Dimensional-analysis and similitude for scale-up of solid-liquid extraction of Eurycoma longifolia roots

[Display omitted] •3 dimensionless groups were developed for extraction of Eurycoma longifolia roots using dimensional analysis.•Optimum conditions at lab-scale were obtained with the aid of regression analysis using response surface methodology.•ShSc−1 is a cubic model, which found to be the best fitted amongst the proposed models by comparing the ANOVA results.•Scaling up by rule of P/V idem and scale-up factor of 7.65 produced the extract yield of Eurycoma longifolia of 8.65%. A dimensionless model was proposed to scale-up the solid-liquid extraction of Eurycoma longifolia roots. ShSc−1 dimensionless number was found to be the best fit of all proposed models. At optimum conditions of the extraction process, which were duration of extraction of 53 min, solvent to raw material ratio of 12.5:1 and roots particle size of 0.5 to 1.0 mm, the extract yield of 8.76% at lab-scale produced ShSc−1 no. of 0.0312. Employing the scale up rule of P/V idem and scale-up factor of 7.65, the extract yield of 8.65% with 1.37% error was obtained at pilot-scale at ShSc−1 no. of 0.0376. The outcome of this study provided useful scale-up knowledge in ensuring smooth transition from lab-scale to pilot-scale.