Mathematical modeling of a hydrophilic cylinder floating on water.

In this paper, a hydrostatic model of the surface profile anchored to the upper edge of a vertical cylinder is proposed to explain why coins can float on water surface. The sharp edge of a cylinder is thus modeled as a round smooth surface on which the contact line may be anchored at a position according to the weight of the cylinder. The mathematical model of the surface profile is established based on the hydrostatics and a third order ordinary differential equation is resulted. Numerical solution of the model demonstrates under practical conditions the existence of the surface profiles that provide reasonable uplifting force at the contact line so that the force is available for floating coins on water surface. The proposed model explains the obviously enlarged apparent contact angle and the edge effect in the literature. The numerical simulation is found in very good agreement with the experimental data in the literature.

Mirror fluid method for numerical simulation of sedimentation of a solid particle in a Newtonian fluid.

The mirror fluid method is proposed for simulating solid-fluid two-phase flow. The whole computational domain is modeled as an Eulerian one for the fluid with a Lagrangian subdomain embedded in it. The boundary condition is enforced implicitly on solid-fluid surface segments by mirror relations. Thus, the total flow is solved in the one domain, in which the solid particle region is replaced with the virtual flow as the mirror image of outside flow. The mirror fluid method is implemented to compute the motion of a rigid spherical or elliptic particle in a Newtonian fluid for the purpose of method validation. The control volume formulation with the SIMPLE algorithm incorporated is used to solve the governing equations on a staggered grid in a two-dimensional coordinate system. A number of numerical experiments on falling particles are performed and the computational results are in good agreement with the reported experimental data.

The Effect of Surfactant on the Motion of a Buoyancy-Driven Drop at Intermediate Reynolds Numbers: A Numerical Approach.

A numerical investigation of the flow field inside and around a deformed drop translating in another quiescent liquid contaminated by surfactant soluble in continuous phase but not soluble in dispersed phase is presented in this paper. The finite difference method was used to solve numerically the coupled Navier-Stokes and convective-diffusion equations in a body-fitted orthogonal coordinate system. The present numerical simulation of a two-fluid free-boundary problem was validated by comparison of the simulation results of a drop contaminated by surfactant at creeping flow with the analytical solution and the predicted rise velocity of a bubble contaminated by SDS with experimental data at the moderate Reynolds number. To evaluate the effect of surfactant on the drag coefficient, the steady motion of a drop of the same volume in the pure and contaminated systems was simulated. The behavior of the recirculating wake behind a contaminated drop was also examined and found that it becomes more closely attached to the rear stagnancy of the drop when the surfactant concentration is increased gradually. Finally, the stagnant-cap model was revisited and its defects and limitations were analyzed against numerical simulation. Copyright 2001 Academic Press.