Electrolyte Filtration
Copper Electrolyte Viscosity: What Temperature, Nickel and Arsenic Do to Filter Sizing
Measured data suggest copper electrolyte is about twice as viscous at 20 °C as at 60 °C. What that does to a filtration test, and what a filter enquiry must state.
The short answer
At 60 °C, copper sulfate and sulfuric acid solutions across the electrorefining range measured 0.89 to 1.08 centipoise, about the same as water at room temperature; at the same copper, acid and temperature, nickel and arsenic push the viscosity higher. On two published measurements of slightly different composition, a solution at 20 °C is about twice as viscous. In cake filtration, the instantaneous flow through a given cake at a given pressure is inversely proportional to the viscosity of the liquid, so the electrolyte's temperature and composition belong in any filter specification, and in any filtration test, as firmly as the flow rate and the solids load.
Three practical consequences follow, and the rest of this article sets out the evidence for each:
A filtration test run on a bottle of electrolyte that has cooled to room temperature, and read at face value, shows roughly half the instantaneous flow that the same cake would pass at about 60 °C and the same pressure. Over a whole test run the shortfall is smaller, but it is still a shortfall.
At a fixed temperature, composition still moves viscosity. In the series the Aalto authors found more valid, the most viscous solution at 60 °C had about 40% higher kinematic viscosity than the most dilute (at 30 g/L arsenic, above the industrial samples they tested). Nickel and arsenic are among the components that raise it.
Of the datasets used here, the Aalto study reports kinematic viscosity (mm²/s) and Price and Davenport dynamic (centipoise). Filtration equations use dynamic. The two differ by the density, which for these solutions is about 1.14 to 1.25 g/cm³.
Where viscosity sits in the filtration equation
Darcy's law gives the flow of a liquid through a porous bed as Q = kAΔP / (μΔx): permeability k, area A, pressure difference ΔP, bed thickness Δx, and μ, the dynamic viscosity of the liquid. Double μ and, with everything else held, the flow halves.
The same term sits inside the cake filtration equations used to size a filter from a test. The standard treatment splits the resistance to flow into the resistance of the filter medium and the resistance of the growing cake, and multiplies both by the viscosity of the filtrate. A constant-pressure filtration test is analysed by plotting filtration time over filtrate volume against filtrate volume; the specific cake resistance and the medium resistance come out of that plot, and the calculation uses the viscosity of the liquid that was actually tested. The textbook derivation assumes an incompressible cake and a constant medium resistance; for a compressible cake the specific resistance itself rises with pressure.
Filter aid grades are rated on the same basis. The Perlite Institute's explanation of filter aids defines one darcy as the permeability that passes 1 cm³/s of a fluid of viscosity 1 cP ("similar to water") under a pressure gradient of 1 atm/cm across 1 cm². A grade's darcy rating is therefore a property of the bed, and the flow you get through that bed depends on the viscosity of whatever you send through it. The same document adds that "the determination of the filter aid grade with optimum filtration performance and effectiveness can only be done after experiments", which is where the temperature of the experiment starts to matter. Grade selection itself is covered in our article on precoat and body-feed filtration.
None of this is specific to copper. What is specific to copper is how far the electrolyte's viscosity moves between the tankhouse and the laboratory bench.
How temperature moves copper electrolyte viscosity
Two independent datasets are useful here, published 37 years apart and measured with different instruments.
The first is Price and Davenport at McGill University, published in Metallurgical Transactions B in 1980. They measured the absolute viscosity of copper sulfate and sulfuric acid solutions across the electrorefining range, 50 to 70 °C, 40 to 55 g/L copper and 160 to 220 g/L sulfuric acid, with a rotational viscometer calibrated against a capillary instrument. For an electrolyte at 45 g/L copper and 182.6 g/L acid, they report:
1.12 cP at 50 °C
0.946 cP at 60 °C
0.811 cP at 70 °C
Across their whole electrorefining grid at 60 °C, the measured values run from 0.891 to 1.08 cP.
The same paper also measured solutions over the electrowinning range, which reached down to 20 °C. One of those solutions, at 35 g/L copper and 191.2 g/L acid, has an acid level within Price and Davenport's electrorefining range. It measured 1.91 cP at 20 °C, 1.48 cP at 30 °C and 1.20 cP at 40 °C.
Put the 20 °C value beside the 60 °C value above and the ratio is about 2.0. That ratio is our arithmetic on two measured points, and the compositions are not identical: the cold solution carries 10 g/L less copper and 8.6 g/L more acid. On the gradients in the same table the copper difference is the larger, so a 45 g/L solution cooled to 20 °C would, if anything, sit higher. The same cold solution at 40 °C, 1.20 cP, is about 27% above the 60 °C figure on the same comparison.
