More rigorous, solving droplet motion and gas energy loss simultaneously. Often used for high-velocity designs (>100 m/s). 3.2 Collection Efficiency Models 3.2.1 Johnstone–Roberts Model (1940s) Single-droplet efficiency ( \eta_d ) for inertial impaction: [ \eta_d = \fracKK + 0.7 ] Where ( K = ) inertial parameter = ( \fracC_c \rho_p d_p^2 v_rel18 \mu_g d_d ), ( C_c ) = Cunningham correction factor (for submicron particles), ( d_p ) = particle diameter, ( d_d ) = droplet diameter, ( \mu_g ) = gas viscosity, ( \rho_p ) = particle density.
Overall efficiency ( \eta_total = 1 - \exp\left( -\frac6 Q_l \eta_d xQ_g d_d \right) ), where ( x ) = throat length, ( Q_l ) = liquid flow rate, ( Q_g ) = gas flow rate. venturi scrubber design
Accounts for droplet acceleration: [ \Delta P = \frac12 \rho_g v_t^2 \left(1 - \fracA_t^2A_e^2\right) + \fracLG \rho_g v_t^2 \left(1 - \fracv_dv_t\right)^2 ] Where ( v_d ) = droplet velocity at throat exit, requiring iterative solution. More rigorous, solving droplet motion and gas energy
The most widely used correlation: [ \Delta P = \frac\rho_g v_t^22 \cdot \left[ 1 - \left( \fracA_tA_e \right)^2 \right] + f \cdot \fracLG \cdot \rho_g v_t^2 ] Where ( v_t ) = throat velocity, ( L/G ) = liquid-to-gas ratio (L/m³ or kg/kg), ( \rho_g ) = gas density, ( A_t/A_e ) = throat-to-exit area ratio, and ( f ) = empirical friction factor (≈ 0.2–0.5). The first term is gas acceleration loss; the second term is due to droplet friction. Overall efficiency ( \eta_total = 1 - \exp\left(
More refined, defines penetration ( P_t = 1 - \eta ): [ P_t = \exp\left( -\frac2 \rho_l Q_l \eta_d L_td_d \rho_g Q_g \right) ] Where ( L_t ) = throat length, ( \rho_l ) = liquid density. This model explicitly includes droplet size prediction via Nukiyama–Tanasawa or Boll’s droplet diameter correlation: [ d_d = \frac0.5 \sigma\rho_g v_t^2 + 0.15 \left( \fracQ_lQ_g \right)^1.5 ] (σ = surface tension).