Small density differences, large Richardson numbers: buoyancy decides where gypsum deposits in a centifluidic confluence cell
Abstract
Predicting crystallization fouling remains difficult because it couples supersaturation, nucleation, crystal growth, transport, and adhesion. Separating these processes requires model systems in which they can be independently controlled. One such system is the confluence flow cell, where two incompatible brines mix and generate supersaturation at their interface. The mixing pattern is often predicted using constant-density simulations because density differences between the brines are typically only a few percent or less. We investigate whether this assumption holds when calcium chloride and sodium sulfate react to form gypsum. A constant-density simulation predicts deposition on the channel floor along the centreline. Experimentally, however, gypsum forms bands on both side walls, with deposition moving upstream as flow rate decreases. Dye experiments spanning density differences of 0.14 to 2.1 %, three channel heights, and 32 flow rates show that the distance required for the dyed stream to reach the opposite wall is governed by the bulk Richardson number, Ri=g'H/U2, following L/H = 3.31 Ri−0.66 over four decades in Ri (R2=0.89). When the stream densities are matched, the dyed stream typically no longer reaches the opposite wall, and a reacting experiment shows gypsum deposition on the floor, consistent with the constant-density simulation. A small density difference alone is therefore insufficient to neglect buoyancy; the Richardson number must also be small. At the low flow rates typical of confluence flow cells, this condition is often not met. Because Ri depends only on density difference, channel height, and flow velocity, we recommend evaluating it before applying constant-density models of mixing, reaction, or fouling.
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BibTeX
@misc{loge2026small,
title = {{Small density differences, large Richardson numbers: buoyancy decides where gypsum deposits in a centifluidic confluence cell}},
author = {Isaac Appelquist Løge and Candela Almazán Pérez and Maike W. Baltussen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07305},
eprint = {2610.07305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Small density differences, large Richardson numbers: buoyancy decides where gypsum deposits in a centifluidic confluence cell
AU - Isaac Appelquist Løge
AU - Candela Almazán Pérez
AU - Maike W. Baltussen
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07305
UR - https://arxiv.org/abs/2610.07305
AB - Predicting crystallization fouling remains difficult because it couples supersaturation, nucleation, crystal growth, transport, and adhesion. Separating these processes requires model systems in which they can be independently controlled. One such system is the confluence flow cell, where two incompatible brines mix and generate supersaturation at their interface. The mixing pattern is often predicted using constant-density simulations because density differences between the brines are typically only a few percent or less. We investigate whether this assumption holds when calcium chloride and sodium sulfate react to form gypsum. A constant-density simulation predicts deposition on the channel floor along the centreline. Experimentally, however, gypsum forms bands on both side walls, with deposition moving upstream as flow rate decreases. Dye experiments spanning density differences of 0.14 to 2.1 %, three channel heights, and 32 flow rates show that the distance required for the dyed stream to reach the opposite wall is governed by the bulk Richardson number, Ri=g'H/U^2, following L/H = 3.31 Ri^−0.66 over four decades in Ri (R^2=0.89). When the stream densities are matched, the dyed stream typically no longer reaches the opposite wall, and a reacting experiment shows gypsum deposition on the floor, consistent with the constant-density simulation. A small density difference alone is therefore insufficient to neglect buoyancy; the Richardson number must also be small. At the low flow rates typical of confluence flow cells, this condition is often not met. Because Ri depends only on density difference, channel height, and flow velocity, we recommend evaluating it before applying constant-density models of mixing, reaction, or fouling.
ER -