Hossein Haj-Hariri

Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers

We present the results of numerical simulations of the three-dimensional thermocapillary motion of deformable viscous drops under the influence of a constant temperature gradient within a second liquid medium. In particular, we examine the effects of shape deformations and convective transport of momentum and energy on the migration velocity of the drop. A numerical method based on a continuum model for the fluid–fluid interface is used to account for finite drop deformations. An oct-tree adaptive grid refinement scheme is integrated into the numerical method in order to track the interface without the need for interface reconstruction. Interface deformations arising from the convection of energy at small Reynolds numbers are found to be negligible. On the other hand, deformations of the drop shape due to inertial effects, though small in magnitude, are found to retard the motion of the drop. The steady drop shapes are found to resemble oblate or prolate spheroids without fore and aft symmetry, with the d...

Effect of inertia on the thermocapillary velocity of a drop

Abstract We consider the effects of inertia on the thermocapillary migration velocity of a small liquid droplet in a microgravity environment. The externally imposed temperature gradient is assumed to be constant, and the fluid surrounding the droplet is taken to be unbounded and otherwise quiescent. With the convective transfer of heat neglected, droplets with densities higher/lower than the outside liquid deform to prolate/oblate spheroidal shapes, at small values of the capillary and Reynolds numbers. The corrections to the temperature field and the migration velocity of the droplet, resulting from this deformation, are obtained using the so-called Lorentz reciprocal theorem. It is found that the migration velocity could increase, decrease, or remain unchanged depending on the value of certain controlling parameters. The results are presented in vector-invariant form.

Thermocapillary migration of slightly deformed droplets

ABSTRACT A small viscous droplet which is suspended in an immiscible liquid in a zero-gravity environment can be made to migrate by subjecting the system to an external temperature gradient. This so-called thermocapillary migration occurs since the surface tension of the interface is a function of temperature. If inertial effects are negligible and the interface is clean, the shape of the migrating droplet remains spherical. However, when inertial effects are significant or when surfactants are present at the interface, the droplet assumes a prolate or oblate spheroidal shape. In this work we calculate the change in the net migration velocity of the droplet which results from such a deformation. This is done by solving the requisite viscous flow problem in the deformed geometry by perturbation, in conjunction with a generalization of the so-called Lorentz reciprocal theorem which simplifies the calculations. It is found that the migration velocity could increase, decrease or remain unchanged depending on ...

Effect of local property smearing on global variables: Implication for numerical simulations of multiphase flows

This work addresses the sensitivity of a calculated global quantity to the smoothing of discontinuous variation of properties. The analysis is based on the very simple model problem of a fully developed, thermocapillary channel flow. The predictions of this simple model are shown to be in excellent agreement with the results for the Navier–Stokes simulations of the thermocapillary migration of a spherical drop. The main conclusion is that the migration velocity depends very strongly on the smearing of the driving interfacial force whereas it is rather insensitive to the smearing of the discontinuous viscosity distribution. This hints at the indispensability of grid adaption for modeling interfacial forces.

Görtler vortices and heat transfer: A weakly nonlinear analysis

A weakly nonlinear analysis of the Gortler vortex problem is performed. It is demonstrated that the system of streamwise vortices enhances the heat transfer rate at the wall. The inherently nonlinear physical mechanism responsible for this enhancement is discussed both mathematically, as well as heuristically; the latter using kinematic arguments. Remarks are made on the relation of the weakly nonlinear results to their fully nonlinear counterparts, as well as on the inadequacy of linear analyses.

Periodic response of fluidic networks with passive deformable features

This paper outlines the scaling parameters governing the frequency response of fluidic networks with embedded deformable features, which are subjected to periodic excitation. These parameters describe the impact of deformable feature properties on the relative importance of potential energy, kinetic energy, and viscous dissipation. They are used to identify device characteristics that produce specific frequency responses, such as low-pass, high-pass, and bandpass filters that exploit (or avoid) the effects of fluid inertia. Simulations illustrate that passive deformable diodes have little effect on the frequency response of high-pass filters comprised of elastomer features.

Towards Occupancy-Driven Heating and Cooling

HVAC systems are eventually needed to maintain comfort for occupants, and as a result sensing and leveraging user context information is critical for the energy-efficient operation of buildings. This article describes an occupancy-driven HVAC control framework for more effective heating and cooling management.

Confined drop motion in viscoelastic two-phase systems

In this study, we numerically examine the buoyancy-driven, axisymmetric motion of drops through vertical cylindrical capillaries. Combinations of Newtonian and viscoelastic drop and suspending fluid phases are considered. The effects of confinement, material properties, and rheological properties of the two phases on drop mobility and deformation are examined. Four dimensionless parameters (Reynolds number, capillary number, Deborah number, and the drop-to-tube size ratio) play critical roles in determining the drop motion. In general, a Newtonian drop immersed in a viscoelastic fluid experiences an extending trailing edge, while a viscoelastic drop in a Newtonian fluid develops an indentation around the rear stagnation point. Under certain conditions, a cusped drop appears due to fluid viscoelasticity that triggers shape instability.

Stability analysis of cusped bubbles in viscoelastic flows

Experiments have established that an axisymmetric sharp trailing edge of a gas bubble in a viscoelastic fluid can develop into a three-dimensional knifelike shape under certain conditions (high capillary number, large bubble size). A numerical study is conducted to discover the physics of this phenomenon. The axisymmetric deformation of a bubble rising buoyantly in a viscoelastic fluid is simulated by solving the axisymmetric flow equations coupled with the constitutive equations of the finitely extensible nonlinear elastic Chilcott-Rallison (FENE-CR) model. The three-dimensional temporal linear stability analysis of this axisymmetric base state is carried out. The dominant eigenvalue which is indicative of the growth rate of the perturbations is computed. The only unstable eigenmode has azimuthal wavenumber m equal to 2. The corresponding eigenfunction shows that indeed a sharp axisymmetric tail develops a knife-edge form. A further investigation of the energy budget of the disturbances for m = 2 is performed to determine the production and dissipation terms affecting the growth of this instability. It is shown that the normal gradient of the base-state pressure along the free surface plays an important role in the evolution of the instability.

Effect of surfactants on the thermocapillary migration of a concentric compound drop

Abstract The quasi-steady thermocapillary motion of a concentric compound drop in the presence of an insoluble surfactant and an externally imposed constant temperature gradient is examined under conditions of negligible convective transport of momentum and energy. Surface tension is assumed to depend much more weakly on surfactant concentration than on temperature. For this case, the surface concentrations of surfactant are found exactly for all Peclet numbers, confirming the intuitively expected result that the surfactant tends to accumulate near the low temperature sides of the inner and outer drops. This, in turn, results in a decrease in the terminal migration velocities of the drops. The effect of surfactant on the shape of the inner and outer drops is also determined for small capillary numbers.