24
3 Simulating Droplet Microfluidic Networks
• Physical Experiments: The behavior of the microfluidic network can directly be
observed (without any abstractions) when a prototype is fabricated and physical
experiments are conducted. However, fabricating a prototype requires a lot of
work by a designer as well as dedicated equipment (e.g., laboratories). Overall,
physical experiments produce the highest costs but allow to observe the actual
behavior of the design.
All of these three levels have their strengths and their application depends on
the stage of the design process. In context of this book, design methods for early
stages in the design process are proposed and, because of that, the following section
focuses on the 1D analysis model. This 1D analysis model provides the basis of
many design methods proposed in this work, which address tasks before a physical
design is available.
3.2 One-Dimensional Analysis Model
In this section, the one-dimensional (1D) analysis model [93, 101] is reviewed which
allows to describe the flow distribution in microfluidic networks. This model is
physically validated and is commonly used for designing, modeling, and simulating
droplet microfluidic networks [4, 13, 21, 37, 66, 67, 93, 101, 105, 106, 109, 110].
First, this section describes the volumetric flow through and pressure across single
components like channels, modules, and pumps. Afterwards, this section describes
how the flow distributes through entire microfluidic networks.
3.2.1 Volumetric Flow, Pressure, and Fluidic Resistance
The Hagen-Poiseuille law describes the relationship between the pressure difference, the volumetric flow, and the fluidic resistance of a channel/module by [10]
P = Q R.
(3.1)
Here, P is the pressure difference (in [mbar]) between the two end nodes
of the channel/module, Q is the volumetric flow rate (in [μl/min]) through the
channel/module, and R is the fluidic resistance (in [mbar/(μl/min)]) posed by the
channel/module.
A low Reynolds number allows to reduce the resistance of channels/modules
(which is defined by their geometry and the viscosity of the continuous phase μ cont )
to a constant value [101] (i.e., the reduction to the 1D-space). For example, the
resistance R c of a rectangular channel c (with length l c , width w c , and height h c ),
where the ratio h c /w c is less than 1, is defined by [32]
R c =
a μ cont l c
w c h 3
c
,
(3.2)
3 Simulating Droplet Microfluidic Networks
• Physical Experiments: The behavior of the microfluidic network can directly be
observed (without any abstractions) when a prototype is fabricated and physical
experiments are conducted. However, fabricating a prototype requires a lot of
work by a designer as well as dedicated equipment (e.g., laboratories). Overall,
physical experiments produce the highest costs but allow to observe the actual
behavior of the design.
All of these three levels have their strengths and their application depends on
the stage of the design process. In context of this book, design methods for early
stages in the design process are proposed and, because of that, the following section
focuses on the 1D analysis model. This 1D analysis model provides the basis of
many design methods proposed in this work, which address tasks before a physical
design is available.
3.2 One-Dimensional Analysis Model
In this section, the one-dimensional (1D) analysis model [93, 101] is reviewed which
allows to describe the flow distribution in microfluidic networks. This model is
physically validated and is commonly used for designing, modeling, and simulating
droplet microfluidic networks [4, 13, 21, 37, 66, 67, 93, 101, 105, 106, 109, 110].
First, this section describes the volumetric flow through and pressure across single
components like channels, modules, and pumps. Afterwards, this section describes
how the flow distributes through entire microfluidic networks.
3.2.1 Volumetric Flow, Pressure, and Fluidic Resistance
The Hagen-Poiseuille law describes the relationship between the pressure difference, the volumetric flow, and the fluidic resistance of a channel/module by [10]
P = Q R.
(3.1)
Here, P is the pressure difference (in [mbar]) between the two end nodes
of the channel/module, Q is the volumetric flow rate (in [μl/min]) through the
channel/module, and R is the fluidic resistance (in [mbar/(μl/min)]) posed by the
channel/module.
A low Reynolds number allows to reduce the resistance of channels/modules
(which is defined by their geometry and the viscosity of the continuous phase μ cont )
to a constant value [101] (i.e., the reduction to the 1D-space). For example, the
resistance R c of a rectangular channel c (with length l c , width w c , and height h c ),
where the ratio h c /w c is less than 1, is defined by [32]
R c =
a μ cont l c
w c h 3
c
,
(3.2)