On Peculiarities of Betatron Oscillations of Accelerated Electron Bunches in Capillary Waveguides

It is shown that the dynamics of electrons accelerated in narrow capillary waveguides is significantly influenced by the parametric excitation of their betatron oscillations. On the one hand, this excitation can irreversibly spoil the emittance of an accelerated electron bunch that limits the possibilities of their practical use. On the other hand, controlled parametric excitation of betatron oscillations can be used to generate short-pulse sources of synchrotron radiation. The article analyzes the regions of parametric instabilities, their dependence on the parameters of accelerated electron bunches and guiding structures, and their influence on the dynamics of accelerated electrons. The parameters of the generated synchrotron radiation are also estimated. Measurements of the spectral parameters of synchrotron radiation can serve as a tool for diagnostics of betatron oscillations and their excitation in the case of parametric resonances.

Transient analysis of combined electroosmotic and pressure driven flow with multi-layer immiscible fluids in a narrow capillary

Because the development of techniques for pumping parallel flows in miniaturized systems are required, in the present investigation, a semi-analytical solution based in the matrix inverse method and by Laplace transform for the transient flow of multi-layer immiscible fluids in a narrow capillary, under electroosmotic and pressure driven effects, is obtained. The dimensionless mathematical model to solve the electric potential distribution and the velocity field in the start-up of flow, consist on the Poisson-Boltzmann and momentum equations, respectively. Here, the transported fluids are considered symmetrical electrolytes and because the interfaces between them are polarizable and impermeable to charged particles, interesting interfacial effects appear on the velocity profiles when an external electric field is applied. The results show graphically the influence of the different dimensionless parameters involved in the dynamics of the fluid flow. This study demonstrates that by considering electrical interfacial effects, produce velocity jumps at liquid-liquid interfaces, whose magnitude and direction depend on the concentration and polarity of electric charges in those regions; finally, it is observed that the time to reach the steady-state regime of the fluid flow is only controlled by the dimensionless viscosity ratios. This investigation is a theoretical contribution to simulate transient multi-layer fluid flows under electric interfacial effects, covering different implications that emerge in the design of small devices into the chemical, biological and clinical areas.

Analysis of Combined Electroosmotic and Pressure Driven Flow of Multilayer Immiscible Fluids in a Narrow Capillary

This paper presents the analytical solution of a combined electroosmotic and pressure driven flow of multilayer immiscible fluids in a narrow capillary. The mathematical model is based in the Poisson-Boltzmann equation and the modified Navier-Stokes equations. In the steady-state analysis, we consider different conditions at the interfaces between the fluids as potential differences, surface charge densities and electro-viscous stresses balances, which are discussed in detail. Results show the transport phenomena coupled in the description of velocity distribution, by the analyzing of the dimensionless parameters obtained, such as: potential differences, surface charge densities, electrokinetic parameters, term involving the external pressure gradient, ratios of viscosity and of dielectric permittivity. Here, the presence of a net electric charges balance at the interfaces breaks the continuity of the electric potential distributions and viscous shear stresses, modifying the flow field; thus, the electrical conditions established at the interfaces play an important role on the flow behavior. The present work, in which the velocity field is described, aims to be an important contribution in the development of theoretical models that provide a better understanding about labs-on-a-chip design.

Transient penetration of a viscoelastic fluid in a narrow capillary channel

This article describes an unexplored transport phenomenon where a mildly viscoelastic medium encroaches a narrow capillary channel under the action of surface-tension force. The ultimate goal of the study is to provide the penetration length and the intrusion rate of the liquid as functions of time. The resulting analysis would be instrumental in building an inexpensive and convenient rheometric device which can measure the temporal scale for viscoelastic relaxation from the stored data of the aforementioned quantities. The key step in the formulation is a transient eigenfunction expansion of the instantaneous velocity profile. The time-dependent amplitude of the expansion as well as the intruded length are governed by a system of integro-differential relations which are derived by exploiting the mass and momentum conservation principles. The obtained integro-differential equations are simultaneously solved by using a fourth-order Runge–Kutta method assuming a start-up problem from rest. The resulting numerical solution properly represents the predominantly one-dimensional flow which gradually slows down after an initial acceleration and subsequent oscillation. The computational findings are independently verified by two separate perturbation theories. The first of these is based on a Weissenberg number expansion revealing the departure in the unsteady imbibition due to small but finite viscoelasticity. In contrast, the second one explains the long-time behaviour of the system by analytically predicting the decay features of the dynamics. These asymptotic results unequivocally corroborate the simulation inferring the accuracy of the numerics as well as the utility of the simplified mathematical models.