Resistance fluidic

Microfluidics handles and analyzes fluids in structures of micrometer scale. At the microscale, different forces become dominant over those experienced in everyday life [161], Inertia means nothing on these small sizes the viscosity rears its head and becomes a very important player. The random and chaotic behavior of flows is reduced to much more smooth (laminar) flow in the smaller device. Typically, a fluid can be defined as a material that deforms continuously under shear stress. In other words, a fluid flows without three-dimensional structure. Three important parameters characterizing a fluid are its density, p, the pressure, P, and its viscosity, r. Since the pressure in a fluid is dependent only on the depth, pressure difference of a few pm to a few hundred pm in a microsystem can be neglected. However, any pressure difference induced externally at the openings of a microsystem is transmitted to every point in the fluid. Generally, the effects that become dominant in microfluidics include laminar flow, diffusion, fluidic resistance, surface area to volume ratio, and surface tension [162]. 

Table 39.2 lists the pressure-volume relationships for various geometries the fluidic capacitance is found simply by differentiating with respect to pressure. For small deformations, volume varies linearly with applied pressure, such that the capacitance is not a function of the pressure it merely defines the proportionality between increases in pressure and increases in stored mass. For such cases, the fluid circuit analysis is linear, because flow rate and pressure drops are related via linear expressions. For large deformations (i.e., the membrane limit), the fluidic capacitance is a function of the pressure this implies that the fluidic circuit behavior will be nonlinear. Obviously, once the fluidic resistance, capacitance and inductance have been identified via geometry (and material properties), complicated networks can be analyzed using commercially available circuit analysis software such as SPICE [42]. 

To see more clearly how this flow control unit works, let us take a simplified model of fluid resistance and consider it in terms of Ohm s law. Equation (12.2) is very similar to resistance of an electrical circuit, and it is applicable to fluidic resistance R in this system with laminar flow conditions. Tlie pressure drop Ap is caused by the restrictor at a specific flow rate F. 

Figure 12. Arrangement for an active flow control unit in parallel HPLC.The partial flows Fi to F resulting from the total flow F, ,a] can be measured by metering the pressure drop along the restrictor capillaries to R . The flows are adjustable by the valves in an individual branch. i yj ito f i,e can be compared to potentiometers in an electrical circuit. The specific settings of the valves lead to an equal flow in all the separation columns with different fluidic resistance i cohumii to, and thus different backpressure.

In (12.5) the quotient Qi resulting from the system pressure Ptotai divided by pressure drop Api has no dimension and thus is not influenced by any fluidic parameters that is, it remains constant during a gradient run. Because of its direct proportionahty to the fluidic resistance of a specific branch, it serves as a perfect regulating variable in the Pl-control circuit, which is now also apphcable for gradient HPLC systems. 

The fluidic resistance is the pressure differential required to obtain a unit flow rate in a fluidic channel. The general formula for the fluidic resistance can be given as... 

The basic operating principle of a bubble logic gate [3] is shown in Fig. 1. This microfluidic circuit consists of two input channels (A and B) and two output channels (Z and T). Channel X is shghtly wider than channel Y, i.e., channel X has a lower fluidic resistance than T. Hence, if a bubble reaches the junction by way of input channel A or B, then it will always take the output channel X owing to the lower fluidic resistance. But if two bubbles arrive simultaneously from input channels A and B, then the first bubble will take the output channel X. This first bubble increases the fluidic resistance of channel X and causes the other bubble to flow through channel Y. For detailed information on other microfluidic logic circuits, readers are advised to consult [3]. 

Case 3 bottom row). One nitrogen bubble was allowed to flow with water from each of the channels A and B. At the junction, the first bubble took the path of the wider channel X. The presence of the first bubble in channel X increased its fluidic resistance, and so the other bubble was forced to take the output channel Y. Therefore, the outputs of X and Y were both 1. 

This design is straightforward and does not require on-chip valves and can be scaled up to feature additional culture chambers and wider ranges of flow rates. For rectangular microchannels with an 0(1) aspect ratio, the fluidic resistance of each component of the network can be designed using the following expression ... 

Automatic macromodel extraction that takes advantage of high-fidelity device simulations (e.g., FEM, FVM, and BEM) to extract RLC values in irregular microchannel geometries has also been reported. Turowski et al. [11] approximate the microfluidic Tesla valve as an/ L circuit (serial connection of a resistor R and an inductor L in Fig. 5) and performed both steady and transient analysis to extract its fluidic resistance and inductance. The macromodels are then stitched together for an overall system simulation on the pumping performance. 

Huang S, Wu M, Cui Z, Cui Z, Lee G (2008) A membrane-based seipentine-shape pneumatic micropump with pumping perframance modulated by fluidic resistance. J Micromech Microeng 18 1—12... 

With the fluidic resistance (R) of the drug delivery channel and the gas law according Equation (15.6), the decrease in pressure inside the drug reservoir can be calculated as given in Equation (15.7) ... 

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