Abstract
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 dropflow rate behaviors for the flow of Newtonian (water), nonNewtonian 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 nonNewtonian fluid flowing through packed bed has been proposed. The correlation predicts the data well to within a reasonable accuracy.
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Abbreviations
 C :

Concentration, g/dl
 CMC:

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
 Eq.:

Equation
 ΔP :

Pressure drop, N/m^{2}
 f :

Friction factor
 f _{mod} :

Modified friction factor
 G :

Mass velocity, kg m^{−2}s^{−1}
 k :

Bed permeability, Eq. 1, m^{2}
 K :

Consistency index, Pa s^{n}, Eq.
 K _{1} :

Power law constant, Pa s^{m}
 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
 M.R.Q.E:

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
 PAA:

Polyacrylamide solution in water
 Q :

Volumetric flow rate, m^{3}/s
 R :

Column radius, m
 Re:

Reynolds number (as defined for different models)
 Re_{mod} :

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
 We:

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 nonNewtonian fluid, \({\left( {={K}\dot {\gamma}^{n1}}\right)}\), Pa s
 ρ _{f} :

Density of the test fluid, kg/m^{3}
 τ :

Shear stress, Pa
References
AbdelKhalik S.I., Hassager O., Bird R.B.: Prediction of melt elasticity from viscosity data. Poly. Eng. Sci. 14, 859–867 (1974)
Al Fariss T.: Flow of polymer solution through porous media. Ind. Eng. Chem. Res. 29, 2150–2151 (1990)
Bird R.B., Steward W.E., Lightfoot E.N.: Transport Phenomena. Wiley, New York (1960)
Blake F.C.: The resistance of packing to fluid flow. Trans. Am. Inst. Chem. Eng. 14, 415–421 (1922)
Burke S.P., Plummer W.B.: Gas flow through packed columns. Ind. Eng. Chem. 20, 1196–1200 (1928)
Christopher R.H., Middleman S.: Powerlaw flow through a packed tube. Ind. Eng. Chem. Fundam. 4, 422–426 (1965)
ElKaisy M.M., Momsy G.M.: A theoretical study of pressure drop and transport in packed bed at intermediate Reynolds number. Ind. Eng. Chem. Fundam. 12, 82–90 (1973)
Ergun S.: Fluid flow through randomly packed column and fluidized beds. Ind. Eng. Chem. 41, 1179–1184 (1949)
Ergun S.: Fluid flow through packed column. Chem. Eng. Prog. 48, 89–94 (1952)
Gaitonde N.Y., Middleman S.: Viscoelastic fluids throught porous media. Ind. Eng. Chem. Fundam. 6, 145–147 (1967)
Hayes R.E., Afacan A., Boulanger B., Shenoy. A.V.: Modelling the power law fluids in a packed bed using a volumeaveraged equation of motion. Transp. Porous Med. 23, 175–196 (1996)
Jones W.M., Maddock J.L.: Onset of instabilities and reductions of drag in the flow of relaxing liquids through tubes and porous beds. Nature (Lond) 212, 388 (1966)
Kemblowski K., Michneiwicz M.: A new look at the laminar flow of power law fluids through granular beds. Rheol. Acta 18, 730–739 (1979)
Kumar S., Upadhyay S.N.: Mass and momentum transfer to Newtonian and nonNewtonian fluids in fixed and fluidized beds. Ind. Eng. Chem. Fundam. 20, 186–195 (1981)
Nagrarajan R., Davies G.S., Venkateshwarlu D.: Flow of polymer solutions through packed beds. Indian Chem. Eng. 19, 10–15 (1977)
Rao P.T., Chhabra R.P.: Viscous nonNewtonian flow in packed beds: effects of column walls and particle size distribution. Powder Technol. 77, 171–176 (1993)
Savins J.G.: NonNewtonian flow through porous media. Ind. Eng. Chem. 61, 18–69 (1969)
Tiu C., Zhu J.Z.Q., Nicolae G., Fang T.N., Chhabra Raj P.: Flow of viscoelastic polymer solutions in mixed beds of particles. Can. J. Chem. Eng. 75, 843–850 (1997)
Wagner M.H.: Prediction of primary normal stress difference from shear viscosity data using single integral constitutive equation. Rheol. Acta 14, 43–50 (1977)
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Kaur, N., Singh, R. & Wanchoo, R.K. Flow of Newtonian and NonNewtonian Fluids Through Packed Beds: An Experimental Study. Transp Porous Med 90, 655 (2011). https://doi.org/10.1007/s1124201198088
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Keywords
 Packed bed
 Flow
 Viscoinelastic
 Viscoelastic
 Pressure drop