Thermo. Velocity v_T—
Gradient |∇T|—
Conc. ratio c_C/c_H—
Soret equilibrium—
Thermophoretic velocity:
v_T = -D·S_T·∇T
Steady-state conc.:
c(x) = c₀ exp(-S_T·ΔT·x/L)
Flux balance:
J = -D(∇c + S_T·c·∇T) = 0
⟹ ∇ln c = -S_T∇T
v_T = -D·S_T·∇T
Steady-state conc.:
c(x) = c₀ exp(-S_T·ΔT·x/L)
Flux balance:
J = -D(∇c + S_T·c·∇T) = 0
⟹ ∇ln c = -S_T∇T
Particles drift along (S_T>0: toward cold) or against (S_T<0: toward hot) temperature gradients. At steady state, Brownian diffusion balances thermophoretic drift.