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Abstract We present Magnetospheric Multiscale observations of electrostatic double layers in quasi‐perpendicular Earth's bow shock. These double layers have predominantly parallel electric field with amplitudes up to 100 mV/m, spatial widths of 50–700 m, and plasma frame speeds within 100 km/s. The potential drop across a single double layer is 2%–7% of the cross‐shock potential in the de Hoffmann‐Teller frame and occurs over the spatial scale of 10 Debye lengths or one tenth of electron inertial length. Some double layers can have spatial width of 70 Debye lengths and potential drop up to 30% of the cross‐shock potential. The electron temperature variation observed across double layers is roughly consistent with their potential drop. While electron heating in the Earth's bow shock occurs predominantly due to the quasi‐static electric field in the de Hoffmann‐Teller frame, these observations show that electron temperature can also increase across Debye‐scale electrostatic structures.
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A model for the electric field-driven flow and deformation of a drop or vesicle in strong electrolyte solutions
A model is constructed to describe the flow field and arbitrary deformation of a drop or vesicle that contains and is embedded in an electrolyte solution, where the flow and deformation are caused by an applied electric field. The applied field produces an electrokinetic flow, which is set up on the charge-up time scale $$\tau _{*c}=\lambda _{*} a_{*}/D_{*}$$ , where $$\lambda _{*}$$ is the Debye screening length, $$a_{*}$$ is the inclusion length scale and $$D_{*}$$ is an ion diffusion constant. The model is based on the Poisson–Nernst–Planck and Stokes equations. These are reduced or simplified by forming the limit of strong electrolytes, for which dissolved salts are completely ionised in solution, together with the limit of thin Debye layers. Debye layers of opposite polarity form on either side of the drop interface or vesicle membrane, together forming an electrical double layer. Two formulations of the model are given. One utilises an integral equation for the velocity field on the interface or membrane surface together with a pair of integral equations for the electrostatic potential on the outer faces of the double layer. The other utilises a form of the stress-balance boundary condition that incorporates the double layer structure into relations between the dependent variables on the layers’ outer faces. This constitutes an interfacial boundary condition that drives an otherwise unforced Stokes flow outside the double layer. For both formulations relations derived from the transport of ions in each Debye layer give additional boundary conditions for the potential and ion concentrations outside the double layer.
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- Award ID(s):
- 1909407
- PAR ID:
- 10345190
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 943
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.469
