TY - JOUR
T1 - Directed migration of microscale swimmers by an array of shaped obstacles
T2 - Modeling and shape optimization
AU - Tong, Jiajun
AU - Shelley, Michael J.
N1 - Funding Information:
\ast Received by the editors September 14, 2017; accepted for publication (in revised form) June 18, 2018; published electronically September 6, 2018. http://www.siam.org/journals/siap/78-5/M114748.html \bfF \bfu \bfn \bfd \bfi \bfn \bfg : This work was partially supported by NSF grant DMS-1463962. \dagger Applied Mathematics Lab, Courant Institute, New York University, New York, NY 10012 ([email protected], [email protected]). \ddagger Flatiron Institute, Simons Foundation, New York, NY 10010.
PY - 2018
Y1 - 2018
N2 - Achieving macroscopic directed migration of microscale swimmers in a fluid is an important step towards utilizing their autonomous motion. It has been experimentally shown that directed motion can be induced, without any external fields, by certain geometrically asymmetric obstacles due to interaction between their boundaries and the swimmers. In this paper, we propose a kinetic-type model to study swimming and directional migration of microscale bimetallic rods in a periodic array of posts with noncircular cross-sections. Both rod position and orientation are taken into account; rod trapping and release on the post boundaries are modeled by empirically characterizing curvature and orientational dependence of the boundary absorption and desorption. Intensity of the directed rod migration, which we call the normalized net flux, is then defined and computed given the geometry of the post array. We numerically study the effect of post spacings on the flux; we also apply shape optimization to find better post shapes that can induce stronger flux. Inspired by preliminary numerical results on two candidate posts, we perform an approximate analysis on a simplified model to show the key geometric features that a good post should have. Based on this, three new candidate shapes are proposed which give rise to large fluxes. This approach provides an effective tool and guidance for experimentally designing new devices that induce strong directed migration of microscale swimmers.
AB - Achieving macroscopic directed migration of microscale swimmers in a fluid is an important step towards utilizing their autonomous motion. It has been experimentally shown that directed motion can be induced, without any external fields, by certain geometrically asymmetric obstacles due to interaction between their boundaries and the swimmers. In this paper, we propose a kinetic-type model to study swimming and directional migration of microscale bimetallic rods in a periodic array of posts with noncircular cross-sections. Both rod position and orientation are taken into account; rod trapping and release on the post boundaries are modeled by empirically characterizing curvature and orientational dependence of the boundary absorption and desorption. Intensity of the directed rod migration, which we call the normalized net flux, is then defined and computed given the geometry of the post array. We numerically study the effect of post spacings on the flux; we also apply shape optimization to find better post shapes that can induce stronger flux. Inspired by preliminary numerical results on two candidate posts, we perform an approximate analysis on a simplified model to show the key geometric features that a good post should have. Based on this, three new candidate shapes are proposed which give rise to large fluxes. This approach provides an effective tool and guidance for experimentally designing new devices that induce strong directed migration of microscale swimmers.
KW - Boundary absorption and desorption
KW - Directed migration
KW - Gauss-Bonnet theorem
KW - Microscale swimmer
KW - Shape optimization
KW - Shaped obstacle
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U2 - 10.1137/17M1147482
DO - 10.1137/17M1147482
M3 - Article
AN - SCOPUS:85055834363
SN - 0036-1399
VL - 78
SP - 2370
EP - 2392
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 5
ER -