The second dataset is from Kalliomäki and co-authors at Aalto University, published in Physicochemical Problems of Mineral Processing in 2017. They measured kinematic viscosity with a capillary viscometer at 50, 60 and 70 °C across copper, nickel, sulfuric acid and arsenic. Their most dilute solution (40 g/L copper, 130 g/L acid, no nickel or arsenic) measured 0.821 mm²/s at 50 °C, 0.697 at 60 °C and 0.602 at 70 °C: a fall of about 27% across the 20 °C span. The authors found temperature had the strongest effect on viscosity of any variable. In the sensitivity analysis of their Model B, a 15% decrease in temperature around the midpoint of the design (about 9 °C near 60 °C) gave approximately a 15% increase in viscosity.
Both groups report the same direction of effect. Price and Davenport put it as viscosity being "minimized by high temperature and by low concentrations of sulfuric acid and copper".
Temperature also changes the solids. The fraction of anode slimes that stays suspended, and how it coalesces and settles, moves with cell temperature in laboratory and pilot work, which we covered in the article on suspended anode slimes in copper electrorefining. That matters for the next section.
What this does to a filtration test on a cooled sample
A bottle of electrolyte drawn from the circuit, shipped to a laboratory and tested at room temperature is a different liquid, hydraulically, from the one the filter will see. On the Price and Davenport figures it is roughly twice as viscous. The instantaneous flow through the same cake at the same pressure is then about half what it would be hot. Over a constant-pressure run the error is smaller, because when the cake dominates the resistance, the volume collected in a given time scales with the inverse square root of viscosity. A filter sized on the cold number would therefore carry somewhere between about 1.4 and 2 times the area the duty needs, depending on how the resistance splits between the cake and the medium.
Correcting the test is straightforward in principle, because viscosity enters the equations as a multiplier on both resistance terms, so the correction belongs in the analysis of the time and volume data, not as a single ratio applied to a flux read off the test. It needs the viscosity at the test temperature and at the operating temperature, which means recording both temperatures and the assay. It also assumes test and plant run at the same pressure, since for a compressible cake the specific resistance changes with pressure.
The correction has a limit, and it is the more important half of the point. Viscosity is a property of the liquid. The cake resistance is a property of the solids. Temperature moves how anode slimes coalesce and settle in the cell, and nothing in the published data says the solids in a cooled sample form the same cake as the solids in the hot stream. Correcting a cold test for viscosity corrects the liquid and leaves the cake as it was in the bottle. The cleaner route is to test at operating temperature and to record both the temperature and the assay. For a viscosity measurement, where the solids do not matter, the Aalto group filtered and heated their industrial samples "to ensure the homogeneity of the samples". For a filtration test the solids are the point, and reheating a cooled sample restores the temperature, not necessarily the solids.
The error can also run the other way. If a test is run hot and the filter sits somewhere in the circuit where the electrolyte is cooler than in the cells, the test will overstate the flow. Whether the filter sees cell-temperature electrolyte depends on where it sits in the circuit, so the temperature to specify is the temperature at the filter inlet, not the cell temperature.
How composition moves it: copper, acid, nickel, arsenic
The Aalto study extended the measurements to nickel and arsenic, which the 1980 paper did not cover; the authors note that arsenic had previously been measured and modelled only once, by Price and Davenport in 1981. The design varied copper (40 to 60 g/L), sulfuric acid (130 to 160 g/L), nickel (0 to 20 g/L) and arsenic (up to 30 g/L in the more valid of their two arsenic models) at each temperature.
Their finding, stated plainly in the abstract, is that increasing concentrations of copper, nickel, arsenic and sulfuric acid each increase viscosity (and, for the arsenic-free solutions they measured, density), while increasing temperature decreases both. Of the concentration terms, sulfuric acid had the weakest effect.
The size of the composition effect shows in their measured table. At 60 °C, the most dilute solution measured 0.697 mm²/s. The most viscous in the same model series, at 60 g/L copper, 130 g/L acid, 20 g/L nickel and 30 g/L arsenic, measured 0.976 mm²/s. That is about 40% higher kinematic viscosity at the same temperature; the more concentrated solution is also denser, so the gap in dynamic viscosity would be wider still. The 30 g/L arsenic and 20 g/L nickel levels are above the three industrial samples the authors tested (10.7 to 15.3 g/L arsenic, 11 to 17 g/L nickel), so the top of the range is the edge of the design rather than the electrolyte the authors sampled.
