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Using basic thermodynamic principles we derive a Cahn--Hilliard--Darcy modelfor tumour growth including nutrient diffusion, chemotaxis, active transport,adhesion, apoptosis and proliferation. The model generalises earlier models andin particular includes active transport mechanisms which ensure thermodynamicconsistency. We perform a formally matched asymptotic expansion and developseveral sharp interface models. Some of them are classical and some are newwhich for example include a jump in the nutrient density at the interface. Alinear stability analysis for a growing nucleus is performed and in particularthe role of the new active transport term is analysed. Numerical computationsare performed to study the influence of the active transport term for specificgrowth scenarios.

A Cahn--Hilliard--Darcy model for tumour growth with chemotaxis and active transport