3.1 Abstraction Levels
23
hence, allow, e.g., precise simulations but also result in higher costs with respect
to setup and computational time.
In the following, abstraction levels and their requirements are reviewed in detail
(ordered from high abstractions to no abstractions).
• 1D Analysis Model: The 1D analysis model is applicable when the flow is laminar, viscous, and incompressible [93]. This model abstracts the exact geometric
design of microfluidic networks by describing its channels and modules only by
their fluidic resistances, i.e., as 1D values. Hence, it only requires a specification
of the design (i.e., the resistances of the channels and modules and how these
are connected, the used phases, and the pressure gradients/volumetric flow rates
applied by the pumps) but does not require a complete physical design.
Although this model abstracts geometric details, the model allows for determining (1) the droplets’ path through the network (this can decide which
experiment is executed on the droplet), (2) the flow changes caused by all droplets
and the resulting impacts (e.g., distance changes between droplets, droplet
patterns, etc.), and (3) the time a droplet takes to pass through the network.
Using these functionalities allows for deriving the design, validating the design
by simulation, and exploring alternative, optimized designs (i.e., to increase the
robustness of a design by different dimensions of channels, applied pressures,
etc.). Hence, this model is especially useful for early stages in the design process
where certain physical details are of no interest yet. Furthermore, the applied
abstractions make corresponding simulations efficient (i.e., only linear equations
need to be solved), which allows to simulate practical large-scale microfluidic
networks.
• Computational Fluid Dynamics (CFD): CFD discusses the behavior of fluids
using numerical modeling and allows to simulate complex physical scenarios.
In general, there exist two main approaches for fluid modeling: Eulerian and
Lagrangian. The Eulerian methods model fluids flowing between elements
in space, while the Lagrangian methods model motion of material elements
representing fluids [128]. Tools like Comsol Multiphysics [18], Ansys [3], or
OpenFoam [42] employ these methods. Comprehensive reviews of the methods
and tools are provided in [35, 128].
Corresponding simulations require a complex simulation setup (e.g., the
generation of a mesh based on the physical design) and yield simulation results
of high precision, i.e. physical effects like turbulences, droplet deformation,
and droplet splitting can be simulated. But the high level of physical details
causes significant computational costs, which limits their applicability to small
designs and single components. For example, these methods are inappropriate
to quickly simulate practically large-scale microfluidic networks [93] and, therefore, recently a hybrid solution querying precomputed results from a database
and combining it with higher abstractions was presented in [125]. Overall, CFD
simulations provide high precisions but therefore require a complex setup and
result in high computational costs.
23
hence, allow, e.g., precise simulations but also result in higher costs with respect
to setup and computational time.
In the following, abstraction levels and their requirements are reviewed in detail
(ordered from high abstractions to no abstractions).
• 1D Analysis Model: The 1D analysis model is applicable when the flow is laminar, viscous, and incompressible [93]. This model abstracts the exact geometric
design of microfluidic networks by describing its channels and modules only by
their fluidic resistances, i.e., as 1D values. Hence, it only requires a specification
of the design (i.e., the resistances of the channels and modules and how these
are connected, the used phases, and the pressure gradients/volumetric flow rates
applied by the pumps) but does not require a complete physical design.
Although this model abstracts geometric details, the model allows for determining (1) the droplets’ path through the network (this can decide which
experiment is executed on the droplet), (2) the flow changes caused by all droplets
and the resulting impacts (e.g., distance changes between droplets, droplet
patterns, etc.), and (3) the time a droplet takes to pass through the network.
Using these functionalities allows for deriving the design, validating the design
by simulation, and exploring alternative, optimized designs (i.e., to increase the
robustness of a design by different dimensions of channels, applied pressures,
etc.). Hence, this model is especially useful for early stages in the design process
where certain physical details are of no interest yet. Furthermore, the applied
abstractions make corresponding simulations efficient (i.e., only linear equations
need to be solved), which allows to simulate practical large-scale microfluidic
networks.
• Computational Fluid Dynamics (CFD): CFD discusses the behavior of fluids
using numerical modeling and allows to simulate complex physical scenarios.
In general, there exist two main approaches for fluid modeling: Eulerian and
Lagrangian. The Eulerian methods model fluids flowing between elements
in space, while the Lagrangian methods model motion of material elements
representing fluids [128]. Tools like Comsol Multiphysics [18], Ansys [3], or
OpenFoam [42] employ these methods. Comprehensive reviews of the methods
and tools are provided in [35, 128].
Corresponding simulations require a complex simulation setup (e.g., the
generation of a mesh based on the physical design) and yield simulation results
of high precision, i.e. physical effects like turbulences, droplet deformation,
and droplet splitting can be simulated. But the high level of physical details
causes significant computational costs, which limits their applicability to small
designs and single components. For example, these methods are inappropriate
to quickly simulate practically large-scale microfluidic networks [93] and, therefore, recently a hybrid solution querying precomputed results from a database
and combining it with higher abstractions was presented in [125]. Overall, CFD
simulations provide high precisions but therefore require a complex setup and
result in high computational costs.