The initial industrial check, three samples, is what gives the models weight. The authors measured three electrolyte samples from a Finnish tankhouse, at 54 to 63 g/L copper, 11 to 17 g/L nickel, 10.7 to 15.3 g/L arsenic and 138 to 157 g/L acid, at 65 °C, and compared them with the models. Their preferred models came within 0.9 to 4.5% and 1.1 to 3.2% of the measured values. Real electrolytes also contain additives such as chloride and thiourea and minor impurities such as bismuth and antimony; the authors write that the validation "suggests that the effect of additives and minor solution elements is small compared to the effect of parameters investigated".
They also cite, from an earlier Russian study by Devochkin and co-authors, a kinematic viscosity range of 0.772 to 1.165 mm²/s for typical electrolytes at 50 to 65 g/L copper, 18 to 24 g/L nickel and 150 to 180 g/L acid, at 55 to 70 °C. We have not read that primary source; it is reported here as the Aalto group cites it.
The practical reading: nickel and arsenic levels are not constants. The Aalto authors write that the effect of impurities "has to be taken into account due to increasing amount of impurities and lowering grade of raw materials used for copper production". The same paper cites a 2016 survey of electrorefining operations reporting that average arsenic and bismuth contents were approximately two and six times their 1987 levels; the paper does not say whether that refers to anodes or electrolyte, so we read it only as a direction of travel. If the electrolyte a filter sees today is not the electrolyte it was specified for, its viscosity is one of the things that has changed.
Kinematic or dynamic: check the units before you use a number
The two sources used here report different units for the same kind of liquid.
Dynamic (absolute) viscosity, in centipoise or mPa·s (the two are the same). This is the μ in Darcy's law and in the cake filtration equations. Price and Davenport report it.
Kinematic viscosity, in mm²/s. This is dynamic viscosity divided by density, and it is what the capillary viscometer the Aalto group used measures. The Aalto study and the Devochkin figures report it.
To use a kinematic figure in a filtration calculation, multiply by the density. For copper electrorefining electrolytes the Aalto study measured densities from about 1.14 to 1.25 g/cm³ across its design, so skipping the step understates the dynamic viscosity by about 12 to 20% (put the other way, the dynamic value is 14 to 25% higher than the kinematic number).
As a cross-check: at the one composition both groups measured (50 g/L copper, about 160 g/L acid), the two datasets agree within about 4% at 50, 60 and 70 °C once the units are aligned, on our arithmetic. The worked example at 60 °C: the Aalto solution at 50 g/L copper and 160 g/L acid measured 0.7695 mm²/s at 60 °C, with a density of 1.187 g/cm³ at 59 °C. That converts, on our arithmetic, to about 0.91 mPa·s. Price and Davenport measured 0.946 cP for 50 g/L copper and 163.4 g/L acid at 60 °C. The two agree within about 4%, which is in line with the Aalto authors' finding that the 1981 Price and Davenport model ran at most 5.2% above the Aalto group's Model B, which is built on the Aalto measurements.
What to put in an electrolyte filter enquiry
Because viscosity moves this much, a flow rate and a solids figure are not enough to size a filter. An enquiry, or a request for a filtration test, should carry:
The design flow rate to be filtered, in m³/hr.
The temperature at the filter inlet, as a normal value and a minimum. Not the cell temperature, unless the two are the same.
The electrolyte assay: copper, free sulfuric acid, nickel and arsenic at least, since these are the terms that move viscosity in the published models. Iron where it is present.
The trend in nickel and arsenic, if the bleed regime is changing or the anode feed is getting dirtier.
Suspended solids load and character, which sets the cake. Our article on electrolyte filtration for copper refineries covers the duty and the modes.
For any test data you send: the temperature the test was run at, when the sample was drawn, and whether viscosity was measured, and if so whether as kinematic or dynamic.
If only one line is added to an existing specification, make it item 2. Temperature is the variable the Aalto authors found to have the strongest effect.
What viscosity does not tell you
Viscosity sets how easily the liquid passes through the cake. It does not set how the cake forms, what clarity it gives or how long the filter cloth lasts; those belong to the solids, the filter aid and the medium. It does set how fast pressure builds as the cake grows at a given flow. For the medium side, see our article on specifying filter cloth for a copper electrolyte duty. A viscosity correction is a correction to one term of the equation.
Nor does any of this give a sizing rule. We have not published a flux figure for electrolyte duties and this article does not offer one; what the data supports is the list of inputs above and the reason each one is there.
Where Sharpenn fits
Sharpenn builds pressure filters for electrolyte clarification, running in leaf (body-feed) or precoat mode on a disposable filter cloth, with a flux-calcined diatomite filter aid on copper duty. Across all applications there are approximately 1,000 units installed worldwide across 460+ installations, with 25 units in copper refining, capacities from 5 to 350 m³/hr, and repeat orders coming after 20 to 25 years.
If you are specifying a new clarification duty, send us the flow rate, the filter inlet temperature and the electrolyte assay, and any test data with the temperature it was taken at.
Insights & Article
