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A Numerical Study on Hydrodynamics of a Soft Particle with Hydrophobic Core

[ Vol. 10 , Issue. 4 ]


Ujjwal K. Ghoshal, Somnath Bhattacharyya* and Partha P. Gopmandal   Pages 304 - 313 ( 10 )


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 addressed before.

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.


Drag force, hydrophobic core, numerical method, slip length, soft particle, softness parameter


Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, Department of Mathematics, National Institute of Technology Patna, Patna-800005

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