How inertial lift affects the dynamics of a microswimmer in Poiseuille flow

The transport of motile microorganisms is strongly influenced by fluid flows that are ubiquitous in biological environments. Here we demonstrate the impact of fluid inertia. We analyze the dynamics of a microswimmer in pressure-driven Poiseuille flow, where fluid inertia is small but non-negligible. Using perturbation theory and the reciprocal theorem, we show that in addition to the classical inertial lift of passive particles, the active nature generates a ‘swimming lift’, which we evaluate for neutral and pusher/puller-type swimmers. Accounting for fluid inertia engenders a rich spectrum of complex dynamics including bistable states, where tumbling coexists with stable centerline swimming or swinging. The dynamics is sensitive to the swimmer’s hydrodynamic signature and goes well beyond the findings at vanishing fluid inertia. Our work will have non-trivial implications on the transport and dispersion of active suspensions in microchannels.

Soft-lubrication interactions between a rigid sphere and an elastic wall

The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic interactions experienced by the particle. Here, we derive a soft-lubrication model, in order to compute all the forces and torque applied on a rigid sphere that is free to translate and rotate near an elastic wall. We focus on the limit of small deformations of the surface with respect to the fluid-gap thickness, and perform a perturbation analysis in dimensionless compliance. The response is computed in the framework of linear elasticity, for planar elastic substrates in the limiting cases of thick and thin layers. The EHD forces are also obtained analytically using the Lorentz reciprocal theorem.

Constraints of Pore-Bulk Strain Ratio and Interference Time on the Evolution of Coal Permeability during CO2 Injection

CO2 injection into coal seam triggers a series of processes that are coupled all together through a permeability model. Previous studies have shown that current permeability models cannot explain experimental data as reported in the literature. This knowledge gap defines the goal of this study. We hypothesize that this failure originates from the assumption that the pore strain is the same as the bulk strain in order to satisfy the Betti-Maxwell reciprocal theorem. This assumption is valid only for the initial state without gas sorption and deformation and for the ultimate state with uniform gas sorption and uniform deformation within the REV (representative elementary volume). In this study, we introduce the pore-bulk strain ratio and interference time to characterize the process of gas sorption and its associated nonuniform deformation from the initial state to the ultimate state. This leads to a new nonequilibrium permeability model. We use the model to fully couple the coal deformation and gas flow. This new coupled model captures the impact of coal local transient behaviors on gas flow. Results of this study clearly show that coal permeability is constrained by the magnitudes of initial and ultimate pore-bulk strain ratios and interference time, that current permeability data in the literature are within these bounds, and that the evolutions of coal permeability all experience similar stages from the initial value to the ultimate one.

A Sphere Held Fixed in a Poiseuille Flow near a Rough Wall

We present here an analytical calculation of the hydrodynamic interactions between a smooth spherical particle held fixed in a Poiseuille flow and a rough wall. By the assumption of a low Reynolds number, the flow around a fixed spherical particle is described by the Stokes equations. The surface of the rigid wall has periodic corrugations, with small amplitude compared with the sphere radius. The asymptotic development coupled with the Lorentz reciprocal theorem are used to find the analytical solution of the couple, lift and drag forces exerted on the particle, generated by the second-order flow due to the wall roughness. These hydrodynamic effects are evaluated in terms of amplitude and period of roughness and also in terms of the distance between sphere and wall.

Nonreciprocal elasticity and the realization of static and dynamic nonreciprocity

The realization of the mechanical nonreciprocity requires breaking either the time-reversal symmetry or the material deformation symmetry. The time-reversal asymmetry was the commonly adopted approach to realize dynamic nonreciprocity. However, a static nonreciprocity requires—with no any other option—breaking the material deformation symmetry. By virtue of the Maxwell–Betti reciprocal theorem, the achievement of the static nonreciprocity seems to be conditional by the use of a nonlinear material. Here, we further investigate this and demonstrate a novel “nonreciprocal elasticity” concept. We investigated the conditions of the attainment of effective static nonreciprocity. We revealed that the realization of static nonreciprocity requires breaking the material deformation symmetry under the same kinematical and kinetical conditions, which can be achieved only and only if the material exhibits a nonreciprocal elasticity. By means of experimental and topological mechanics, we demonstrate that the realization of static nonreciprocity requires nonreciprocal elasticity no matter what the material is linear or nonlinear. We experimentally demonstrated linear and nonlinear metamaterials with nonreciprocal elasticities. The developed metamaterials were used to demonstrate that nonreciprocal elasticity is essential to realize static nonreciprocal-topological systems. The nonreciprocal elasticity developed here will open new venues of the design of metamaterials that can effectively break the material deformation symmetry and achieve, both, static and dynamic nonreciprocity.

Shear behavior of I-shaped wood-steel composite beam

To expand the application of wood as a building material, a new type of I-shaped wood-steel beam that consisted of laminated veneer lumber and cold-formed thin-walled steel was considered in this paper. The shear performance of nine wood-steel composite beams was tested to evaluate the effects of shear span ratio, web thickness, and flange thickness. Then, the failure pattern and failure mechanism of the composite beams were analyzed. The main affecting factors of shear capacities were also discussed. Furthermore, the calculation formula for bearing capacities of composite beams was established and the calculation results were compared with the experimental results. The experimental results showed that the combined effect of composite beams was excellent. The shear capacity was mainly affected by shear span ratio and web thickness. The calculation formula of the shear capacity was established based on the shear flow theory and the specification for structural steel buildings. The formula was derived from the micro-segment balance method and the reciprocal theorem of shear stress. The calculation results according to the formula were in good agreement with the experimental values.

Some Results in Green–Lindsay Thermoelasticity of Bodies with Dipolar Structure

The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive.

Variational principles and generalized Hill’s bounds in micromechanics of linear peridynamic random structure composites

We consider a static problem for statistically homogeneous matrix linear peridynamic composite materials (CMs). The basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated non-local force interactions between infinitesimal particles. In contrast to these classical local and non-local theories, the peridynamic equation of motion introduced by Silling ( J Mech Phys Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. Estimation of effective moduli of peridynamic CMs is performed by generalization of some methods used in locally elastic micromechanics. Namely, the admissible displacement and force fields are defined. The theorem of work and energy, Betti’s reciprocal theorem, and the theorem of virtual work are proved. Principles of minimum of both potential energy and complimentary energy are generalized. The strain energy bounds are estimated for both the displacement and force homogeneous volumetric boundary conditions. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CM are generalized to the case of peridynamics, and the energetic definition of effective elastic moduli is proposed. Generalized Hill’s bounds on the effective elastic moduli of peridynamic random structure composites are obtained. In contrast to the classical Hill’s bounds, in the new bounds, comparable scales of the inclusion size and horizon are taken into account that lead to dependance of the bounds on both the size and shape of the inclusions. The numerical examples are considered for the 1D case.