Transient vertically motion of a soluble particle in a Newtonian fluid media

• The equation of motion for a soluble particle in Newtonian media is presented.
• DTM-Padé is introduced as an efficient method for solving this problem.
• Numerical and analytical results are compared.
• Positions and variation of particle diameter versus time are depicted.

Unsteady settling behavior of a soluble spherical particle falling in a Newtonian fluid media is investigated using a drag coefficient of the form given by Ferreira et al. (Chem. Eng. Commun. 1998). It is considered that the mass of the particle reduces due to its solubility in the fluid, and consequently diameter of the particle will be reduced by a linear function. In a current study, the equation of the motion for described variable-mass particle is introduced for the first time and is solved by Padé approximation of Differential Transformation Method (DTM-Padé) and numerical Runge–Kutta method. Also the influence of solubility parameter on velocity profile is discussed and particle's positions are depicted graphically in each 1 s time step.

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