Date:
Wed, 22/01/202512:00-13:30
Location:
Danciger B Building, Seminar room
Lecturer: Prof. Yoav Tsori, Ben-Gurion University in the Negev
Abstract:
The Hall effect in flowing electrolytes had been speculated and tested just a few years after the discovery of the original effect in 1879. The initial attempts were unsuccessful or controversial. In 1897, Donnan calculated the weak Hall voltage for an electrolyte in uniform magnetic field whose charge carriers are driven by an electric field. In the following decades, theoretical works missed important terms or incorrectly calculated the electric field distribution. Here, we describe the stronger ``Hall effects'' in laminar, one-dimensional, and incompressible flows of electrolytes driven by pressure gradients or moving surfaces. In a steady state, the hydrodynamic stress and Lorentz and entropic forces add to give a vanishing ionic flux. The electrical charge, ion densities, and conductivity are subsequently found from solution of a nonlinear eigenvalue Poisson-Boltzmann equation with an external ``force'' that depends on the hydrodynamic flow profile and magnetic field. For Poiseuille flow in a channel, Hall voltage and other quantities depend continuously the magnetic field. For a fluid in Taylor-Couette flow between coaxial cylinders rotating parallel to a magnetic field, we calculate the electric field and ion distribution and find Manning-Oosawa-like counterion condensation with a renormalized Manning parameter. We then examine a simple Couette flow of a fluid sheared by a charged moving surface in a perpendicular magnetic field. The nonlinear eigenvalue equation has a position-dependent term. Surprisingly, this one-dimensional system has counterion run-off in the limit of infinite width even though the classical Manning-Oosawa condensation occurs only in two dimensions.
Abstract:
The Hall effect in flowing electrolytes had been speculated and tested just a few years after the discovery of the original effect in 1879. The initial attempts were unsuccessful or controversial. In 1897, Donnan calculated the weak Hall voltage for an electrolyte in uniform magnetic field whose charge carriers are driven by an electric field. In the following decades, theoretical works missed important terms or incorrectly calculated the electric field distribution. Here, we describe the stronger ``Hall effects'' in laminar, one-dimensional, and incompressible flows of electrolytes driven by pressure gradients or moving surfaces. In a steady state, the hydrodynamic stress and Lorentz and entropic forces add to give a vanishing ionic flux. The electrical charge, ion densities, and conductivity are subsequently found from solution of a nonlinear eigenvalue Poisson-Boltzmann equation with an external ``force'' that depends on the hydrodynamic flow profile and magnetic field. For Poiseuille flow in a channel, Hall voltage and other quantities depend continuously the magnetic field. For a fluid in Taylor-Couette flow between coaxial cylinders rotating parallel to a magnetic field, we calculate the electric field and ion distribution and find Manning-Oosawa-like counterion condensation with a renormalized Manning parameter. We then examine a simple Couette flow of a fluid sheared by a charged moving surface in a perpendicular magnetic field. The nonlinear eigenvalue equation has a position-dependent term. Surprisingly, this one-dimensional system has counterion run-off in the limit of infinite width even though the classical Manning-Oosawa condensation occurs only in two dimensions.