Particle-resolved direct numerical simulations on particle–fluid density ratio effects in liquid–solid suspensions

Particle-resolved direct numerical simulations are employed to investigate homogeneous steady liquid–solid suspensions over an extended range of particle–fluid density ratios ( 0.05 less than or slanted equals rho Superscript asterisk Baseline less than or slanted equals 5.5 0.05 ⩽ ρ ∗ ⩽ 5.5 $0.05\leqslant \rho ^\ast \leqslant 5.5$ ). This parameter span, which includes floating ( rho Superscript asterisk Baseline less than 1 ρ ∗ < 1 $\rho ^\ast \lt 1$ ), nearly neutrally buoyant ( rho Superscript asterisk Baseline almost equals 1 ρ ∗ ≈ 1 $\rho ^\ast \approx 1$ ) and settling ( rho Superscript asterisk Baseline greater than 1 ρ ∗ > 1 $\rho ^\ast \gt 1$ ) regimes, enables a systematic assessment of deviations from kinetic theory for granular flows (KTGF). We show that the Richardson–Zaki correlation for the mean relative velocity requires modification: the exponent depends on log rho Superscript asterisk log ⁡ ρ ∗ $\log \rho ^\ast$ at low Reynolds number, while the scaling law between the prefactor and an effective density ratio left parenthesis rho Superscript asterisk Baseline plus upper C Subscript m Baseline right parenthesis ( ρ ∗ + C m ) $(\rho ^\ast +C_m)$ , implicating the virtual mass force. Analysis of particle velocity fluctuations reveals a granular temperature that departs markedly from both algebraic models and KTGF predictions, exhibiting complex coupling with rho Superscript asterisk ρ ∗ $\rho ^\ast$