# Ohmic Heating of Liquid Whole Egg: Rheological Behaviour and Fluid Dynamics

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## Abstract

Although ohmic heating is used as an alternative heating method for liquid egg products commercially, there is a lack of information on the change of rheological properties and fluid dynamics characteristics of ohmically heated liquid whole egg in the literature. The change of rheological behaviour of the ohmically heated liquid whole egg, across a temperature range of 4–60 °C, was determined by using a concentric rotational viscometer. The ohmic heating was conducted by applying the voltage gradient (20 V/cm) at 50 Hz. The temperature dependency of the electrical conductivity of liquid egg was linear (*R* ^{2} = 0.999). The rheological behaviour was found to be shear thinning since power law model had higher regression coefficient and lower *χ* ^{2} and root mean square error values than Newtonian model. Ohmically heated liquid whole egg exhibited higher degree of thixotropic index indicating the occurrence of the protein denaturation at 60 °C. The flow behaviour of liquid whole egg in the continuous ohmic heating system was predicted as laminar (GRe range of 87.59–538.87) for the mass flow rate range of 0.0056–0.0166 kg/s. The friction factors and pressure losses in the system in those mass flow rates were also assessed. The result of this study will give necessary information on flow characteristics of liquid whole egg for the modelling, designing and the scaling up of the continuous ohmic heating systems for pasteurisation of liquid egg products.

## Keywords

Ohmic heating Liquid whole egg Rheology Fluid dynamics Non-Newtonian fluid## Nomenclature

- ∆
*P* Pressure drop (Pa)

*A*_{e}Area of cross-section of the electrodes (m

^{2})*D*Diameter of pipe (m)

*E*_{a}Activation energy (kJ/mol)

*f*Friction factor (dimensionless)

- GRe
Generalised Reynolds number (dimensionless)

*I*Current (A)

*K*Consistency coefficient, (Pa s

^{ n })*K*_{0}Consistency coefficient at reference temperature (Pa s

^{ n })*L*The distance between the electrodes (m)

*n*Flow behaviour index (dimensionless), number of constants in Eq. (12)

*N**R*- Ideal gas constant (8,314 J/mol K) in Eq. (3) (Table 1), radius (m) in Eq. (9), Eq. (10) in Table 1Table 1
Some general relations used

Equation

Equation number

References

Newtonian model

\( \tau = \mu \dot \gamma \)

Eq. (1)

Rao et al. 1984

Power law model (Ostwald–de Waale model)

\( \tau = K{\dot \gamma^n} \)

Eq. (2)

Rao et al. 1984

Temperature dependency of consistency coefficient

\( K = {K_0}{e^{ - \frac{E_a}{R}\left( {\frac{1}{T_0} - \frac{1}{T}} \right)}} \)

Eq. (3)

Rao et al. 1984

Generalised Reynolds number

\( {\text{G}}{\rm Re} = \frac{{{D^n}{\upsilon^{\left( {2 - n} \right)}}\rho }}{{{8^{\left( {n - 1} \right)}}K{{\left( {\frac{3n + 1}{4n}} \right)}^n}}} \)

Eq. (4)

Geankoplis 2003

Friction factor for non-Newtonian fluid, laminar flow

\( f = \frac{16}{{{\text{G}}{\rm Re} }} \)

Eq. (5)

Geankoplis 2003

Pressure drop

\( \Delta P = 4f\frac{L}{D}\frac{{\rho \upsilon_{\text{ave}}^2}}{2} \)

Eq. (10)

Geankoplis 2003

Electrical conductivity

\( \sigma = \frac{I}{V}\frac{L}{{{A_{\text{e}}}}}\,\,\,\,\,({\text{S/m}}) \)

Eq. (11)

Sastry and Salengke 1998

*Re*Reynolds Number (dimensionless)

*T*Temperature (°C), (K) in Eq. (3) (Table 1)

*t*Time (s)

*T*_{0}Reference temperature (K)

*V*Voltage (V)

## Abbreviations

- RM
Raw material

- RMSE
Root mean square error

- RPM
Revolutions per minute

- SE
Standard error

- SS
Shear stress

- SR
Shear rate

## Greek Letters

*τ*Shear stress (Pa)

*σ*Electrical conductivity (S/m)

*ρ*Density (kg/m

^{3})- \( \dot \gamma \)
Shear rate (s

^{−1})*υ*Velocity (m/s)

- \( \dot \upsilon \)
Volumetric flow rate (m

^{3}/s)*µ*Viscosity (Pa s)

*τ*_{0}Yield stress (Pa)

*χ*^{2}Chi square

## Subscripts

- ave
Average

- exp
Experimental

- N
Predicted by using Newtonian model

- NN
Predicted by using non-Newtonian model

- max
Maximum

- OH
In the ohmic heating test cell

- pred
Predicted

- P
In the pipe

- S
In the overall system

- w
At the tube wall

## Notes

### Acknowledgements

Authors are grateful to the editor and reviewers for their valuable comments, which have been utilised to improve the quality of the paper.

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