Spatiotemporal morphological transitions in thin-layer electrodeposition: The Hecker effect

Through history to growth dynamics: deciphering the evolution of spatial networks

Many ramified, network-like patterns in nature, such as river networks or blood vessels, form as a result of unstable growth of moving boundaries in an external diffusive field. Here, we pose the inverse problem for the network growth-can the growth dynamics be inferred from the analysis of the final pattern? We show that by evolving the network backward in time one can not only reconstruct the growth rules but also get an insight into the conditions under which branch splitting occurs. Determining the growth rules from a single snapshot in time is particularly important for growth processes so slow that they cannot be directly observed, such as growth of river networks and deltas or cave passages. We apply this approach to analyze the growth of a real river network in Vermont, USA. We determine its growth rule and argue that branch splitting events are triggered by an increase in the tip growth velocity.

Effect of mobility ratio on interaction between the fingers in unstable growth processes

We investigate interactions between thin fingers formed as a result of an instability of an advancing front in growth processes. We show that the fingers can both attract and repel each other, depending on their lengths and the mobility ratio between the invading and displaced phase. To understand the origin of these interactions we introduce a simple resistor model of the fingers. The predictions of the model are then compared to the numerical simulations of two unstable growth processes: dissolution of partially cemented rock fracture and viscous fingering in a regular network of channels.

Recent Progress in Electrochemical Deposition without Supporting Electrolyte

Electrochemical deposition (ECD) of metals is a very old subject[l], which has considerable applications in the context of electroshaping or electroplating. Electrochemists and chemical engineers have long known the different growth conditions of these metal aggregates and the different parameters which drive morphological changes, at least empirically [2-4]. However, in the recent years, after the introduction of the concept of fractal aggregation[5,6], in the field of non-linear pattern formation[7,8], a lot of work has been devoted to the specific problem of growth of electrodeposits from binary electrolytes [9-51] (i.e. without supporting electrolyte). These studies aimed at understanding the morphology, on the large scale (∼1cm) of the deposits and, more specifically, the transitions between morphologies. It is the aim of this paper to review the progress which has been achieved in the past five years on this question.

Diffusion-limited and advection-driven electrodeposition in a microfluidic channel

Self-terminating electrochemical fabrication was used within a microfluidic channel to create a junction between two Au electrodes separated by a gap of 75 microm . During the electrochemical process of etching from the anode to deposition at the cathode, flow could be applied in the anode-to-cathode direction. Without applied flow, dendritic growth and dense branching morphologies were typically observed at the cathode. The addition of applied flow resulted in a densely packed gold structure that filled the channel. A computer simulation was developed to explore regimes where the diffusion, flow, and electric field between the electrodes individually dominated growth. The model provided good qualitative agreement relating flow to the experimental results. The model was also used to contrast the effects of open and closed boundaries and electric field strength, as factors related to tapering.

Transition between two dendritic growth mechanisms in electrodeposition

We report in this paper the observation of a transition between two different dendritic growth mechanisms in the electrodeposition of a metal from a binary electrolyte. Our results, in particular concerning the dendritic growth velocities, enable us to explain this behavior in terms of models previously proposed in the literature.

Alternating morphology transitions in crystallization of NH4Cl on agar plates

Two types of alternating morphology transitions have been observed in crystallization of NH4Cl on agar plates. One is the alternating morphology transitions between dense branching morphology and sparse branching morphology, and the other is the alternating morphology transitions between dense branching morphology and zigzag branching morphology. The appearance of them is found to depend on the mass proportion of agar to NH4Cl in the initial solution and the relative humidity. It is suggested that both the two alternating morphology transitions result from the oscillation of solute concentration in front of the growing interface caused by the competition of crystal growth and solute transfer at a moderate mass proportion. Which one of them occurs depends on the relative humidity, which controls the supersaturation.

Fingered growth in channel geometry: a Loewner-equation approach

A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. Following Carleson and Makarov [L. Carleson and N. Makarov, J. Anal. Math. 87, 103 (2002)], the evolution of the fingers is studied with use of the deterministic Loewner equation. The method is then extended to study the growth in a linear channel with reflecting sidewalls. One- and two-finger solutions are found and analyzed. It turns out that the presence of the walls has a significant influence on the shapes of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones.

Morphological evolution in the electrodeposition of the Pb-Sn binary system

Morphological evolution in the electrodeposition of Pb-Sn binary system is studied. As the second component increases, the morphology of the codeposit changes from dendrite to ramification, to dense branch, and finally to fractal structure, respectively. The evolution arises from the influence of crystallographic texture, which leads to a splitting of dendritic tips and the formation of ramified morphology. This work provides direct evidence to explore the crystallographic influence on the morphological evolution in electrodeposition.

Influence of ohmic heating on the flow field in thin-layer electrodeposition

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular, we find that the thermal gradients at the electrodes act similar to a weak additional driving force to the convection rolls driven by concentration gradients.

Internal structure of dense electrodeposits

We report experimental investigations of the structure of dense patterns obtained during electrochemical deposition of copper in thin cells. The deposit correlation function reveals the periodic structuration of the patterns but shows that the primary spacing is not steady during the growth and that moreover it is not simply related to the diffusion length. Another measurable quantity is the occupancy ratio of the fingers in the cell. Its variation as a function of the experimental parameters is interpreted from specific properties of electrochemical growth. The results are discussed with respect to the well-known behavior of cellular solidification fronts.

Pattern selection induced by electroconvection in the electrodeposition of iron

The morphology of iron electrodeposit is shown to relate closely to the pH of the electrolyte solution. Macroscopically, depending on the strength of the interbranch convection, which is associated with the concentration of H3O+ in the electrolyte, the deposit morphology varies from treelike pattern to meshlike pattern and dense-branching morphology. Microscopically the deposit is ramified and dense-branching at lower concentration of H3O+, while it becomes relatively smooth and stringy at higher H3O+ concentration. The symmetry of the convective vortices on the two sides of the growing tip is observed to decide the growth behavior of the tip. We suggest that H3O+ influences the pattern formation and pattern selection in the electrodeposition of iron from FeSO4 solution by either initiating interbranch convection or changing the effective interfacial energy of the deposit and the electrolyte.

Fingering instability in combustion: an extended view

We detail the experimental situation concerning the fingering instability that occurs when a solid fuel is forced to burn against a horizontal oxidizing wind. The instability appears when the Rayleigh number for convection is below criticality. The focus is on the developed fingering state. We present direct measurements of the depletion of oxygen by the front as well as new results that connect heat losses to the characteristic scale of the instability. In addition, we detail the experimental system, elaborate (qualitatively and quantitatively) on the results that were previously presented, and discuss new observations. We also show that the same phenomenological model applies to electrochemical deposition.