1. Give one example on how scaling laws benefit miniaturized systems 2. A microc
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Question
1. Give one example on how scaling laws benefit miniaturized systems
2. A microchannel seeded with cells is perfused with medium. The channel has a width of 500 mm and a height of 100 mm. Assume all cells are attached to the bottom of the channel. (1) Estimate the Reynolds number for the medium flow velocity of 5 mm/s, use the density (103 kg/m3 ) and viscosity (10-3 kg/s m) of water for the estimation. (2) Show schematically the steady state velocity profile inside the channel. (3) If the channel height is changed to 50 mm, how will your answer to (2) change if the flow rate stays the same? (4) The flow downstream is to be split and flow into two channels. Both channels have a height of 100 mm. One channel has a width of 60 mm and the other 75 mm. Which channel will have a higher flow rate? Why?
3. For the same microchannel in Question #1 but no cells seeded, an electric field is applied to move a protein solution. 2 (1) Show schematically the steady state velocity profile inside the channel. (2) Describe one microfluidic application utilizing this electro-osmotic phenomenon.
Explanation / Answer
In this era of “think small,” one would intuitively simply scale down the size of all components to a device to make it small. Unfortunately, the reality does not work out that way. It is true that nothing is there to stop one from down sizing the device components to make the device small. There are, however, serious physical consequences of scaling down many physical quantities.
Miniaturizing machines and physical systems is an ongoing effort in human civilization. This effort has been intensified in recent years as market demands for: Intelligent, Robust, Multi-functional and Low cost consumer products has become more strong than ever. The only solution to produce these consumer products is to package many components into the product – making it necessary to miniaturize each individual components. Miniaturization of physical systems is a lot more than just scaling down device components in sizes. Some physical systems either cannot be scaled down favorably, or cannot be scaled down at all!
*Surface and volume are two physical quantities that are frequently involved in micro-device design.
- Volume: related to the mass and weight of a device, which are related to both mechanical and thermal inertial. (thermal inertial: related to the heat capacity of a solid, which is a measure of how fast we can heat or cool a solid. important in designing a thermal actuator)
- Surface: related to pressure and the buoyant forces in fluid mechanics, as well as heat absorption or dissipation by a solid in convective heat transfer. z Surface to volume ration (S/V ratio) - ; 2 S l 3 V l - 1 / S V l - As the size l decreases, its S/V ratio increases.
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