Background: In several practical contexts, the core-shell interface of a soft particle may
exhibit hydrodynamic slip. A significant enhancement in fluid transport over a hydrodynamically slipping
surface is expected. However, in the present context, the hydrophobic surface is covered by a permeable
shell. The impact of the hydrophobic core on the hydrodynamics of a soft particle has not been
Objective: We investigate the hydrodynamics of a soft particle in which the surface of the rigid core is
hydrophobic. The impact of the shell thickness and permeability on the hydrodynamics of this type of
soft particle is analyzed. The fluid inertia effect is also assessed for O(1) Reynolds number.
Methods: A single-domain approach, in which two sets of equations for the fluid and the porous regions
are combined into one set by introducing a binary parameter, is adopted. The Finite volume
method is used to discretize the governing equation and a pressure correction based iterative method
SIMPLE (Semi-Implicit Method for Pressure Linked Equation) is used to solve the resulting algebraic
equations. The numerical solutions for the soft particle with no-slip core are in good agreement with the
analytic solutions based on the linear Stokes-Brinkman model for a lower range of the Reynolds number.
Results: The effect of the slip length of the inner core as well as the thickness and permeability of the
soft layer on the hydrodynamics and settling velocity of the soft particle in the creeping flow regime is
studied extensively. The validity of the linear analysis in describing the hydrodynamics of a soft particle
with hydrophobic core has been illustrated. We have also addressed the situation when the fluid
inertia has a non-negligible effect. In addition, the effect of volume fraction on the drag force experienced
by the concentrated suspension of soft particles is addressed. Recent patents on the design of soft
particles with a hydrophobic core are also discussed.
Conclusion: Our results show that the impact of the core hydrophobicity is strongly influenced by the
shell permeability. The core hydrophobicity creates a significant reduction in the drag of the soft particle
with highly permeable shell. For a low permeable shell, the hydrophobicity of the core has a negligible
impact when the shell thickness exceeds the core radius.