Analytical Solution of Stationary Coupled Thermoelasticity Problem for Inhomogeneous Structures

A mathematical statement for the coupled stationary thermoelasticity is given on the basis of a variational approach and the contact boundary problem is formulated to consider inhomogeneous materials. The structure of general representation of the solution from the set of the auxiliary potentials is established. The potentials are analyzed depending on the parameters of the model, taking into account the restrictions associated with additional requirements for the positive definiteness of the potential energy density for the coupled problem in the one-dimensional case. The novelty of this work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields. From a mathematical point of view, this leads to a change in the roots of the characteristic equation and affects the structure of the solution. Contact boundary value problems are formulated for modeling inhomogeneous materials and a solution for a layered structure is constructed. The analysis of the influence of the model parameters on the structure of the solution is given. The features of the distribution of mechanical and thermal fields in the region of phase contact with a change in the parameters, which are characteristic only for gradient theories of coupled thermoelasticity and stationary thermal conductivity, are discussed. It is shown, for example, that taking into account the additional parameter of connectivity of gradient fields of deformations and temperatures predicts the appearance of rapidly changing temperature fields and significant localization of heat fluxes in the vicinity of phase contact in inhomogeneous materials.

Removal of Heavy Metal Ions from One- and Two-Component Solutions via Adsorption on N-Doped Activated Carbon

This paper deals with the adsorption of heavy metal ions (Cu2+ and Zn2+) on the carbonaceous materials obtained by chemical activation and ammoxidation of Polish brown coal. The effects of phase contact time, initial metal ion concentration, solution pH, and temperature, as well as the presence of competitive ions in solution, on the adsorption capacity of activated carbons were examined. It has been shown that the sample modified by introduction of nitrogen functional groups into carbon structure exhibits a greater ability to uptake heavy metals than unmodified activated carbon. It has also been found that the adsorption capacity increases with the increasing initial concentration of the solution and the phase contact time. The maximum adsorption was found at pH = 8.0 for Cu(II) and pH = 6.0 for Zn(II). For all samples, better fit to the experimental data was obtained with a Langmuir isotherm than a Freundlich one. A better fit of the kinetic data was achieved using the pseudo-second order model.

The wettability and micro-equilibrium of different essence liquids to alkali-treated kapok fiber

Kapok fiber is a natural hollow fiber that has superior biocompatibility and biodegradability and is naturally antibacterial. Because of its unique properties, it has great potential in the application of postoperative repair dressings. The wettability and micro-equilibrium of kapok fibers play a critical role in dressing applications. In this study, the critical adhesion volume and adhesion energy of essence liquid to alkali-treated kapok fiber (AKF) were quantitatively calculated to explore the wettability and micro-equilibrium through the equilibrium wetting theory. Meanwhile, the three-phase contact line (TCL) structure was described. The results showed that the critical adhesion volumes of the three types of essence liquid for AKF were 3.45, 3.81, and 4.12 μL, respectively. Moreover, the critical volumes and low error rates derived from the equilibrium wetting theory were 3.41 μL and 1.16%, 3.99 μL and 4.51%, and 4.60 μL and 10.43%, respectively. Therefore, the critical volume of adhesion could be well calculated by the theoretical model. The average adhesive energies of essence liquid to the AKF were 0.38, 0.45, and 0.56 J, respectively, caused by the difference in liquids properties. The TCL showed a mechanical lock and bonding points at both ends because of the curvature difference and higher surface energy. These results are proposed to inspire the design of a liquid carrier of kapok fibers based on the fiber network structure.

Reduced-Order Model With Foot Tipping Allowance for Legged Balancing

Tipping is an instrumental aspect of multi-phase contact situations that arise during common tasks such as the locomotion of legged systems. Despite its importance in balance recovery, tipping is often ignored in trajectory optimization due to the lack of existing methods that are able to actively plan and optimize for unspecified contacts. Trajectory Optimization based on nonlinear programming requires a priori knowledge about anticipated contact changes, such as their order and timing, in order to generate physically feasible motions. In this paper, an optimization framework with conditional constraints is established for direct collocation in trajectory optimization for legged balancing with foot tipping allowance. The proposed approach can evaluate the timing of contact phases without preplanned contact forces or sequences of events, which is not possible with conventional methods. This optimization framework is demonstrated by computing the balanced regions of two reduced-order models of a legged system, namely, inverted-pendulum-based models without and with a flywheel, and is verified with control simulations. The contribution of tipping to balance stability is quantified and compared to prior results obtained without tipping allowance. The framework presented can also be generalized to other multi-phase contact scenarios, such as rolling and sliding, where unspecified discontinuous changes in contact occur with important consequences in the performance of legged systems.

Pattern Formation upon Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers

The formation of coffee-ring deposits upon evaporation of sessile droplets containing mixtures of poly(diallyldimethylammonium chloride) (PDADMAC) and two different anionic surfactants were studied. This process is driven by the Marangoni stresses resulting from the formation of surface-active polyelectrolyte–surfactant complexes in solution and the salt arising from the release of counterions. The morphologies of the deposits appear to be dependent on the surfactant concentration, independent of their chemical nature, and consist of a peripheral coffee ring composed of PDADMAC and PDADMAC–surfactant complexes, and a secondary region of dendrite-like structures of pure NaCl at the interior of the residue formed at the end of the evaporation. This is compatible with a hydrodynamic flow associated with the Marangoni stress from the apex of the drop to the three-phase contact line for those cases in which the concentration of the complexes dominates the surface tension, whereas it is reversed when most of the PDADMAC and the complexes have been deposited at the rim and the bulk contains mainly salt.

On the mechanism of droplet rolling and spinning in inclined hydrophobic plates in wedge with different wetting states

A water droplet rolling and spinning in an inclined hydrophobic wedge with different wetting states of wedge plates is examined pertinent to self-cleaning applications. The droplet motion in the hydrophobic wedge is simulated in 3D space incorporating the experimental data. A high-speed recording system is used to store the motion of droplets in 3D space and a tracker program is utilized to quantify the recorded data in terms of droplet translational, rotational, spinning, and slipping velocities. The predictions of flow velocity in the droplet fluid are compared with those of experimental results. The findings revealed that velocity predictions agree with those of the experimental results. Tangential momentum generated, via droplet adhesion along the three-phase contact line on the hydrophobic plate surfaces, creates the spinning motion on the rolling droplet in the wedge. The flow field generated in the droplet fluid is considerably influenced by the shear rate created at the interface between the droplet fluid and hydrophobic plate surfaces. Besides, droplet wobbling under the influence of gravity contributes to the flow inside the rolling and spinning droplet. The parallel-sided droplet path is resulted for droplet emerging from the wedge over the dusty surface.