraction belonging to species one is

f_{1} (x) = \frac{v _{1} c _{10} e ^{- v_{1} x / q}}{v _{1} c _{10} e ^{- v_{1} x / q} + v _{2} c _{20} e ^{- v_{2} x / q}} .

For

v_{1} > v_{2} > 0

f_{1}

decreases strictly downstream, since

f_{1}^{'} = (v_{2} - v_{1}) f_{1} (1 - f_{1}) / q

. If

g_{i}^{'} = g_{0 i} c_{i}

, use

c_{i} = g_{i}^{'} / g_{0 i}

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_{i 0} (1 - e^{- v_{i} x / q})

 New to topics? Read the docs here!