Nanofluidics

I study the behavior of confined sub-micron and nano-scale bubbles and liquid films via electron microscopy. Primarily, I have become interested in how the movement of the contact line - the region where the liquid, gas, and solid all meet - can actually govern the growth dynamics of bubbles in certain regimes. Contact line motion impacts mass transfer because in order for the contact line to move, the contact angle must deviate from its equilibrium value. In this way, the movement of the contact line is coupled to the global geometry of an interface. When one considers a bubble or droplet that is soluble by the continuous phase, the amount of mass transfer into or out of the bubble is proportional to the internal pressure of the bubble/droplet which is in turn roughly proportional to the mean curvature of the bubble (when bubbles are small). For a sphere, this mean curvature is 2 / radius. Thus, at the nanoscale, even small changes in the radius of curvature introduced by dynamics of the contact line can strongly impact mass transfer. I can provide a manuscript detailing these findings upon request.

The studies are possible with electron microscopy expertise of Dr. Frances Ross (IBM T.J. Watson) using a novel liquid cell developed by a previous graduate student, Dr. Joseph Grogan. The bubbles are created by the very radiation that allows their visualization; the high energy electrons used to illuminated aqueous samples disassociate water into molecular hydrogen and oxygen (think of this as electrode-less electrolysis).

(Left) TEM image of a sub-micron bubble (Middle) Surface Evolver prediction (Right) Intensity profile from the TEM image illustrating the anisotropic growth.

(Left) TEM image of a sub-micron bubble (Middle) Surface Evolver prediction (Right) Intensity profile from the TEM image illustrating the anisotropic growth.

Interpreting the movement, growth, and coalescence of bubbles through only gray-scale microscopy images is a non-trivial endeavor. I’ve found that breathing meaning into the images requires me to be equal parts forensic detective and physicist. By constructing physical models in Mathematica and Surface Evolver, I have been able to de-convolute many aspects of bubble dynamics and create a quantitative framework useful for liquid cell microscopists and investigators of interfacial phenomena.  My final year at the University of Pennsylvania will be focused on publishing my findings.

The results of a simulation describing the growth of  a bubble in a non-uniform Hele-Shaw device (a wedge). While the bubble begins as a sphere, as it grows the contact line evolves non-uniformly according to the Blake-Haynes mechanism. This leads to translation as well as the development of tear-drop-like geometries. The model is implemented using a Mathematica program I wrote to access Surface Evolver.

The results of a simulation describing the growth of  a bubble in a non-uniform Hele-Shaw device (a wedge). While the bubble begins as a sphere, as it grows the contact line evolves non-uniformly according to the Blake-Haynes mechanism. This leads to translation as well as the development of tear-drop-like geometries. The model is implemented using a Mathematica program I wrote to access Surface Evolver.


Microfluidics

My microfluidics research has been concerned primarily with the creation of novel emulsions that feature solid cores. Understanding such emulsions is important for performing high through-put screenings of biological specimens and the creation of novel metal-materials. 

An ellipsoidal polystyrene particle (minor diameter is 100 microns) is encapsulated by water surrounded by a continuous phase of oil using a glass-capillary flow focusing device. Video was captured at ~10,000 frames a second.

An ellipsoidal polystyrene particle (minor diameter is 100 microns) is encapsulated by water surrounded by a continuous phase of oil using a glass-capillary flow focusing device. Video was captured at ~10,000 frames a second.

Encapsulation of a C. elegans nematode in water surrounded by a continuous phase of light mineral oil using a glass capillary flow-focusing device. The injection nozzles (left) is 80 microns is diameter.

Encapsulation of a C. elegans nematode in water surrounded by a continuous phase of light mineral oil using a glass capillary flow-focusing device. The injection nozzles (left) is 80 microns is diameter.

In my most recent publication, I analyze the geometry of the interface between two immiscible phases when the disperse phase is pinned to an ellipsoidal particle. The ellipsoidal particle was intended to help us understand the encapsulation of slender bodies (such as C. elegans, above) using flow-focusing. However, the dynamics of the ellipsoidal encapsulation process and the resultant geometry were of theoretical interest in and of themselves. The geometry of the particle coupled with its finiteness introduces the possibility of encapsulation hysteresis between geometries that are adhered to the particle (unduloidal geometry) and complete encapsulation (spherical geometry) as illustrated below. 

Free energy of all three states relative to the expelled state (ellipsoid completely encapsulated in the continuous phase). Insets indicate the morphology at the position of the contact line; the open circles present on the ellipsoids indicate the position of the contact line at point C (maximum volume that an ellipsoid can "hold").

Free energy of all three states relative to the expelled state (ellipsoid completely encapsulated in the continuous phase). Insets indicate the morphology at the position of the contact line; the open circles present on the ellipsoids indicate the position of the contact line at point C (maximum volume that an ellipsoid can "hold").

While the axisymmetric shapes are thoroughly understood, there are outstanding questions regarding the stability limit of solutions, especially when the axial symmetry constraint is relaxed. Furthermore, I am continuing to investigate the impact that the elongated particles have on the stability of the liquid jet. In the regime where the radius of the particle is large compared to that of the native jet, I am finding that "dripping" type (or more generally, linearly globally unstable flows) can be switched into "jetting" type flows; this has a large impact on the amount of inner phase volume V* ultimately "captured" by the solid phase.