Reexamining the Emergence and Stability of the Square Cylinder Phase in Block Copolymers.

Recently, a few AB-type multiblock copolymers have been successfully designed to form stable square cylinder phase based on self-consistent field theory (SCFT) calculations. The previous works only identify the stability region of the square phase but not analyzing its stability, which is closely related to the free-energy landscape. In this work, we have reexamined the stability of the square phase in B 1 A 1 B 2 A 2 B 3 ${{{\rm B}}_{1}{{\rm A}}_{1}{{\rm B}}_{2}{{\rm A}}_{2}{{\rm B}}_{3}}$ linear pentablock and ( B 1 A B 2 )​ 5 ${({{\rm B}}_{1}{\rm A}{{\rm B}}_{2}{)}_{5}}$ star triblock copolymers by drawing the free-energy landscape with respect to the two dimensions of a rectangular unit cell. Our results demonstrate that the square phase continuously transfers to the rectangular phase as the degree of packing frustration is gradually released. Moreover, the prolate contour lines of the free-energy landscape indicate the weak stability of the square phase in the B 1 A 1 B 2 A 2 B 3 ${{{\rm B}}_{1}{{\rm A}}_{1}{{\rm B}}_{2}{{\rm A}}_{2}{{\rm B}}_{3}}$ copolymer. In contrast, the stability of the square phase is notably improved in the ( B 1 A B 2 )​ 5 ${({{\rm B}}_{1}{\rm A}{{\rm B}}_{2}{)}_{5}}$ copolymer due to its enhanced concentration of bridging configurations. Our work sheds light on the understanding of the stability of the square cylinder phase in block copolymers. Accordingly, we propose some possible strategies for further designing new AB-type block copolymer systems to obtain more stable square phase.

Reduction of fluid forces for flow past side-by-side cylinders using downstream attached splitter plates.

A two-dimensional numerical simulation is performed to investigate the drag reduction and vortex shedding suppression behind three square cylinders with attached splitter plates in the downstream region at a low Reynolds number (Re = 150). Numerical calculations are carried out using the lattice Boltzmann method. The study is carried out for various values of gap spacing between the cylinders and different splitter plate lengths. The vortices are completely chaotic at very small spacing, as observed. The splitter plates are critical in suppressing shedding and reducing drag on the objects. The splitter plates with lengths greater than two fully control the jet interaction at low spacing values. There is maximum percentage reduction in CDmean for small spacing and the selected largest splitter plate length. Furthermore, systematic investigation reveals that splitter plates significantly suppress the fluctuating lift in addition to drastically reducing the drag.