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Technische Universität Darmstadt

1. Thammanna Gurumurthy, Vignesh. Dynamics of corner flows driven by wettability.

Degree: PhD, 16 Department of Mechanical EngineeringFluid Mechanics and Aerodynamics (SLA), 2018, Technische Universität Darmstadt

Capillary driven flows in confined spaces such as grooves, microchannels and in polygonal containers arise in numerous contexts found in microfluidic devices, porous media, coating of textured surfaces, etc. The interior corners in these geometries enhance the capillary effects resulting in the rise of rivulets in the corner. These rivulets are known to affect the performance of the devices simply by influencing the amount of liquid in different regions of the channel or groove. Understanding the behaviour and optimizing the performance in aforementioned applications requires quantitative modelling of the dynamics of capillary flows in corners. The objective of this thesis is to understand the dynamics of fluid flows in the corners, and their influence on the bulk flow using numerical simulations and theoretical analyses. Within this framework, three studies investigating the spontaneous and forced wetting flows in two model geometries under the influence of gravity are carried out. The spontaneous wetting of rivulets in the interior corners of a square capillary is investigated using numerical simulations. The shape of the rivulet and the flow inside the rivulet is also studied using lubrication theory. The spontaneous rise in an array of connected open rectangular channels is studied using numerical simulations. Here, the dynamics of fluid flow inside the channel (bulk flow), on the outer face and on the outer corner are also investigated, in addition to the rivulets inside the channel. The dynamics of bulk flow are compared with the capillary rise model extended for the open channels. Two types of forced wetting - immersion and pumping - are investigated in a square capillary, where the behavior of the bulk flow and the rivulet in the corner are studied separately. Results from the spontaneous wetting simulations in both geometries show that at long times, the rivulets rise according to the one-third power-law, and their rise rate is weakly dependent on the geometry. A similarity solution is obtained using the lubrication approximation of the flow inside the rivulet, which matches the simulations in describing the rivulet profile. Also, a scaling relation based on the similarity solution for the non-dimensional growth rate is proposed. The simulations in the open rectangular channel reveals that the typical cusp formation at the outer corner smoothens out when the channel dimensions are smaller than the capillary length of the liquid. In addition, the simulations also highlight the limitations of the capillary rise model when extended to describe the bulk flow in open channels, and also indicate the similarities between the spontaneous wetting of the outer face and a planar wall. The forced wetting experiments of the bulk flow reveals that the liquid column starts falling down at a steady speed, which is predicted by the extended capillary rise model with sufficient accuracy. The rivulets under forced wetting reaches a fixed length, which decreases with increasing capillary number, eventually leading… Advisors/Committee Members: Tropea, Cameron (advisor), Garoff, Stephen (advisor), Roisman, Ilia V. (advisor).

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APA (6th Edition):

Thammanna Gurumurthy, V. (2018). Dynamics of corner flows driven by wettability. (Doctoral Dissertation). Technische Universität Darmstadt. Retrieved from

Chicago Manual of Style (16th Edition):

Thammanna Gurumurthy, Vignesh. “Dynamics of corner flows driven by wettability.” 2018. Doctoral Dissertation, Technische Universität Darmstadt. Accessed December 12, 2018.

MLA Handbook (7th Edition):

Thammanna Gurumurthy, Vignesh. “Dynamics of corner flows driven by wettability.” 2018. Web. 12 Dec 2018.


Thammanna Gurumurthy V. Dynamics of corner flows driven by wettability. [Internet] [Doctoral dissertation]. Technische Universität Darmstadt; 2018. [cited 2018 Dec 12]. Available from:

Council of Science Editors:

Thammanna Gurumurthy V. Dynamics of corner flows driven by wettability. [Doctoral Dissertation]. Technische Universität Darmstadt; 2018. Available from: