1. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Illustration of a three-pillar flow sculpting device with a three-channel inlet. The middle channel contains the fluid that is “sculpted” by the micropillar sequence. In this sequence, each pillar has the same normalized diameter D/w and is at the same location y/w in a microchannel of height h. With sufficient interpillar spacing (≥6D/w, for Re ≤ 40), the fluid deformation from each pillar has time to saturate before reaching the next pillar. The cross-sectional images showing the inlet flow condition and fluid deformations after each pillar are shown below the microchannel. These images are created by the same simulation method as in Ref. [6], which is used in this work as well.

2. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
A comparison of the workflow necessary for pillar programming design based on the baseline GA framework (a) and the one presented in this paper (b). Previously, the user needed to specify both a desired flow shape (a-i) and the inlet flow configuration (a-ii). This could require multiple user-guided iterations on inlet configurations before a solution is found (a-iii). Now that the inlet is a part of the GA chromosome the user simply supplies the GA framework their desired image (b-i) and the number of possible channels at the microchannel inlet (b-ii). The solution chromosome (b-iii) contains the optimized inlet design as well as the pillar sequence.

3. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
(a) Schematic for the inlet design portion of the chromosome, where the number of values in the chromosome represents the number of channels being joined at the inlet. The values are binary, where 0 represents nontracked fluid and 1 is the fluid of interest being sculpted. (b) The ℝ-chromosome design uses two values for each pillar: diameter and location. ((c) and (d)) These values are given equal probability by their bounds in the GA, and interpreted in real-time to select the nearest available precomputed transition matrix. The entire chromosome for the design as shown would be [0, 1, 0, 1, 0, 0.375, 0.0, 0.375, 0.25, 0.375, −0.375].

4. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
(a) Graphical user interface (GUI) for using the GA framework. Note the drawing canvas (top of GUI) with enforced channel symmetry, GA parameters (lower left), and inlet/sequence design for a microfluidic device (bottom). (b) UML class diagram of custom GA framework.

5. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Examples of randomly generated target images and results from the GA framework (without using FFT postprocessing in the fitness function), with their fitness values. Sculpted fluid is shown in black. The target images were all made with the same inlet design of [0, 0, 1, 0, 0] (see Fig. 3(a)).

6. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Results for case 1, which tested different transition matrix resolutions for accuracy and speed. Sixty different flow shape images were generated using transition matrices from sequences determined by the quasi-random Sobol set, and a fixed inlet configuration. Each target image was blurred and thresholded to mimic a realistic user-supplied design. Framework accuracy (a) and runtime (b) are shown for each transition matrix size, for all 60 target images. Note that the fitness function accuracy (a) has been normalized relative to the baseline (NY = 801).

7. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Results for case 2. (a) Use of a multiresolution fitness function (NY(ML)=51, NY(MH)=601) resulted in similar optimal fitness to the baseline of NY = 601. (b) Use of NY = 51 transition matrices for the first 50 generations resulted in substantially decreased runtime.

8. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Results for case 3, which tests the ℝ-chromosome against the integer-proxy ℤ-chromosome. The inlet design is fixed in the chromosome, thus isolating the test to the choice of pillar sequence encoding. (a) The ℝ-chromosome results in comparable accuracy in optimal fitness for each target image. Here, the fitness for the best result from each GA framework search is reported for all 60 images. (b) Use of the ℝ-chromosome shows faster convergence in the GA with a mean of 63 generations per GA. Note that the ℤ-chromosome, with a mean of 111 generations, had a significant proportion of GA searches terminate at the generation limit of 200. (c) Fewer generations translate into less framework runtime, with a median of ≈7000 s for the ℤ-chromosome, and ≈3600 s for the ℝ-chromosome.

9. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Results for case 4, which tested the GA's ability to design the inlet flow configuration. (a) Optimal fitness results for 60 target flow shapes with randomly generated pillar sequences and inlet flow configurations. Sculpted fluid is shown in black. The best match by fitness, with f = 5.43, is shown in (b), while the worst match, with f = 45.56, is shown in (c). Although the discrepancies between the target fluid shape and the GA result in (c) are clearly discernible, the overall design has still been found.

10. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Result for case 5, which compares performance of the custom GA to the matlab implementation. (a) Comparison of optimal fitness values for each of the 60 target images, which are identical to those used in case 1. Unlike case 1, the portion of the chromosome which governs the inlet design was accessible to the GA, thus making the problem more difficult. Note that the custom GA accuracy matches, and in some cases exceeds that of the matlab GA. (b) Runtime distributions for the custom GA and matlab GA. The high complexity of the problem compared to case 1 (designing the inlet as well as the pillar sequence) requires additional generations for convergence, which increases the runtime.

11. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Results for case 6, which uses the new GA framework for hand-drawn flow shapes of the letters that spell IOWA, for microchannel aspect ratio h/w = 0.25

12. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
(a) A simple illustration of how reverse advection is used to create an advection map (b) that contains uniformly distributed information for fluid displacement at the microchannel outlet. The advection map can then be converted into a column-stochastic transition matrix (c), for which every row and column represents a fluid element in the two-dimensional (2D) cross section shown in (a) for the inlet and outlet, respectively. Thus, the displacement for a fluid element that would otherwise be calculated by streamtracing through a 3D domain (d) can be computed using only matrix multiplication (e). The inlet fluid states are discretized in the same way as the transition matrix (e-i), and then reshaped to form a row vector (e-ii). This is then multiplied by a transition matrix (e-iii), which produces the outlet fluid states as a row vector (e-iv). This can then be reshaped into the 2D representation of the domain (e-v).

13. Date of download: 9/29/2017
Copyright © ASME. All rights reserved.
From: Automated Design for Microfluid Flow Sculpting: Multiresolution Approaches, Efficient Encoding, and CUDA Implementation
J. Fluids Eng. 2017;139(3): doi: /
Figure Legend:
Additional results for case 6, which uses the new GA framework for hand-drawn flow shapes of the letters that spell IOWA, for microchannel aspect ratios h/w = 0.5 (a) and h/w = 1.0 (b)