Table 3: The empirical constants for reported in the literature and in the current study.

ReferenceLiquid systemType of impellerConstant βConstant αConstant γValid for (kW/m3) Average error, %Correlation

[10]Perfluorocarbon (PFC) in YPD medium with inactive cellsRushton turbine0.3020.699−1.378NANA15.7 Nielsen et al. [20]
(10)
[20] n-Hexadecane in broth mediumRushton turbine0.310.701.70NANANA
[27]Methyl ricinoleate in Yarrowia  lipolytica brothRushton turbine0.60.8−22NANANA
[27]Tween 80 in Yarrowia  lipolytica brothRushton turbine0.40.7−449NANANA

Current studyXanthan gum solution with 0 to 10% palm oil fractionRushton turbine0.47730.1620−6.60290.079 to 1.110.7758.75 Nielsen et al. [20]
(10)
Xanthan gum solution with 0% palm oil fractionRushton turbine0.66740.2076−6.60290.141 to 1.110.8946.55

Current studyXanthan gum solution with 5% palm oil fractionRushton turbine0.53610.1225−6.16220.094 to 0.890.7858.74
Xanthan gum solution with 10% palm oil fractionRushton turbine0.40780.1702−8.28960.079 to 0.890.6846.47
Xanthan gum solution with 15% palm oil fractionRushton turbine0.44010.4253−2.78650.058 to 0.830.7440.93Nielsen et al. [20]
(10)
Xanthan gum solution with 20% palm oil fractionRushton turbine0.48850.2777−1.62700.039 to 0.720.9815.59
Xanthan gum solution with 50% palm oil fractionRushton turbine0.43340.1605−0.06970.031 to 0.640.8634.40

Current studyXanthan gum solution with 0% palm oil fractionRushton turbine0.66740.20760.141 to 1.110.8946.55 Cooper et al. [18]
(9)
Xanthan gum solution with 5% palm oil fractionRushton turbine0.53610.12250.094 to 0.890.7858.73
Xanthan gum solution with 10% palm oil fractionRushton turbine0.40780.17020.079 to 0.890.6846.47
Xanthan gum solution with 15% palm oil fractionRushton turbine0.53430.30540.058 to 0.830.9618.80
Xanthan gum solution with 20% palm oil fractionRushton turbine0.49940.27400.039 to 0.720.9814.00
Xanthan gum solution with 50% palm oil fractionRushton turbine0.44580.33910.031 to 0.640.9127.67