A dialysis apparatus includes a dialysis liquid circuit for circulating sodium chloride and sodium bicarbonate through a haemodialyser and a circuit for infusing a patient with at least one solution containing at least one ionic substance “A” absent from the dialysis liquid. The substance “A” has a determined concentration (A)sol in the infusion solution. A dialysance detector determines the actual dialysance “D” of the haemodialyser for sodium, and a flow rate detector determines the flow rate Qinf of infusion solution such that the concentration of the substance “A” inside the patient's body tends towards a desired concentration (A)des, as a function of the dialysance “D”, the concentration (A)sol of the substance “A” in the infusion solution and the desired concentration (A)des, A regulator regulates the flow rate of infusion solution, and a controller drives the regulator to control the flow rate of the infusion solution such that this flow rate is substantially equal to the determined flow rate Qinf.