In a new study, MIT scientists have explained why, under certain conditions, a droplet of liquid should not coalesce with the liquid surface below. On the off chance that the bead is exceptionally frosty and the shower adequately hot, at that point, the drop should “levitate” on the shower’s surface because of the streams initiated by the temperature contrast.
Through this, scientists learned how biological or chemical substances are spread by rain or other sprays in nature. They could likewise fill in as a guide for bead-based plans, such as, in microfluidic chips, where beads conveying different reagents can be intended to blend just in specific areas in a chip at specific temperatures. With this new understanding, analysts could likewise design beads to go about as mechanical metal balls in zero-gravity conditions.
Michela Geri, a graduate student in MIT’s Department of Mechanical Engineering, said, “Based on our new theory, engineers can decide what is the initial critical temperature difference they need to maintain two drops separately, and what is the maximum weight that a bearing constructed from these levitating drops would be able to sustain.”
“If you have a fundamental understanding, you can start designing things the way you want them to work.”
Courtesy of the researchers
She built a small box, about the size of an espresso cup, with acrylic walls and a metal floor, which she placed on a hot/cold plate. She filled the cube with a bath of silicone oil, and just above the bath’s surface, she set a syringe through which she pumped droplets of silicone oil of the same viscosity. In each series of experiments, she set the temperature of the hot/cold plate and measured the temperatures of the oil pumped through the syringe and at the bath’s surface.
She utilized a high-speed camera to record each droplet at 2,000 frames per second. The experiment used silicone oils with a range of viscosities, from water-like to 500 times thicker.
She found that droplets appeared to levitate on a bath’s surface as the temperature gradient between the two fluids increased. She was able to levitate a droplet, delaying its coalescence, by as long as 10 seconds, by maintaining a temperature difference of up to 30 degrees Celsius or 86 degrees Fahrenheit, comparable to the difference between a drop of cold milk on a bath of hot black coffee.
Later, she mapped the data and observed that the droplet’s residence time on the bath’s surface seemed to depend on the initial temperature difference between the two fluids, raised to the power of two-thirds.
They found a critical temperature difference at which a droplet of a given viscosity will not mix but instead levitate on a liquid surface.
Geri said, “We saw this relationship clearly in the lab and then tried to develop a theory to rationalize that dependence.”
“We found the force coming from the droplet’s weight and the force coming from the recirculation of the air layer will balance at a point, and get that balance, you need a minimum, or critical temperature difference, for the droplet to levitate.”
Scientists primarily observed the layer of air separating the droplet from the bath. They then hypothesized that a temperature difference between the two fluids may influence this air cushion, which may in turn act to keep a droplet afloat.
To investigate this idea mathematically, the researchers performed a calculation, referred to in fluid mechanics as a lubrication analysis, in which they appropriately simplified the complex equations describing fluid motion to describe the flow of air between the droplet and the bath.
Through these equations, they found that temperature differences between the fluid drop and the fluid bath create convection or circulating currents in the intervening layer of air. The greater the temperature difference, the stronger the air currents, and the greater the pressure that pushes against the droplet’s weight, preventing it from sinking and making contact with the bath.
Geri said, “We found the force coming from the droplet’s weight and the force coming from the recirculation of the air layer will balance at a point, and get that balance, you need a minimum, or critical temperature difference, in order for the droplet to levitate.”
“For that, we had to think about how the temperature of the drop changes over time and approaches the temperature of the bath.”
“With a temperature difference, you generate a flow inside the drop, drawing up heat from the bath, which circulates around until the droplet temperature is the same as the bath, and you don’t levitate anymore. We were able to describe that process mathematically.”
To do so, the analysts adjusted another arrangement of conditions, which portrays the blending of two liquids. They utilized the conditions to display a warm package of fluid inside the bead that has been warmed by the shower underneath. They could describe how that package of fluid blended with the colder parts of the bead, warming the whole drop after some time.
Geri said, “If you study that process mathematically, you can show the way temperature is changing in the droplet over time is exactly with this power law of 2/3 that we observed in our experiments.”
“There are a lot of biological and chemical mixing events that involve droplet interactions, including in the surf zone, with waves breaking and small drops flying everywhere, and in hot tubs, with bubbles bursting and releasing droplets that skitter along the surface.”
“The rate at which these agents mix will depend on how long drops stay afloat before coalescing. Now we know that depends on temperature, and we can say exactly how.”
Journal Reference:
- Geri, M., Keshavarz, B., McKinley, G., & Bush, J. (2017). Thermal delay of drop coalescence. Journal of Fluid Mechanics, 833, R3. DOI: 10.1017/jfm.2017.686