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Register a new userCritical behaviour in the nonlinear elastic response of hydrogels
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In this paper we study the elastic response of synthetic hydrogels to an applied shear stress. The hydrogels studied here have previously been shown to mimic the behaviour of biopolymer networks when they are sufficiently far above the gel point. We show that near the gel point they exhibit an elastic response that is consistent with the predicted critical behaviour of networks near or below the isostatic point of marginal stability. This point separates rigid and floppy states, distinguished by the presence or absence of finite linear elastic moduli. Recent theoretical work has also focused on the response of such networks to finite or large deformations, both near and below the isostatic point. Despite this interest, experimental evidence for the existence of criticality in such networks has been lacking. Using computer simulations, we identify critical signatures in the mechanical response of sub-isostatic networks as a function of applied shear stress. We also present experimental evidence consistent with these predictions. Furthermore, our results show the existence of two distinct critical regimes, one of which arises from the nonlinear stretch response of semi-flexible polymers..
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Taking into account the structural transition and long-range interaction (lattice effect), we resort to the Ewald-Kornfeld formulation and developed Maxwell-Garnett theory for uniaxially anisotropic suspensions to calculate the effective permeability of inverse ferrofluids. And we also consider the effect of volume fraction to the magnetophoretic force on the nonmagnetic spherical particles submerged in ferrofluids in the presence of nonuniform magnetic field. We find that the coupling of ac and dc field case can lead to fundamental and third harmonic response in the effective magnetophoresis and changing the aspect ratio in both prolate and oblate particles can alter the harmonic and nonharmonic response and cause the magnetophoretic force vanish.
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