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Flow of Newtonian and Non-Newtonian Fluids Through Packed Beds: An Experimental Study

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The phenomena of flow reduction and flow enhancement was observed in case of viscoelastic and viscoinelastic fluids flowing through packed beds, respectively. In this study, the pressure drop-flow rate behaviors for the flow of Newtonian (water), non-Newtonian viscoinelastic (Carboxy methyl cellulose solution in water, CMC) and viscoelastic (Polyacrylamide solution in water, PAA) fluids have been experimentally studied and pressure drop behavior compared with existing models for viscoinelastic and viscoelastic fluids. Based on the observed data, an appropriate empirical correlation for pressure drop prediction in case of non-Newtonian fluid flowing through packed bed has been proposed. The correlation predicts the data well to within a reasonable accuracy.

$${f}_{\rm mod}=\frac{150}{{\rm Re}} (1+3.23 \times 10^{6}{\rm We}^{4.7})\left({\frac{{3n}+1}{{4n}}}\right)^{-9n}$$

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C :

Concentration, g/dl


Carboxymethyl cellulose solution

D :

Capillary diameter, m

D c :

Column diameter, m

D e :

Bed equivalent diameter

D p :

Diameter of the particle, m

D H :

Hydraulic diameter, (D H = 4R H), m



ΔP :

Pressure drop, N/m2

f :

Friction factor

f mod :

Modified friction factor

G :

Mass velocity, kg m−2s−1

k :

Bed permeability, Eq. 1, m2

K :

Consistency index, Pa sn, Eq.

K 1 :

Power law constant, Pa sm

k 1 :

Coefficient of the viscous energy term, Eq. 2

k 2 :

Coefficient of the kinetic energy term, Eq. 2

L :

Height of the packed bed, m


Mean relative quadratic error, Eq. 5

m :

Power law flow behaviour index

N 1 :

Primary normal stress difference, Pa

n :

Power law flow behaviour index


Polyacrylamide solution in water

Q :

Volumetric flow rate, m3/s

R :

Column radius, m


Reynolds number (as defined for different models)

Remod :

Modified Reynolds number (as defined for different models)

R H :

Hydraulic radius, \({(= {D}-_{\rm p}\varepsilon/6\alpha (1-\varepsilon))}\), m

t :

Time, s

T :

Temperature,° C

U o :

Superficial velocity, m/s


Wessinberg number, \({\frac{\lambda U_{\rm o}}{\varepsilon D_{\rm p}}}\)

α :

Wall correction factor \((= {1+2{D}_{\rm p}/ (3{D}_{\rm c}(1-\varepsilon)))}\)

\({\varepsilon}\) :

Fractional void volume

λ :

Fluid relaxation time, \({\frac{N_1}{2\tau \dot {\gamma}}}\),s

\({\phi_{\rm s}}\) :

Sphericity of the bed packing

\({\dot {\gamma}}\) :

Shear rate, (= 8U o/ D H), s−1

μ :

Viscosity of Newtonian fluid, Pa s

μ :

Infinite shear viscosity, Pa s

μ a :

Apparent viscosity of non-Newtonian fluid, \({\left( {={K}\dot {\gamma}^{n-1}}\right)}\), Pa s

ρ f :

Density of the test fluid, kg/m3

τ :

Shear stress, Pa


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Correspondence to R. K. Wanchoo.

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Kaur, N., Singh, R. & Wanchoo, R.K. Flow of Newtonian and Non-Newtonian Fluids Through Packed Beds: An Experimental Study. Transp Porous Med 90, 655 (2011).

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  • Packed bed
  • Flow
  • Viscoinelastic
  • Viscoelastic
  • Pressure drop