Acoustic streaming in Maxwell fluids generated by standing waves in two-dimensional microchannels

In this work, a semianalytic solution for the acoustic streaming phenomenon, generated by standing waves in Maxwell fluids through a two-dimensional microchannel (resonator), is derived. The mathematical model is non-dimensionalized and several dimensionless parameters that characterize the phenomenon arise: the ratio between the oscillation amplitude of the resonator and the half-wavelength ( $\eta =2A/\lambda _{a}$ ); the product of the fluid relaxation time times the angular frequency known as the Deborah number ( $De=\lambda _{1}\omega$ ); the aspect ratio between the microchannel height and the wavelength ( $\epsilon =2 H_{0}/\lambda _{a}$ ); and the ratio between half the height of the microchannel and the thickness of the viscous boundary layer ( $\alpha =H_{0}/\delta _{\nu }$ ). In the limit when $\eta \ll 1$ , we obtain the hydrodynamic behaviour of the system using a regular perturbation method. In the present work, we show that the acoustic streaming speed is proportional to $\alpha ^{2.65}De^{1.9}$ , and the acoustic pressure varies as $\alpha ^{6/5}De^{1/2}$ . Also, we have found that the growth of inner vortex is due to convective terms in the Maxwell rheological equation. Furthermore, the velocity antinodes show a high dependency on the Deborah number, highlighting the fluid's viscoelastic properties and the appearance of resonance points. Due to the limitations of perturbation methods, we will only analyse narrow microchannels.

The Impact of Variable Fluid Properties on Biomagnetic Maxwell Fluids Past a Stretching Sheet with Slip Velocity and Heat Generation/Absorption

The impact of variable fluid properties (viscosity and thermal conductivity) and magnetic dipole on biomagnetic Maxwell fluid past a stretching sheet with slip velocity and heat generation/absorptionhave been studied. Similarity transformation technique is adopted to obtain the self-similar coupled nonlinear ordinary differential equations. Using similarity variable, the basic governing equations with boundary conditions are transformed and solved in bvp4c technique with MATLAB software. The contribution of different pertinent parameters such as viscosity, thermal conductivity and ferromagnetic parameter on the flow profiles with physical quantities are analyzed and examined through graphically. Results shown that with increasing ferromagnetic parameter, slip parameter, Maxwell parameter, velocity decreases but temperature increases. For accuracy of the proposed model to compare our numerical results in numerically and graphically with the previousliterature under some limiting cases and a good agreement is found. Dhaka Univ. J. Sci. 69(2): 109-115, 2021 (July)

Programmable viscoelasticity in protein-RNA condensates with disordered sticker-spacer polypeptides

Liquid-liquid phase separation of multivalent proteins and RNAs drives the formation of biomolecular condensates that facilitate membrane-free compartmentalization of subcellular processes. With recent advances, it is becoming increasingly clear that biomolecular condensates are network fluids with time-dependent material properties. Here, employing microrheology with optical tweezers, we reveal molecular determinants that govern the viscoelastic behavior of condensates formed by multivalent Arg/Gly-rich sticker-spacer polypeptides and RNA. These condensates behave as Maxwell fluids with an elastically-dominant rheological response at shorter timescales and a liquid-like behavior at longer timescales. The viscous and elastic regimes of these condensates can be tuned by the polypeptide and RNA sequences as well as their mixture compositions. Our results establish a quantitative link between the sequence- and structure-encoded biomolecular interactions at the microscopic scale and the rheological properties of the resulting condensates at the mesoscale, enabling a route to systematically probe and rationally engineer biomolecular condensates with programmable mechanics.

Effect of Heat and Mass Transfer and Magnetic Field on Peristaltic Flow of a Fractional Maxwell Fluid in a Tube

Magnetic field and the fractional Maxwell fluids’ impacts on peristaltic flows within a circular cylinder tube with heat and mass transfer were evaluated while assuming that they are preset with a low Reynolds number and a long wavelength. The analytical solution was deduced for temperature, concentration, axial velocity, tangential stress, and coefficient of heat transfer. Many emerging parameters and their effects on the aspects of the flow were illustrated, and the outcomes were expressed via graphs. Finally, some graphical presentations were made to assess the impacts of various parameters in a peristaltic motion of the fractional fluid in a tube of different nature. The present investigation is essential in many medical applications, such as the description of the gastric juice movement of the small intestine in inserting an endoscope.

Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

Two unsteady motions of incompressible Maxwell fluids between infinite horizontal parallel plates embedded in a porous medium are analytically studied to get exact solutions using the finite Fourier cosine transform. The motion is induced by the lower plate that applies time-dependent shear stresses to the fluid. The solutions that have been obtained satisfy all imposed initial and boundary conditions. They can be easily reduced as limiting cases to known solutions for the incompressible Newtonian fluids. For a check of their correctness, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The effects of physical parameters on the fluid motion are graphically emphasized and discussed. Required time to reach the steady-state is also determined. It is found that the steady-state is rather obtained for Newtonian fluids as compared with Maxwell fluids. Furthermore, the effect of the side walls on the fluid motion is more effective in the case of Newtonian fluids.

Exact Solution of the Start-Up Electroosmotic Flow of Generalized Maxwell Fluids in Triangular Microducts

Unsteady electroosmotic flow of generalized Maxwell fluids in triangular microducts is investigated. The governing equation is formulated with Caputo-Fabrizio time-fractional derivatives whose orders are distributed in the interval [0, 1). The linear momentum and the Poisson-Boltzmann equations are solved analytically in tandem in the triangular region with the help of the Helmholtz eigenvalue problem and Laplace transforms. The analytical solution developed is exact. The solution technique we use is new, leads to exact solutions, is completely different from those available in the literature and is applicable to other similar problems. The new expression for the velocity field displays experimentally observed 'velocity overshoot' as opposed to existing analytical studies none of which can predict the overshoot phenomenon. We show that when Caputo-Fabrizio time-fractional derivatives approach unity the exact solution for the classical upper convected Maxwell fluid is obtained. The presence of elasticity in the constitutive structure alters the Newtonian velocity profiles drastically. The influence of pertinent parameters on the flow field is explored.