ALBERT

Description: Applied temperature gradients produce thermocapillary stresses that can force liquid films to spread along solid surfaces. These films are susceptible to a rivulet instability at the advancing solid-liquid-vapor contact line, which is linked to the development of a capillary ridge near the advancing front. The application of a sufficiently strong gravitational counterflow has been shown to drain fluid from the ridge and stabilize the film against rivulet formation and lead to interesting spreading dynamics. In this work, the dynamics and stability of thermocapillary driven films are analyzed for the entire range of drainage. Boundary slip is allowed at the solid-liquid interface, which introduces the static contact angle and slip coefficient as parameters that can typically be specified independently. The contact angle of the spreading film is allowed to depend on the velocity of the contact line, and the effects of this dependence on the film profile, linear stability, and transient response of perturbations are examined. Increasing the influence of gravitational drainage relative to the thermocapillary stress from zero has a stabilizing influence on the traveling wave solutions but is accompanied by an increase in the amplitude of the capillary ridge, which is contrary to stability results for spreading films with only one driving force. Results for the different spreading regimes are generally consistent with predictions based on the more extensively used precursor film model of the contact line, although some differences are observed due to the additional parameters in the slip model that are relevant to partially wetting fluids.

Description: A key purpose of this paper is to demonstrate that the introduction of slip changes the structure of viscous flow past plates and disks by precluding edge singularities in the stresses. It is well-known that the inviscid limit flow is not recovered by letting the viscosity tend to zero. Here it is demonstrated that, similarly, the no-slip limit flow is not recovered by letting the slip coefficient tend to zero. For each of the three cases involving a translating plate and a rotating or translating disk, the determination of the tangential stress is reduced to a linear system of equations with simple coefficients. Values of the drag or torque and edge stresses are displayed.

Description: The effect of non-uniformity in bulk particle mass loading on the linear development of a particle-laden shear layer is analyzed by means of a stochastic Eulerian-Eulerian model. From the set of governing equations of the two-fluid model, a modified Rayleigh equation is derived that governs the linear growth of a spatially periodic disturbance. Eigenvalues for this Rayleigh equation are determined numerically using proper conditions at the co-flowing gas and particle interface locations. For the first time, it is shown that non-uniform loading of small-inertia particles (Stokes number (St)