Parallel Plate Electrochemical Reactor Model

A model is presented for a parallel plate electrochemical reactor which has electrodes that are the same size and are close together. That is, the distance between the electrodes (S) is much smaller than the length (L) or width (W) of the electrodes. Consideration of the material balance equations in light of this small aspect ratio (S/L) condit ion leads to predict ions of derived quanti t ies of interest (e.g., current efficiency) that depend on the product of the aspect ratio and the Peclet number, where Pe = 2VavgS/DR. Predict ions of such derived quantit ies are made for electrolysis of an aqueous, hydrochloric acid solution containing copper in a cell with no separator. The design of a pa ra l l e l p la te e lec t rochemical reac tor (see Fig. 1) of ten requi res p red ic t ing such quant i t ies as the cu r ren t and energy efficiency for mul t ip le e lect rode reactions, the conversion per pass of a reac tan t or product , and the se lec t iv i ty of a des i red product . Fo r example , in a cell wi th no separator , the e lec t rode react ions for e lec t rowinning of copper f rom a chlor ide solut ion might be CuC132, CuCI+ ~ 2C1-te (anode, reac t ion 1) CuC1 + + 2C1§ e -> CuCla 2(cathode, reac t ion 2) CuCIa 2 ~e -* Cu -t3C1(cathode, react ion 3) Note tha t CuC132-, or C u ( I ) reacts at both e lect rodes and CuCI +, o r C u ( I I ) , is a p roduc t a t the anode and a reac tan t a t the cathode. This scheme is presented here as a hypothe t i ca l i l lus t ra t ion of a complex system. The poss ib i l i ty of Cu (I I ) reac t ing wi th copper deposi ted on the ca thode was ignored for convenience. Many, if not most, e lec t rochemical processes of in teres t a re s imil a r l y compl ica ted and often i t is some aspect of the complex i ty tha t dictates the pe r fo rmance of the system. The des ign of an e lec t rochemical cell based on the above react ions should include predic t ions of the cur ren t and energy efficiency for copper deposit ion, the convers ion pe r pass of both Cu( I ) and C u ( I I ) , and the se lec t iv i ty of copper deposit ion. These predic t ions would be expec ted to depend on, among o ther things, the cell potent ia l , the flow ra te of the e lec t ro ly te th rough the cell, and the length of the e lectrodes at a fixed separat ion. Classical design techniques [see Ref. (1), e.g.] cannot be used to make these predic t ions because they do not include the capabi l i t ies to hand le the complexi t ies due to the above reactions. P icke t t ( I ) , for example , presents models for pa ra l l e l p la te cells which a re based on the assumpt ion tha t on ly one e lec t rode react ion is impor t an t and tha t i t is mass t r ans fe r control led. He does presen t a me thod for in c luding an undes i red side reac t ion , bu t i t is cumber some to use. In a different work, he and S tanmore (2) do present a model for the case where different e lect rode react ions occur at the anode and cathode but do not include mul t ip le e lec t rode reactions. Other more compl ica ted (3-10) models have been presented for pa ra l l e l p l a t e cells, bu t they are also not su i tab le here for one reason or another . Sakel la ropoulos and Francis (3-5) present a model for a pa ra l l e l p la te cell which does include both series and pa ra l l e l e lec* E l e c t r o c h e m i c a l Socie ty Ac t ive Member .