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We assign a value of k/2 to those springs that are located on the cilia surfaces and k/4 to the springs at the edges. We also set the LSM masses equal to m/2 and m/4 for nodes at the surfaces and edges, respectively
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We assign a value of k/2 to those springs that are located on the cilia surfaces and k/4 to the springs at the edges. We also set the LSM masses equal to m/2 and m/4 for nodes at the surfaces and edges, respectively.
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Note that the Poisson's ratio of polymers can vary from 0.3 to -0.7 and be tailored by blending.32 Thus, polymers blends with Poisson's ratios of ∼0.25 can be synthesized.33
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Note that the cilia are constructed from a lattice with only four nodes across. To verify the accuracy of the model, we simulated the bending of a cilium due to a perpendicular force applied to its free end and found that an increase in lattice resolution effectively does not affect the deflection. Note also that for a 50% declination me difference between our LSM model and the linear theory prediction is about 10% and it increases to about 20% for a 100% declination (i.e., when declination is equal to the cilium length).
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Note that the cilia are constructed from a lattice with only four nodes across. To verify the accuracy of the model, we simulated the bending of a cilium due to a perpendicular force applied to its free end and found that an increase in lattice resolution effectively does not affect the deflection. Note also that for a 50% declination me difference between our LSM model and the linear theory prediction is about 10% and it increases to about 20% for a 100% declination (i.e., when declination is equal to the cilium length).
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A range of polymeric materials could be used to manufacture artificial cilia with these sperm numbers. As an example, let us consider a cilium that is 10 μm in length and 1 μm in diameter oscillating with a frequency of about 10 Hz in water, whose viscosity is μ ≈ s 10-3 kg/m·s and density is ρ ≈ 103 kg/m3. For such cilia, a sperm number in the range from 1 to 10 can be obtained with polymers having a modulus of approximately 20 Pa-200 kPa, which is in the range of experimentally realistic values. These values yield a bending rigidity EI in the range of 10-24 to 10-20 N·m2 and a driving force amplitude of 0.1 pN < a < 1 nN. Alternatively, the relevant oscillation regimes can be excited by varying the driving frequency in the range of 10 Hz and 100 kHz
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2 and a driving force amplitude of 0.1 pN < a < 1 nN. Alternatively, the relevant oscillation regimes can be excited by varying the driving frequency in the range of 10 Hz and 100 kHz.
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