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This paper investigates the peristaltic flow of viscoelastic fluid represented by Jeffrey model in presence of transverse magnetic field under long wavelength and low Reynolds number assumptions. The expressions of pressure gradient, volume flow rate, average volume flow rate and local wall shear stress are obtained. The effects of transverse magnetic field, electrical conductivity (i.e., Hartman number M), relaxation time and retardation time on pressure difference, local wall shear stress, and mechanical efficiency of peristaltic pump are discussed. Reflux limit for viscoelastic fluid is also found and the effects of all parameters on reflux phenomena are discussed. Comparative study of integral and nonintegral number of waves propagate in a train is presented.

Peristaltic motions are used in a variety of industrial and real-world problems such as pumping mixture with such a high solid content from the mining sector, biogases, sewers facilities, food flow through the gastrointestinal system, urinary tract, and fallopian tube of human females where extremely abrasive, gritty, and viscous fluids are present. The goal of this theoretical study is to examine the impact of the lubricated walls on the peristaltic transport of a viscous fluid in an asymmetric medium. The interfacial condition is derived under the assumptions of thin film lubrication and long wavelength approximation. The theory of a dynamical system is utilized to examine the lubrication effects on the position and bifurcation of stagnation points in the flow. For this, three flow distributions, backward flow, trapping, and augmented flow, are discussed. The obtained system of equations is solved numerically by the shooting method based on Newton–Raphson root-finding algorithm in Mathematica. The prime findings for the velocity profile, pressure increase, trapping, and reflux criteria are illustrated through graphs. Bifurcation occurs earlier by increasing the influence of lubrication. The trapping area diminishes and the augmented flow section expands with the lubrication parameter. This will be useful for medical engineering, industrial and physiological systems. The comparison for the particular case of no-slip condition is presented and found to be in excellent agreement.

This is an attempt to investigate swallowing of a food bolus through oesophagus by modelling it as an unsteady peristaltic transport of Maxwell and magnetohydrodynamic (MHD) fluids in channels of finite length. The walls of the channels are subjected to progressive transverse contraction waves so that the natural oesophageal wall contractions are matched. The analysis is carried out in non-dimensional form by using long wavelength approximations. The expressions for axial and transverse velocities are derived and pressure across a wavelength is estimated. The reflux limit is determined for both the fluids. Mechanical efficiency for MHD fluids is also obtained. Physical interpretations reveal the behaviour of the flows of masticated viscoelastic food materials such as bread, white eggs etc. and saline water that is represented by MHD model in the oesophagus. It is found that fluids represented by Maxwell fluid are more swallow-friendly than Newtonian fluids while normal water is easier to swallow than saline water which is an MHD fluid. It is also revealed that relaxation time, a parameter of Maxwell model, has no effects on local wall shear stress and reflux limit whereas magneto-hydrodynamic parameters make the fluid more prone to flow reversal. It is found that if the transverse magnetic field and the electric conductivity increase, the pumping machinery requires more pressure for pushing the fluid forward. In other words, pumping has to work more efficiently. Finally, it is revealed that the peaks of pressure are identical, in case, an integral number of waves propagate along the channel while the peaks are of unequal size in the non-integral case.

Transporting content in most biological systems is done through peristaltic transport phenomenon, examples of which include urine transport from kidney to bladder, swallowing of food through esophagus, the movement of chyme in small intestine, lymph transport in the lymphatic vessels, and in the vasomotion of small blood vessels such as arterioles. The present investigation simulated a transient peristaltic transport by developing a model based on fluid–solid interaction (FSI) method. The conduit in which peristaltic flow occurred was assumed to be axisymmetric. The propagating wave was simulated by prescribing a set of displacements, along the radial direction, on the wall. Both fluid and solid domains underwent large deformations as load applied. Due to large deformations, the adaptive discretization was considered. The ADINA 8.5 software, as finite element analytical software, was applied to study peristaltic transport. The results indicated that the present numerical method can properly introduce the features of the flow. The obtained results reveal that as amplitude ratio increases, axial velocity will increase, resulting in an increase in volume flux. Volume flux fluctuates through the passage of time in a cycle and along a wavelength. An increase in index of non-Newtonian fluid results in a decrease in velocity and increase in wall shear stress. It is observed that by increasing the amplitude of propagating wave, reflux will be increased; meanwhile, peristalsis works as a more efficient pumping process against the pressure applied as a boundary condition. The discussion on reflux according to its physiological importance seems to be helpful, thus the net displacement of the fluid particles after the transit of a single wave was calculated.

The investigation is to explore the transportation of a viscoelastic fluid by peristalsis in a channel as well as in a circular cylindrical tube by considering Jeffrey-model. In order to apply the model to the swallowing of food-bolus through the oesophagus, the wave equation assumed to propagate along the walls is such that the walls contract in the transverse/radial direction and relax but do not expand further. Solutions have been presented in the closed form by using small Reynolds number and long wavelength approximations. The expressions of pressure gradient, volume flow rate and average volume flow rate have been derived. It is revealed on the basis of computational investigation that for a fixed flow rate, pressure decreases when the ratio of relaxation time to retardation time is increased. In both the channel and tubular flows, the pressure decreases on increasing the ratio of relaxation time to retardation time if the averaged flow rate is less than the maximum flow rate. It is also revealed that the maximum tubular flow rate is higher than that of the channel-flow. It is further found through the theoretical analysis that mechanical efficiency, reflux and local wall shear stress remain unaffected by viscoelastic property of the fluid modelled as Jeffrey-fluid.

This model is targeted to study the swallowing of peristaltically driven food stuff such as jelly, tomato puree, soup, concentrated fruit juices and honey in the aboral direction confined to an oesophagus by modeling it as finite channel. Considering such highly concentrated fluids as Casson fluid in the fully stretched activated state, the dependence of pressure on space and time has been investigated for time averaged flow rate. Pressure distribution has been studied along the oesophageal length for an integral and also a non-integral number of waves at different time instants. Local wall shear stress and the role of yield stress have also been the areas of investigation. Mechanical efficiency of oesophageal pump during the Casson food transportation has been obtained. Reflux limit of perstaltically driven flow of Casson food bolus has also been discussed. The effect of Casson food bolus vis-à-vis Newtonian food bolus has been compared analytically, numerically and computationally from investigation point of view. It is observed that the pressure distribution is even and uneven respectively for the case of integral and non-integral number of waves. It is also concluded that it is not as easy to swallow Casson fluids (such as concentrated jelly, honey, soup, juice, etc.) as Newtonian fluids (such as water). As plug flow region widens, the pressure difference increases, indicating thereby that the averaged flow rate will be less for a Casson fluid. Physically, the oesophagus works more to swallow fluids with high concentration. It is also inferred that such fluids are more prone to reflux.

To obtain the best appropriate method and optimum extraction conditions of total alkaloids from zizyphi spinosi semen (ZSS), the conditions of reflux extraction were optimized by single factor experiment and orthogonal design respectively. the experiment results were as follows: 20% acetic acid resolved in ethanol as extracting solvent (EtOH:HAc=80:20 (v/v)), ratio of liquid to solid=20:1(ml:g), 4.0 h, 70 °C, and these conditions were optimum conditions after validation of experiment. The total alkaloids of ZSS extracted by this method could provide a powerful guarantee for studying ingredients and activities of alkaloids in ZSS.