• Unsteady nature of dispersion of a solute in electro - hydrodynamic pulsatile flow of Carreau fluid in a uniform channel filled is studied. • The new observation is that the convection coefficient and dispersion coefficient (dispersion of a solute) is enhanced due to increase in the Debye–Hückel parameter. • Dispersion process of a solute is remarkably improved by an increment in the pulsatile Reynolds number ( α ) and unsteady part pressure gradient ( A ) . • It is, for the first time, revealed that solute dispersion in Carreau fluid flow is maximum for the case of diabetic diseased blood and minimum in the anemic disorder case. The present mathematical model discusses the solute dispersion mechanism in a circular conduit by considering pulsatile flow of Carreau fluid. The axial solute distribution process in a circular tube has been analyzed using the generalized dispersion technique and finite Hankel transforms. The momentum equations and constitutive equation to describe the rheology of Carreau fluid are solved by perturbation method with suitable boundary condition and obtained fluid velocity profile. The coefficients of solute dispersal and convection of the concentration profile have been analytically obtained with the help of the assumptions of low zeta potential and a low Reynolds number. The effects of the Debye–Hückel parameter, Weissenberg number, Pulsatile Reynolds number, chemical reaction parameter, and time-dependent pressure gradient on the dispersion environment have been premeditated. The development in fluid velocity and solute concentration profiles are studied realistically for accurate ranges of the distinct physical parameters. The most important outcome of the present investigation is an increment in the Debye–Hückel parameter enhancing the dispersion mechanism in the circular tube. Furthermore, this study highlights the clinical aspect of the electrohydrodynamic solute dispersion's nature in normal as well as disease-affected blood. The present study might contribute to the design and fabrication of surgical tools and development of laboratory equipment in the fields of medical and bioengineering. Furthermore, the results obtained could play a key role in understanding the transportation of nutrients and dispersion process of drugs in the blood circulation.