Forces on a porous particle in an oscillating flow

• Published in: Journal of colloid and interface science 2009-02, Vol.330 (1), p.149-155
• Main Authors: Vainshtein, P., Shapiro, M.
• Format: Article
• Language: English
• Subjects: Added mass force; Chemistry; Colloidal state and disperse state; Drag force; Exact sciences and technology; General and physical chemistry; Oscillations; Particle; Permeability; Porous materials; Surface physical chemistry
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1016/j.jcis.2008.10.050

We investigate theoretically forces acting on a porous particle in an oscillating viscous incompressible flow. We use the unsteady equations describing the creeping flow, namely the Stokes equations exterior to the particle and the Darcy or Brinkman equations inside it. The effect of particle permeability and oscillation frequency on the flow and forces is expressed via the Brinkman parameter β = a / k and the frequency parameter Y = a 2 ω / 2 ν = a / δ , respectively. Here a is particle radius, k is its permeability, ω is the angular frequency, δ is the thickness of Stokes layer (penetration depth) and ν is the fluid kinematic viscosity. It is shown that the oscillations interact with permeable structure of the particle and affect both the Stokes-like viscous drag and the added mass force components. We investigate theoretically forces acting on a porous particle in an oscillating viscous incompressible flow. We use the unsteady equations describing the creeping flow, namely the Stokes equations exterior to the particle and the Darcy or Brinkman equations inside it. The effect of particle permeability and oscillation frequency on the flow and forces is expressed via the Brinkman parameter β = a / k and the frequency parameter Y = a 2 ω / 2 ν = a / δ , respectively. Here a is particle radius, k is its permeability, ω is the angular frequency, δ is the thickness of Stokes layer (penetration depth) and ν is the fluid kinematic viscosity. It is shown that the oscillations interact with permeable structure of the particle and affect both the Stokes-like viscous drag and the added mass force components.