Abstract
Author solves problems about interaction of two spherical particles with different radii and also about interaction of a sphere and a plane that are immersed in electrolyte. Double electric layer near the objects' surfaces is supposed to be wide, so Poisson -- Boltzmann equation describing the distribution of electric potential in the medium may be linearized. The problems stated are solved by multipole expansion method; the plane is modelled by a dummy particle. Asymptotic expressions are obtained for the coefficients of the expansion. Basing on this solution, forces acting between bodies in electrolyte are found. The particular case when the size of one sphere is much larger than the size of another particle is examined. Author shows that this case can't transform to interaction of a sphere and a plane. The unexpected result of calculation is that under certain conditions the plane may attract spherical particle which has potential of the same sign on its surface, while the interaction between two spheres having potentials of the same sign is always repulsion.
Highlights
Author solves problems about interaction of two spherical particles with dierent radii and about interaction of a sphere and a plane that are immersed in electrolyte
Double electric layer near the objects' surfaces is supposed to be wide, so Poisson Boltzmann equation describing the distribution of electric potential in the medium may be linearized
The problems stated are solved by multipole expansion method; the plane is modelled by a dummy particle
Summary
Ðàñ÷åò ýëåêòðè÷åñêîãî ïîëÿ â æèäêîì ýëåêòðîëèòå, ñîäåðæàùåì âçâåøåííûå ÷àñòèöû, çàäà÷à íå íîâàÿ, íî ïî-ïðåæíåìó àêòóàëüíàÿ. Èõ ïåðåêðûòèå ïðèâîäèò ê èñêàæåíèþ ýëåêòðè÷åñêîãî ïîëÿ è âçàèìîäåéñòâèþ òåë. Ìàòåìàòè÷åñêîé ìîäåëüþ ýëåêòðè÷åñêîãî ïîëÿ â ýëåêòðîëèòå ñëóæèò óðàâíåíèå ÏóàññîíàÁîëüöìàíà [4], êîòîðîå ìîæåò áûòü ëèíåàðèçîâàíî â ñëó÷àå øèðîêèõ ÄÝÑ [5].  áîëüøèíñòâå ñëó÷àåâ ïðåäïîëàãàåòñÿ, ÷òî èíîðîäíûå òåëà â æèäêîñòè ÿâëÿþòñÿ ñôåðàìè ðàâíîãî ðàäèóñà [6]. Îäíàêî ñëåäóåò ðàññìàòðèâàòü òàêæå âçàèìîäåéñòâèå ðàçíîðàçìåðíûõ ÷àñòèö, ïîñêîëüêó íåñóùàÿ æèäêîñòü ìîæåò ñîäåðæàòü ïðèìåñè íåñêîëüêèõ ñîðòîâ. Åùå îäèí êëàññ çàäà÷, âîçíèêàþùèé ïðè èçó÷åíèè äèñïåðñíûõ ñèñòåì è òåñíî ñâÿçàííûé ñ ïðåäûäóùèì, ìîäåëèðîâàíèå âçàèìîäåéñòâèÿ òåëà è áåñêîíå÷íîé ïîâåðõíîñòè (íàïðèìåð, ïëîñêîñòè èëè êðóãëîãî öèëèíäðà). Öåëåñîîáðàçíî ïðåäëîæèòü èíîé ìåòîä ðàñ÷åòà ýëåêòðè÷åñêèõ ïîëåé, êîòîðûé áû ïîçâîëÿë ìîäåëèðîâàòü ïåðåêðûòèå øèðîêèõ ÄÝÑ è ó÷èòûâàòü íàëè÷èå â æèäêîñòè ìíîãèõ òåë îäíîâðåìåííî.  íàñòîÿùåé ñòàòüå òàêîé ìåòîä ïðèìåíÿåòñÿ ê ìîäåëèðîâàíèþ âçàèìîäåéñòâèÿ äâóõ ñôåð ðàçíûõ ðàçìåðîâ, à òàêæå ñôåðû è ïëîñêîñòè; æèäêîñòü, ñîäåðæàùàÿ èíîðîäíûå òåëà, ñ÷èòàåòñÿ íåïîäâèæíîé
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