This paper presents an analytical study of an infinite expanse of uniform flow of steady axisymmetric Stokes flow of an incompressible Newtonian fluid around the spherical drop of Reiner-Rivlin liquid coated with the permeable layer with the assumption that the liquid located outside the capsule penetrates into the permeable layer, but it is not mingled with the liquid located in the internal concave of capsule. The flow inside the permeable layer is described by the Brinkman equation. The viscosity of the permeable medium is assumed to be same as pure liquid. The stream function solution for the outer flow field is obtained in terms of modified Bessel functions and Gegenbauer functions, and for the inner flow field, the stream function solution is obtained by expanding the stream function in terms of S. The flow fields are determined explicitly by matching the boundary conditions at the pure liquid-porous interface, porous-Reiner-Rivlin liquid interface, and uniform velocity at infinity. The drag force experienced by the capsule is evaluated, and its variation with regard to permeability parameter a, dimensionless parameter S, ratio of viscosities l2, and thickness of permeable layer d is studied and graphs plotted against these parameters. Several cases of interest are deduced from the present analysis. It is observed that the cross-viscosity increases the drag force, whereas the thickness d decreases the drag on capsule. It is also observed that the drag force is increasing or decreasing function of permeability parameter for l2 < 1.

This paper concerns an analytical study of a steady axisymmetric uniform flow of an incompressible micropolar fluid past a permeable sphere that contains a solid sphere. The mathematical expression for the flow fields are obtained in terms of stream function by using modified Bessel’ s function and Gegenbauer function. No-slip condition, zero microrotation components, continuity of normal velocity which is equal to the filtration velocity on the surface of the sphere are used as boundary conditions. It is assumed that the fluid obeys Darcy law at the permeable surface. The internal and external drag force exerted by the fluid on the sphere, flow rate and the relevant quantities such as pressures, microrotation vectors have been calculated. It is observed that drag is greater for impermeable sphere as compared to permeable sphere. As permeability parameter increases the flow rate also increases rapidly. Various useful results are obtained and compared with the previous particular cases.

This study focuses on the investigation of intelligent form-finding and vibration analysis of a triangular polyhedral tensegrity that is enclosed within a sphere and subjected to external loads. The nonlinear dynamic equations of the system are derived using the Lagrangian approach and the finite element method. The proposed form-finding approach, which is based on a basic genetic algorithm, can determine regular or irregular tensegrity shapes without dimensional constraints. Stable tensegrity structures are generated from random configurations and based on defined constraints (nodes located on the sphere, parallelism, and area of upper and lower surfaces), and shape finding is performed using the fitness function of the genetic algorithm and multi-objective optimization goals. The genetic algorithm's efficacy in determining the shape of structures with unpredictable configurations is evaluated in two distinct scenarios: one involving a known connection matrix and the other involving fixed or random member positions (struts and cables). The shapes obtained from the algorithm suggested in this study are validated using the force density approach, and their vibration characteristics are examined. The findings of the comparative study demonstrate the efficacy of the proposed methodology in determining the vibrational behavior of tensegrity structures through the utilization of intelligent shape seeking techniques.

The aim of this study was to evaluate the effect of addition of three different permeable (Glycerol, Dimethyl formamide and Dimethyl acetamid) and two different non-permeable cryoprotectant (Trehalose and sucrose) to the extender on freezing capacity of Turkmen stallions’ sperm. Four healthy mature Turkmen stallions (8-10 years old) were used. Collected semen from stallions were processed and pooled after gel removal and before allocating to treatments [glycerol, dimethyl formamide and dimethyl acetamid (5 or 7 percent) and trehalose or sucrose (50 and 100 mM)]. The prepared treatments were frozen according to a standard method. After thawing viability and motility of all treatments were accessed. The results showed that the viability and motility of spermatozoa treated with extender containing 5 or 7 % dimethyl formamide (68. 6 ± 0. 93 and 63. 2 ± 2. 22 respectively) or dimethyl acetamid (68. 6 ± 1. 69 and 63. 6 ± 2. 76 respectively) were significantly higher than those which treated with 5 or 7 % glycerol (56. 8 ± 3. 06 and 55. 6 ± 1. 03 respectively) (P<0. 05). Also, results showed that the viability and motility of stallion spermatozoa were not influenced by the non-permeable cryoprotectants (P<0. 05). We concluded that dimethyl acetamid and dimethyl formamide can be proper alternatives for glycerol as a common stallion spermatozoa cryoprotectant and the sucrose and trehalose had no significant effect on the stallion sperm quality after freeze-thawing process.