Table 1 Dimensionless variables Variable... | Emerald Publishing

Table 1

Dimensionless variables

Variable	Description
x* = x/L, y* = y/L, z* = z/L	Dimensionless position with respect to the characteristic length L
t* = t/(L/u₀)	Dimensionless time with respect to the inlet velocity, u₀
u_t = U_t/u₀	Dimensionless total Darcy flux
r = r_p/r₀	Dimensionless average pore radius
A_v = a_v/a₀	Dimensionless interfacial area
κ = K/K₀	Dimensionless permeability
c_f = C_f /C₀, c_s = C_s/C₀	Dimensionless concentrations with respect to the inlet concentration of the acid, C₀
p = (P − P_out)/(u₀L/K₀)	Dimensionless pressure with respect to the constant pressure at boundary, P_out
$h_{T}^{2} = 2 k_{s} r_{0} / D_{m}$	Pore-scale Thiele modulus (reaction rate over diffusion rate) with respect to molecular diffusion D_m
$H_{T}^{2} = k_{s} a_{0} L^{2} / D_{m} = DaPe$	Macroscopic Thiele modulus
Da = k_sa₀L/u₀	Damköhler number
N_ac = αC₀/ρ_s	Acid capacity number
η = 2r₀/L	Ratio of average pore diameter to characteristic length
Sh = 2k_cr_p/D_m	Sherwood number (the ratio of the convective mass transfer to the rate of diffusive mass transport)

Variable	Description
x* = x/L, y* = y/L, z* = z/L	Dimensionless position with respect to the characteristic length L
t* = t/(L/u₀)	Dimensionless time with respect to the inlet velocity, u₀
u_t = U_t/u₀	Dimensionless total Darcy flux
r = r_p/r₀	Dimensionless average pore radius
A_v = a_v/a₀	Dimensionless interfacial area
κ = K/K₀	Dimensionless permeability
c_f = C_f /C₀, c_s = C_s/C₀	Dimensionless concentrations with respect to the inlet concentration of the acid, C₀
p = (P − P_out)/(u₀L/K₀)	Dimensionless pressure with respect to the constant pressure at boundary, P_out
$h_{T}^{2} = 2 k_{s} r_{0} / D_{m}$	Pore-scale Thiele modulus (reaction rate over diffusion rate) with respect to molecular diffusion D_m
$H_{T}^{2} = k_{s} a_{0} L^{2} / D_{m} = DaPe$	Macroscopic Thiele modulus
Da = k_sa₀L/u₀	Damköhler number
N_ac = αC₀/ρ_s	Acid capacity number
η = 2r₀/L	Ratio of average pore diameter to characteristic length
Sh = 2k_cr_p/D_m	Sherwood number (the ratio of the convective mass transfer to the rate of diffusive mass transport)