Longwave nonlinear theory for chemically active droplet division instability

PHYSICA D-NONLINEAR PHENOMENA

卷:391

Article

Abu Hamed, Mohammad^1,2  Nepomnyashchy, Alexander A.¹ 

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[2] Acad Coll Teacher Educ, Coll Sakhnin, Dept Math, IL-30810 Sakhnin, Israel

关键词: Active droplet;    Droplet division;    Amplitude equation;   

DOI  :  10.1016/j.physd.2019.02.002

来源: Elsevier

【 摘 要 】

It has been suggested recently that growth and division of a protocell could be modeled by a chemically active droplet with simple chemical reactions driven by an external fuel supply. This model is called the continuum model. Indeed its numerical simulation reveals a shape instability which results in droplet division into two smaller droplets of equal size resembling cell division (Zwicker et al., 2017). In this paper, we investigate the reduced version of the continuum model, which is called the effective model. This model is studied both in the linear and nonlinear regime. First, we perform a linear stability analysis for the flat interface, and then we develop a nonlinear theory using the longwave approach. We find that the interface at the leading order is governed by the modified Kuramoto-Sivashinsky equation. Therefore the interface is subject to a logarithmic blow up after a finite time. In addition, an expression for the interface local velocity is obtained. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free