טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentFrumkin Valeri
SubjectNonlinear Dynamics of Bilayer Fluid Systems
Subjected to Thermocapillarity
DepartmentDepartment of Applied Mathematics
Supervisor Professor Alexander Oron


Abstract

We investigate the dynamics of a two-layer system consisting of a thin liquid film and an overlying gas layer, sandwiched between an underlying substrate of general topography and a flat upper plate held at a constant temperature. The flow in question is driven by the Marangoni instability induced, in one case, by thermal waves propagating along a flat, solid substrate, and in another case, by the asymmetric topographical structure of the substrate, uniformly heated from below. 
 
Using long-wave approximation, we derive an evolution equation for the liquid-gas
interface, and study the nonlinear dynamics of the interface with respect to topographical variations, various frequencies of the thermal wave, different thermal properties and different values of the Marangoni number.
 
For the case of travelling thermal waves, we assume the substrate to be flat and demonstrate that for a stationary thermal wave with sufficiently large amplitude and Marangoni number, liquid film rupture takes place with a flattish wide trough. 
For sufficiently small but not too small frequencies of the thermal wave, a periodical structure consisting of localized drops interconnected by thin liquid bridges emerges. 
This train of drops travels unidirectionally along the heated substrate following the thermal wave. For larger thermal wave frequencies, the thickness of the bridges increases enabling fluid flow between the neighbouring drops.   
 
For the case of a uniformly heated, corrugated substrate, a closed-form expression indicating a non-zero value for a liquid flow rate is derived in a steady state of the system. We show that in a broad variety of parameters, the interface attains a deformed steady state with a nonzero average flow rate, thus the described mechanism may be used as means of transport in microfluidic devices. 
We describe two different mechanisms for the amplification of the average flow-rate through the system. The first method uses periodic temporal variation of the Marangoni number, creating a "pumping" mechanism which amplifies the average flow-rate by two orders of magnitude. The second method uses the effects of the ratio between the thermal conductivity of the liquid layer to that of the solid substrate, on the dynamics of the flow, amplifying the average flow rate by at least three orders of magnitude.
 

Finally, we demonstrate the prevention of rupture at the upper plate by assuming it to be hydrophobic through the introduction of a disjoining pressure potential. We show that this mechanism can be applied in order to significantly increase the average flow-rate through the system.